Gastric cancer (GC) is the third leading cause of cancer death in the world. It is associated with the stimulation of microenvironment, aberrant epigenetic modification, and chronic inflammation. However, few researches discuss the GC molecular progression mechanisms from the perspective of the system level. In this study, we proposed a systems medicine design procedure to identify essential biomarkers and find corresponding drugs for GC. At first, we did big database mining to construct candidate protein-protein interaction network (PPIN) and candidate gene regulation network (GRN). Second, by leveraging the next-generation sequencing (NGS) data, we performed system modeling and applied system identification and model selection to obtain real genome-wide genetic and epigenetic networks (GWGENs). To make the real GWGENs easy to analyze, the principal network projection method was used to extract the core signaling pathways denoted by KEGG pathways. Subsequently, based on the identified biomarkers, we trained a deep neural network of drug-target interaction (DeepDTI) with supervised learning and filtered our candidate drugs considering drug regulation ability and drug sensitivity. With the proposed systematic strategy, we not only shed the light on the progression of GC but also suggested potential multiple-molecule drugs efficiently.

This study investigates a simple design method of the robust state/fault estimation and fault-tolerant control (FTC) of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To avoid the corruption of the fault signal on state estimation, a novel smoothing signal model of fault signal is embedded in the T-S fuzzy model for the robust$H_{\infty }$state/fault estimation of the discrete-time nonlinear system with external disturbance by the traditional fuzzy observer. When the component and sensor faults are generated from different fault sources, two smoothing signal models for component and sensor faults are both embedded in the T-S fuzzy system for robust state/fault estimation. Since the nonsingular smoothing signal model and T-S fuzzy model are augmented together for signal reconstruction, the traditional fuzzy Luenberger-type observer can be employed to robustly estimate state/fault signal simultaneously from the$H_{\infty }$estimation perspective. By utilizing the estimated state and fault signal, a traditional$H_{\infty }$observer-based controller is also introduced for the FTC with powerful disturbance attenuation capability of the effect caused by the smoothing model error and external disturbance. Moreover, the robust$H_{\infty }$observer-based FTC design is transformed into a linear matrix inequality (LMI) -constrained optimization problem by the proposed two-step design procedure. With the help of LMI TOOLBOX in MATLAB, we can easily design the fuzzy Luenberger-type observer for efficient robust$H_{\infty }$state/fault estimation and solve the$H_{\infty }$observer-based FTC design problem of discrete nonlinear systems. Two simulation examples are given to validate the performance of state/fault estimation and FTC of the proposed methods.

The multiplayer stochastic noncooperative tracking game (NTG) with conflicting target strategy and cooperative tracking game (CTG) with a common target strategy of the mean-field stochastic jump-diffusion (MFSJD) system with external disturbance is investigated in this study. Due to the mean (collective) behavior in the system dynamic and cost function, the designs of the NTG strategy and CTG strategy for target tracking of the MFSJD system are more difficult than the conventional stochastic system. By the proposed indirect method, the NTG and CTG strategy design problems are transformed into linear matrix inequalities (LMIs)-constrained multiobjective optimization problem (MOP) and LMIs-constrained single-objective optimization problem (SOP), respectively. The LMIs-constrained MOP could be solved effectively for all Nash equilibrium solutions of NTG at the Pareto front by the proposed LMIs-constrained multiobjective evolutionary algorithm (MOEA). Two simulation examples, including the share market allocation and network security strategies in cyber-social systems, are given to illustrate the design procedure and validate the effectiveness of the proposed LMI-constrained MOEA for all Nash equilibrium solutions of NTG strategies of the MFSJD system.

In this article, a robust leader–follower tracking control scheme is proposed to deal with the stochastic multi-unmanned aerial vehicle (UAV) networked team tracking control problem to achieve a prescribed$H_{\infty }$robust tracking performance. By taking the leader’s desired path and every UAV networked system into account, the leader–follower tracking error networked system is constructed by arranging the UAVs network systems into a leader–follower formation. To effectively reduce the effect of the external disturbance on the team tracking process, a robust$H_{\infty }$controller is proposed. With the help of the Itô–Lévy formula, the robust team tracking control design of the multi-UAV system is transformed to a Hamilton–Jacobin inequality (HJI)-constrained optimization problem. Since the HJI constraint cannot be easily solved, the Takagi–Sugeno (T–S) fuzzy interpolation method is employed to approximate the nonlinear networked system with a set of local linearized stochastic networked systems to simplify the design procedure. By the proposed T–S fuzzy control method, the$H_{\infty }$robust leader–follower tracking control design of the stochastic multi-UAV networked system can be transformed to equivalent linear matrix inequalities (LMIs)-constrained optimization problem which can be efficiently solved by using the convex optimization techniques. Finally, a design example is given with simulation to illustrate the design procedure of the robust team tracking control of desired attitude and path and validate the effectiveness of the proposed robust$H_{\infty }$team tracking control method of the multi-UAV networked system.

Only partial system knowledge for the generalized robotic dynamics with input saturation, i.e., the regression matrix for the specific robot, is required to design the proposed adaptive finite-time saturated tracking control (AFTSTC). It contains a nonlinear auxiliary tracking error, which can shape the system frequency response. As the operating point is in the neighborhood of the zero auxiliary tracking error, nonlinear filtering gains can be increased to accelerate its tracking ability. Moreover, the traditional skew-symmetric matrix's condition for the time derivative of inertia matrix and the Coriolis and centrifugal force matrix is not necessarily required such that the uncertainties and the finite-time convergence are reduced. The computational complexity as compared with the fuzzy neural network adaptive control is also addressed. The stability of the closed-loop system is verified by the Lyapunov stability theory. Finally, two practical robotic examples are given to validate the effectiveness and robustness of the proposed control.

In this study, the robust stochastic H infinity reference tracking control design is proposed for stochastic polynomial fuzzy system (SPFS) under external disturbance and continuous and discontinuous random fluctuations. To simplify the tracking control design, the desired reference trajectory is generated by a reference polynomial system. Under the concept of H infinity control, the designed control strategy aims to attenuate the effect of all possible finite energy disturbance on the tracking error to a prescribed level. Based on the polynomial Lyapunov function, with the help of Itô-Lévy formula, the sufficient conditions for robust stochastic H infinity reference tracking control design of SPFS is transformed to Hamilton-Jacobi inequalities (HJIs) problem. Due to the difficulties in solving HJIs problem, by using quadratic Lyapunov function, the solvable sum-of-squares (SOS) conditions are established for the robust stochastic H infinity reference tracking control design and it can be efficiently solved via MATLAB SOSTOOLS toolbox. An investment tracking strategy design for the stochastic financial system is provided to validate the effectiveness of proposed method.

In this article, we consider the multiplayer H∞ noncooperative and cooperative game strategy designs for a class of stochastic jump diffusion systems with external disturbance. To attenuate the effect from the competitive strategies of other players and unpredictable external disturbance on the desired target tracking performance of each player, a multiplayer H∞ noncooperative game strategy design problem is proposed and formulated as an equivalent multiobjective optimization problem (MOP) with a Nash equilibrium solution. Also, the multiplayer H∞ cooperative game strategy design problem is discussed and formulated as an equivalent single-objective optimization problem. To overcome the difficulties in solving multiple Hamilton-Jacobi-Issacs inequalities (HJIIs) for noncooperative and cooperative game strategy designs, the Takagi-Sugeno fuzzy model is introduced to approximate the nonlinear stochastic system and HJII could be transformed into a set of linear matrix inequalities (LMIs). Besides, an LMI-constrained multiobjective evolution algorithm is developed to efficiently solve the MOP of a noncooperative multiplayer H∞ stochastic game strategy design problem. A financial market with multiple investors is provided as a simulation example to demonstrate the effectiveness of the proposed noncooperative and cooperative game investment strategies.

Recently, stochastic Poisson jump diffusion system has attracted much attention in stochastic control. Poisson jump process has been used to model the random discontinuous jump behavior of the intrinsic discontinuous perturbation in stochastic system. Wiener process also called diffusion process represents the continuous random fluctuation to the system. In this paper, a robust adaptive control is introduced for multi-input multioutput (MIMO) nonlinear stochastic Poisson jump diffusion system with continuous and discontinuous random fluctuations to achieve the H tracking performance with a prescribed disturbance attenuation level. The system structure is of a strictfeedback form. Based on the backstepping design technique and H control theory, a robust adaptive control law is constructed for MIMO nonlinear stochastic Poisson jump diffusion system to achieve the H tracking performance with a prescribed attenuation level of external disturbance, despite of fuzzy approximation error and the effect of continuous and discontinuous random fluctuations. The proposed H adaptive control law combines both merits of H tracking control and adaptive control scheme to sufficiently solve the robust H adaptive tracking control problem for MIMO stochastic nonlinear systems with continuous and discontinuous random fluctuations. In addition, the uniformly positive definite assumption of control coefficient matrix is relaxed for the proposed MIMO adaptive control as well. A stochastic quadrotor trajectory tracking control simulation is provided to show the effectiveness of the proposed H robust adaptive control law.

In this study, the multiobjective H2/H∞fuzzy control design is investigated for nonlinear mean-field jump diffusion (MFSJD) systems for concurrently minimizing both H2and H∞performance. Since H2and H∞performance usually conflict with one another, the optimization problem that concurrently minimizes H2and H∞performance can be regarded as a dynamically constrained multiobjective optimization problem (MOP). Because Hamilton-Jacobi inequalities of the nonlinear MFSJD systems are difficult to derive, multiobjective H2/H∞ control design problems of nonlinear MFSJD system are difficult to solve. The Takagi-Sugeno fuzzy interpolation scheme and an indirect method are introduced to help transform the dynamically constrained MOP into linear matrix inequalities (LMIs) constrained MOP. Thus, one can accomplish the multiobjective H2/H∞fuzzy control design via LMI-constrained multiobjective evolutionary algorithms (MOEAs). To efficiently solve the multiobjective H2/H∞control design problem, we propose a novel LMI-constrained MOEA called fronts-squeezing. The fronts-squeezing LMI-constrained MOEA can concurrently search Pareto front from both sides of feasible and infeasible regions and narrow the search region down to increase efficiency. Finally, we present a simulation example about the multiobjective regulation of nonlinear MFSJD financial system to illustrate the design procedure and verify the proposed theories.

This paper proposes a robust joint transceiver and power splitting (PS) design according to a minimax mean-squar-error (MSE) scheme for multiuser multi- input multi-output (MU-MIMO)simultaneous wireless information and power transfer (SWIPT) system. The proposed scheme considers channel uncertainty as a bound on the spectral matrix norm of each estimated error. Since the proposed robust minimax MSE design problem jointly optimizes the precoder, the equalizers and the PS factors, the proposed design problem is non-convex and non-deterministic polynomial-time hard (NP-hard). Thus, we transform the original optimization problem into an iteratively linear matrix inequalities (LMIs)- constrained optimization problem, which can be solved efficiently by the convex optimization toolbox. According to the simulation results of the MU-MIMO PS SWIPT wireless system with the benchmark of robust precoder, the proposed method can validate the theoretical analysis to achieve robust transceiver design effectively.

The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope their investment policies to be with the not only high profit but also low risk. Managers and investors involved pursue their own interests which are partly conflicting with others. Stochastic game theory has been widely applied to multiperson noncooperative decision making problem of financial market. However, for the nonlinear stochastic financial system with random fluctuations, it still lacks an analytical or computational scheme to effectively solve the complex noncooperative game strategy design problem. In this paper, the stochastic multiperson noncooperative game strategy in cyber-financial systems is transformed to a multituple Hamilton-Jacobi-Isacc inequalities (HJIIs)-constrained multiobjective optimization problem (MOP). This HJIIs-constrained MOP solution is also found to be the Nash equilibrium solution of multiperson noncooperative game strategy in nonlinear stochastic financial systems. In order to simplify design procedure by the global linearization theory, a set of local linear systems are interpolated to approximate the nonlinear stochastic financial system so that the m-tuple HJIIs-constrained MOP for noncooperative game strategy of cyber-financial system could be converted to a linear matrix inequalities (LMIs)-constrained MOP. Finally, an LMIs-constrained multiobjective evolution algorithm is explored for effectively solving the multiperson noncooperative game strategy in cyber-financial systems. Two design examples are also given for the illustration of the design procedure and the performance validation of the proposed stochastic noncooperative investment strategy in the nonlinear stochastic financial systems.

The financial market always suffers from continuous and discontinuous (jump) changes and can be regarded as a nonlinear stochastic jump diffusion system. Most investors expect their investment policies to be not only higher benefits but also lower risk as a multiobjective optimization problem (MOP). In this study, a multiobjective H2/H∞fuzzy investment is proposed for nonlinear stochastic jump diffusion financial systems to achieve the desired target with minimum investment cost and risk in Pareto optimal sense, simultaneously. The Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear stochastic jump diffusion financial system to simplify the multiobjective H2/H∞investment policy design procedure. By the help of the T-S fuzzy model, the multiobjective H2/H∞fuzzy investment policy problem of nonlinear stochastic financial system can be transformed to a linear-matrix-inequality-constrained (LMI-constrained) MOP to avoid solving the annoying Hamilton-Jacobi inequalities. Because the LMI-constrained MOP is not easy to directly calculate its Pareto optimal solutions, an indirect method is proposed to solve this MOP for the multiobjective H2/H∞fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems. An LMI-constrained multiobjective evolution algorithm (LMI-constrained MOEA) is also developed to efficiently solve the Pareto optimal solutions of the LMI-constrained MOP for the multiobjective H2/H0',fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems. When the Pareto optimal regulation solutions are solved by the proposed LMI-constrained MOEA, investors can select one investment policy to achieve their desired target with minimum investment cost and risk according to his/her own preference.

In this paper, a new robust fuzzy$H_{\infty }$estimator-based stabilization design for a class of$N$-dimensional nonlinear parabolic partial differential systems (PDSs) with either the Dirichlet or Neumann boundary conditions is proposed. First, an$N$-dimensional parabolic Takagi–Sugeno (T–S) fuzzy PDS is used to approximate the$N$-dimensional nonlinear parabolic PDS via the knowledge-based T–S fuzzy system technique. Second, based on the$N$-dimensional parabolic T–S fuzzy PDS, a robust fuzzy estimator-based controller is employed not only to stabilize the PDS, but also to attenuate the effects of external and measurement noises on the PDS in the spatiotemporal domain below a prescribed attenuation level. The robust fuzzy$H_{\infty }$estimator-based stabilization design problem can be formulated as a diffusion matrix inequality (DMI) problem. To solve DMIs via the traditional algebraic matrix techniques, we utilize the divergence theorem and the Poincaré inequality to transform the DMIs into bilinear matrix inequalities with a Poincaré constant defined according to the spatial domain of the corresponding PDS. Finally, the robust fuzzy$H_{\infty }$estimator-based stabilization design problem can be effectively solved by a set of linear matrix inequalities instead of the BMIs with the help of the proposed decoupled method. Additionally, an optimal robust fuzzy$H_{\infty }$estimator-based stabilization design can be realized via minimizing the noise attenuation level. A simulation example is provided to illustrate the design procedure and verify the performance of the proposed optimal design.

In general, the design cost of a fuzzy controller for nonlinear partial differential systems (PDSs) is very expensive. In this paper, a new approach for robust fuzzy H∞stabilization design is developed for a class of N-dimensional nonlinear parabolic PDSs. Further, two low design-cost robust fuzzy controllers, called the robust fuzzy area-controller and point-controller, as well as a normal design-cost robust fuzzy full-controller are proposed for this problem. The difference between the three control designs lies in their controller placement in the spatial domain. First, we present the N-dimensional parabolic Takagi-Sugeno (T-S) fuzzy PDS based on the knowledge-based fuzzy system technique. Next, these three robust fuzzy controllers are constructed via solving diffusion matrix inequality (DMI) problems. With the proposed simple but general method using the Poincareinequality, the linear matrix inequality problems are provided to replace DMI problems for the robust fuzzy H∞stabilization designs for computational simplicity. Further, the comparison of these three robust fuzzy controllers are demonstrated to enable a designer to select a low-cost option. Finally, a simulation example is provided to illustrate the design procedure and verify the performance of the proposed designs.

One of the ultimate goals of computational neuroscience is to quantitatively connect between complex neural circuits and behaviors. In the past decades, the touch response circuit in Caenorhabditis elegans (C. elegans) has extensively been investigated in studies using genetically modified or laser-ablated worms. Synaptic connections, including chemical and electrical synapses, have been identified for most neurons in the C. elegans. However, we still do not know whether the empirically observed touch responses can be derived from connectome reconstructed from databases. To address this issue, we defined the transmission abilities (or levels) of neurons in a rate model in order to infer the behaviors of wild-type and ablated worms in response to posterior/nose/anterior touch stimuli. Our analysis showed that transmission abilities can be used to identify sensorimotor mapping from stimuli to movements and then to infer the C. elegans behaviors under simulations based on the perspective of decision-making, and provide useful information about how chemical and electronic synapses should be combined in the neural network movement analysis. This paper reveals an efficient tool that provided insights into the functions of complex neural circuits.

In this study, robust biological filters with an external control to match a desired input/output (I/O) filtering response are engineered based on the well-characterized promoter-RBS libraries and a cascade gene circuit topology. In the field of synthetic biology, the biological filter system serves as a powerful detector or sensor to sense different molecular signals and produces a specific output response only if the concentration of the input molecular signal is higher or lower than a specified threshold. The proposed systematic design method of robust biological filters is summarized into three steps. Firstly, several well-characterized promoter-RBS libraries are established for biological filter design by identifying and collecting the quantitative and qualitative characteristics of their promoter-RBS components via nonlinear parameter estimation method. Then, the topology of synthetic biological filter is decomposed into three cascade gene regulatory modules, and an appropriate promoter-RBS library is selected for each module to achieve the desired I/O specification of a biological filter. Finally, based on the proposed systematic method, a robust externally tunable biological filter is engineered by searching the promoter-RBS component libraries and a control inducer concentration library to achieve the optimal reference match for the specified I/O filtering response.

This paper is concerned with the multiobjective H2/H∞filtering design problem in nonlinear signal processing, which can be approximated by a Takagi-Sugerno (T-S) fuzzy signal system. We propose a multiobjective filter design to estimate state variables from noisy measurements for nonlinear signal systems, and we focus our effort on achieving optimal concurrent performance for H2and H∞filtering. In general, it is difficult to solve the multiobjective (MO) H2/H∞fuzzy filter problem directly, and we therefore propose an indirect approach to minimize the upper bounds and transform the MO H2/H∞filtering problem in to a linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we propose an LMI-based multiobjective evolution algorithm to efficiently find Pareto optimal solutions for the MOP of multiobjective fuzzy filter design for nonlinear stochastic signal processing. Furthermore, for comparison, we also suggest the MO H2/H∞filter design problem based on the weighted sum method. Our proposed indirect method can be widely employed to practically address the MO filter design problem in nonlinear signal processing. Finally, a trajectory estimation of reentry vehicle by radar is provided to illustrate the design procedure of the Pareto MO optimal filter.

Aging, an extremely complex and system-level process, has attracted much attention in medical research, especially since chronic diseases are quite prevalent in the elderly population. These may be the result of both gene mutations that lead to intrinsic perturbations and environmental changes that may stimulate signaling in the body. Therefore, analysis of network robustness to tolerate intrinsic perturbations and network response ability of gene networks to respond to external stimuli during the aging process may provide insight into the systematic changes caused by aging. We first propose novel methods to estimate network robustness and measure network response ability of gene regulatory networks by using their corresponding microarray data in the aging process. Then, we find that an aging-related gene network is more robust to intrinsic perturbations in the elderly than the young, and therefore is less responsive to external stimuli. Finally, we find that the response abilities of individual genes, especially FOXOs, NF-κB, and p53, are significantly different in the young versus the aged subjects. These observations are consistent with experimental findings in the aged population, e.g., elevated incidence of tumorigenesis and diminished resistance to oxidative stress. The proposed method can also be used for exploring and analyzing the dynamic properties of other biological processes via corresponding microarray data to provide useful information on clinical strategy and drug target selection.

To track a desired signal-to-interference-plus-noise-ratio (SINR) that allows for higher system throughput and better link quality in an interference limited wireless communication system, a feedback power controller is designed to obtain the optimal SINR tracking control. In this paper, we propose the multi-objective (MO) H2/H∞optimal power control for interference limited wireless systems that provides quality solutions for both objectives. The considered multi-objective H2/H∞power tracking control is complicated in nature and an equivalent formulation that minimizes the upper bounds of both objectives is proposed. Furthermore, the resulting constraints for the MO H2/H∞power control problem is transformed as three linear matrix inequalities (LMIs), leading to a LMIs-constrained MO problem (MOP). By combining the LMI toolbox in MATLAB with an evolutionary searching algorithm, a set of H2/H∞solutions called Pareto optimal solutions can be obtained and a particular solution can be selected based on the tradeoff determined by the system designer. Finally, to illustrate our design procedure, we provide numerical simulations for a typical interference limited wireless system, i.e., a direct-sequence code division multiple access (DS-CDMA) cellular system. Simulation results demonstrate that the optimal tradeoff indeed can be achieved by the proposed MO H2/H∞power control.

This paper studies a robust synchronization of nonlinear stochastic coupled networks under time-delays and environmental noises. A nonlinear stochastic dynamic model with time delays is proposed for describing a coupled nonlinear network under time delays, intrinsic parameter fluctuations, and extrinsic disturbances. We propose a robust synchronization criterion for attenuating these intrinsic parameter fluctuations and compensating process delays to achieve robust synchronization of nonlinear stochastic coupled networks from the nonlinear stochastic stability perspective. Furthermore, in order to avoid solving the complicated Hamilton-Jacobi inequalities (HJI) for the robust synchronization behavior, based on Takagi-Sugeno (T-S) fuzzy time-delay model and linear matrix inequalities (LMIs) technique, a systematic synchronization is proposed. Finally, a simulation example of coupled Brusselator systems is provided to illustrate our main results.

MOTIVATION: The major function of signal transduction pathways in cells is to sense signals from the environment and process the information through signaling molecules in order to regulate the activity of transcription factors. On the molecular level, the information transmitted by a small number of signal molecules is amplified in the internal signaling pathway through enzyme catalysis, molecular modification and via the activation or inhibition of interactions. However, the dynamic system behavior of a signaling pathway can be complex and, despite knowledge of the pathway components and interactions, it is still a challenge to interpret the pathways behavior. Therefore, a systematic method is proposed in this study to quantify the signal transduction ability. RESULTS: Based on the non-linear signal transduction system, signal transduction ability can be investigated by solving a Hamilton-Jacobi inequality (HJI)-constrained optimization problem. To avoid difficulties associated with solving a complex HJI-constrained optimization problem for signal transduction ability, the Takagi-Sugeno fuzzy model is introduced to approximate the non-linear signal transduction system by interpolating several local linear systems so that the HJI-constrained optimization problem can be replaced by a linear matrix inequality (LMI)-constrained optimization problem. The LMI problem can then be efficiently solved for measuring signal transduction ability. Finally, the signal transduction ability of two important signal transduction pathways was measured by the proposed method and confirmed using experimental data, which is useful for biotechnological and therapeutic application and drug design.

This study addresses a robustH∞filter design problem for nonlinear stochastic partial differential systems (NSPDSs) with random external disturbance and measurement noise in the spatiotemporal domain. For NSPDSs, a robustH∞filter design through a set of sensor measurements needs to solve a complex second-order Hamilton Jacobi integral inequality (HJII). In order to simplify the design procedure, a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the NSPDS. Then, a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semidiscretization finite difference scheme and the Kronecker product. Based on this model, a robustH∞filter design is proposed to achieve the robust state estimation via solving linear matrix inequalities (LMIs) instead of a second-order HJII. The proposed robust fuzzyH∞filter efficiently attenuates the effect of spatiotemporal external disturbances and measurement noise on the state estimation of NSPDSs from the area energy point of view. Finally, a robustH∞state estimation example of heat transfer system is given to illustrate the design procedure and to confirm theH∞filtering performance of the proposed robust filter design method.

In this paper, the relative location estimation problem, a prominent issue faced by several applications in wireless sensor networks (WSNs), is considered. Sensors are classified into two categories: location-aware and location-unaware sensors. To estimate the positions of location-unaware sensors, exact positions are often assumed for location-aware sensors. However, in practice, such precise data may not be available. Therefore, determining the positions of location-unaware sensors in the presence of inexact positions of location-aware sensors is the primary focus of this study. A robust min-max optimization method is proposed for the relative location estimation problem by minimizing the worst-case estimation error. The corresponding optimization problem is originally nonconvex, but after it is transformed into a convex semidefinite program (SDP), it can be solved by existing numerical techniques. In the presence of inexact positions of location-aware sensors, the robustness of the proposed approach is validated by simulations under different WSN topologies. Modified maximum-likelihood (ML) estimation and second-order cone programming (SOCP) relaxation methods have been used for localization in comparison with the proposed approach.

Signal transduction plays an important role in biological organisms. Here, we proposed a method to access the information of the signal transduction ability of signal transduction pathway in the cells. Due to the nonlinear signal transduction pathway model, we have to solve the Hamilton-Jacobi inequalities (HJIs) to get the measurement. Instead of directly solving HJIs, fuzzy interpolation method was employed such that we can systematically measure signal transduction ability by solving the linear matrix inequalities (LMIs). The measurement will provide an insight to the characteristics of the signal transduction networks.

MOTIVATION: Synthetic biology aims to develop the artificial gene networks with desirable behaviors using systematic method. These networks with desired behaviors could be constructed using diverse biological parts, which may limit the development to complex synthetic gene networks. Fortunately, some well-characterized promoter libraries for engineering gene networks are widely available. Thus, a synthetic gene network can be constructed by selecting adequate promoters from promoter libraries to achieve the desired behaviors. However, the present promoter libraries cannot be directly applied to engineer a synthetic gene network. In order to efficiently select adequate promoters from promoter libraries for a synthetic gene network, promoter libraries are needed to be redefined based on the dynamic gene regulation. RESULTS: Based on four design specifications, a library-based search method is proposed to efficiently select the most adequate promoter set from the redefined promoter libraries by a genetic algorithm (GA) to achieve optimal reference tracking design. As the number and size of promoter libraries increase, the proposed method can play an important role in the systematic design of synthetic biology. CONTACT: [email protected]; [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Photosynthetic light acclimation is an important process that allows plants to optimize the efficiency of photosynthesis, which is the core technology for green energy. However, currently little is known about the molecular mechanisms behind the regulation of the photosynthetic light acclimation response. In this study, a systematic method is proposed to investigate this mechanism by constructing gene regulatory networks from microarray data of Arabidopsis thaliana. METHODS: The potential TF-gene regulatory pairs of photosynthetic light acclimation have been obtained by data mining of literature and databases. Following the identification of these potential TF-gene pairs, they have been refined using Pearson's correlation, allowing the construction of a rough gene regulatory network. This rough gene regulatory network is then pruned using time series microarray data of Arabidopsis thaliana via the maximum likelihood system identification method and Akaike's system order detection method to approach the real gene regulatory network of photosynthetic light acclimation. RESULTS: By comparing the gene regulatory networks under the PSI-to-PSII light shift and the PSII-to-PSI light shift, it is possible to identify important transcription factors for the different light shift conditions. Furthermore, the robustness of the gene network, in particular the hubs and weak linkage points, are also discussed under the different light conditions to gain further insight into the mechanisms of photosynthesis. CONCLUSIONS: This study investigates the molecular mechanisms of photosynthetic light acclimation for Arabidopsis thaliana from the physiological level. This has been achieved through the construction of gene regulatory networks from the limited data sources and literature via an efficient computation method. If more experimental data for whole-genome ChIP-chip data and microarray data with multiple sampling points becomes available in the future, the proposed method will be improved on by constructing the whole-genome gene regulatory network. These advances will greatly improve our understanding of the mechanisms of the photosynthetic system.

This paper describes the robust static output feedback H∞fuzzy control design for a class of nonlinear stochastic systems. The system dynamic is modelled by Itô-type stochastic differential equations. For general nonlinear stochastic systems, the H∞control can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality. In general, it is difficult to solve the second-order nonlinear Hamilton-Jacobi inequality. Using fuzzy approach (T-S fuzzy model), the H∞fuzzy control design for the nonlinear stochastic systems can be given via solving linear matrix inequalities (LMIs) instead of a second-order Hamilton-Jacobi inequality. A singular value decomposition (SVD) method is proposed in this study to solve the H∞static output feedback fuzzy control problem. By the proposed SVD method, the problem of H∞static output feedback fuzzy control design for nonlinear stochastic systems is characterized in terms of solving an eigenvalue problem (EVP). This EVP can be easily solved by using a LMI-based optimization method. Simulation example is provided to illustrate the design procedure and the expected performances.

Self-constructing neural fuzzy inference network (SONFIN) is a neural fuzzy system and owing to its structure learning capability, SONFIN has been demonstrated to have excellent learning performance. However, various parameters must be selected in the implementation of SONFIN. In this paper, the learning behavior of SONFIN is studied. First, the SONFIN system with different thresholds and variances are considered. Different selections will result in different rule numbers and membership function widths. Our experiment results indicate that when there are possibilities of overfitting, more rules may not always come up with better performance. Secondly, two different learning algorithms are considered; the backpropagation (BP) learning algorithm and the recursive least square (RLS) algorithm. It can found that the learning of using RLS is much faster than that of using BP as expected. However, it can be found that when overfitting may occur, BP can have better learning performance in terms of testing errors. Finally, the use of reset for the covariance matrix in the RLS algorithm is investigated. From this primitive study, it can be found that the learning algorithms or some parameter selections may have both good effects in the testing performance and the training performance before the learning does not have significant overfitting. However, when the learning crosses this point, any selection is good for learning may bring bad effects on the testing performance.

This paper addresses the robust reference tracking control problem for nonlinear distributed parameter systems (NDPSs) with time delays, external disturbances and measurement noises. The NDPS is measured at several sensor locations for output feedback tracking control. A fuzzy spatial state space model derived via finite difference approach is introduced to represent the nonlinear distributed parameter time-delayed system. Based on this model, a robust fuzzy observer-based reference tracking controller is proposed to control the nonlinear distributed parameter system to track a desired reference trajectory. Firstly, a two-dimensional H∞reference tracking performance in a spatio-temporal domain is proposed for robust tracking design of nonlinear distributed parameter time-delayed systems. Finally, a tracking control design example for the nervous system is given to confirm the proposed reference tracking control scheme of nonlinear distributed parameter time-delayed systems.

BACKGROUND: Candida albicans is a commonly encountered fungal pathogen in humans. The formation of biofilm is a major virulence factor in C. albicans pathogenesis and is related to antidrug resistance of this organism. Although many factors affecting biofilm have been analyzed, molecular mechanisms that regulate biofilm formation still await to be elucidated. RESULTS: In this study, from the gene regulatory network perspective, we developed an efficient computational framework, which integrates different kinds of data from genome-scale analysis, for global screening of potential transcription factors (TFs) controlling C. albicans biofilm formation. S. cerevisiae information and ortholog data were used to infer the possible TF-gene regulatory associations in C. albicans. Based on TF-gene regulatory associations and gene expression profiles, a stochastic dynamic model was employed to reconstruct the gene regulatory networks of C. albicans biofilm and planktonic cells. The two networks were then compared and a score of relevance value (RV) was proposed to determine and assign the quantity of correlation of each potential TF with biofilm formation. A total of twenty-three TFs are identified to be related to the biofilm formation; ten of them are previously reported by literature evidences. CONCLUSIONS: The results indicate that the proposed screening method can successfully identify most known biofilm-related TFs and also identify many others that have not been previously reported. Together, this method can be employed as a pre-experiment screening approach that reveals new target genes for further characterization to understand the regulatory mechanisms in biofilm formation, which can serve as the starting point for therapeutic intervention of C. albicans infections.

Recently noise has been shown to be useful in enhancing neuron sensitivity by stochastic resonance. In this study, in order to measure the noise-enhancing factor (NEF), a nonlinear stochastic model is introduced for the Hodgkin-Huxley (HH) neuron system with synaptic noise input stimulation and channel noises in the sodium and potassium channels. The enhancing factor of the HH neuron system is measured from the point of view of the noise-exploiting level of nonlinear stochastic H(infinity) signal processing. Since the nonlinear stochastic-enhancing measure problem of HH neuron systems requires a solution for the difficulty presented by the Hamilton Jacobi inequality (HJI), a fuzzy interpolation of locally linearized systems is employed to simplify the nonlinear noise-enhancing problems by solving only a set of linear matrix inequalities. The NEF of the HH neuron system is found to be related to the locations of eigenvalues of linearized HH neuron systems and can be estimated through the H(infinity) signal processing method. Based on a stochastic fuzzy linearized HH neuron system, we found that channel noises are enhanced by the active eigenvalues of ionic channels while synaptic noises are attenuated by the passive eigenvalues of synaptic process.

A nervous system consists of a large number of highly interconnected nerve cells. Nerve cells communicate by generation and transmission of short electrical pulses (action potential). In addition, membrane voltage is the only measurable state in nervous systems. A robust observer-based model reference tracking control is proposed for Hodgkin-Huxley (HH) neuron systems to generate a desired reference response in spite of environmental noises, uncertain initial values, and diffusion currents from other interconnected nerve cells. In order to simplify the robust tracking control design of nonlinear stochastic HH neuron systems, a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic HH neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. The proposed robust observer-based tracking control scheme can provide new methods for desired action potential generation, suppression of oscillations, and blockage of action potential transmission under environmental noise and diffusion currents. These new methods are useful for patients with different neuron system dysfunctions. Finally, three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method.

This paper addresses the robust reference-tracking-control problem for nonlinear distributed parameter systems (NDPSs) with time delays, external disturbances, and measurement noises. The NDPS is measured at several sensor locations for output-feedback tracking control. A fuzzy-spatial state-space model derived via finite-difference approach is introduced to represent the nonlinear distributed parameter time-delayed system. Thus, we use a fuzzy interpolation method with several local linear systems to approximate the nonlinear system and employ the finite-difference method to approximate the partial differential operators in fuzzy-spatial state-space model. Based on this model, a robust fuzzy-observer-based reference-tracking controller is proposed to control the NDPS to track a desired reference trajectory. First, a 2-D tracking performance in a spatiotemporal domain is proposed for robust tracking design of nonlinear distributed parameter time-delayed systems. Then, an equivalent 1-D reference-tracking design is developed to simplify the design procedure, and the linear-matrix-inequality (LMI) technique is applied to solve the control gains and observer gains for the robust tracking-design problem via a systematic control-design procedure. Finally, a tracking-control-design example for the nervous system is given to confirm the proposed reference-tracking-control scheme of nonlinear distributed parameter time-delayed systems.

At present, the development in the nascent field of synthetic gene networks is still difficult. Most newly created gene networks are nonfunctioning due to intrinsic parameter fluctuations, uncertain interactions with unknown molecules and external disturbances of intra and extracellular environments on the host cell. How to design a completely new gene network, that is to track some desired behaviors under these intrinsic and extrinsic disturbances on the host cell, is the most important topic in synthetic biology. In this study, the intrinsic parameter fluctuations, uncertain interactions with unknown molecules and environmental disturbances, are modeled into the nonlinear stochastic systems of synthetic gene networks in vivo. Four design specifications are introduced to guarantee the stochastic synthetic gene network, which can achieve robust optimal tracking of a desired reference model in spite of these intrinsic and extrinsic disturbances on the host cell. However, the robust optimal reference-tracking design problem of nonlinear synthetic gene networks is still hard to solve. In order to simplify the design procedure of the robust optimal nonlinear stochastic-tracking design for synthetic gene networks, the Takagi-Sugeno (T-S) fuzzy method is introduced to solve the nonlinear stochastic minimum-error-tracking design problem. Hence, the robust optimal reference-tracking design problem under four design specifications can be solved by the linear matrix inequality (LMI)-constrained optimization method using convex optimization techniques. Further, a simple design procedure is developed for synthetic gene networks to meet the four design specifications to achieve robust optimal reference tracking. Finally, an eigenvalue-shifted design method is also proposed as an expedient scheme to improve the stochastic optimal-tracking design method of synthetic gene oscillators.

In this paper, the mobile location estimation problem in urban areas is considered. The time of arrival (TOA) technique is employed to obtain distance measurements. The position of the mobile station (MS) under consideration is estimated according to the position coordinates of the base stations (BSs) and the corresponding distance measurements. The Manhattan and euclidean norms are used to deal with the line-of-sight (LOS) and non-line-of-sight (NLOS) radio propagation. A mixed-norm approach using simulated annealing with changeable neighborhood (SA-CN) is proposed. The position of the MS is located by using the SA-CN algorithm to search for good solutions of a mixed-norm optimization problem. During the search process, the SA algorithm simulates the annealing of solids, whereas the CN method changes the search step size. Simulations show that the concept of SA-CN outperforms the original SA method with fixed neighborhood. The proposed approach can be applied to the urban area with various shapes of obstructions and can work without the knowledge of noise statistics.

The location of mobile station is an important issue for wireless communication systems. A location estimation scheme using fuzzy-based Interacting Multiple Model (IMM) smoother is proposed in this paper. It combines the time-of-arrival (TOA) and the received signal strength (RSS) measurements to achieve high location accuracy. The fuzzy technique is used to interpolate several linear equations to approximate the nonlinear RSS measurement. The IMM is employed as a switch between the line-of-sight (LOS) and non-line-of-sight (NLOS) states which are considered to be a Markov process with two interactive modes. By integrating the fuzzy filtering and the IMM method for range estimation between the corresponding base station (BS) and mobile station (MS), the proposed robust scheme, in association with data fusion, can efficiently mitigate the NLOS effects on the measurement range error. Simulation results are given to confirm the performance of the proposed method.

The mobile location estimation problem in general urban areas is considered. Using the unobstructed distance measurements between mobile stations (MSs) and base stations (BSs), the locations of MSs are estimated. Unlike those methods focusing only on the estimation accuracy, this work also concerns the computational time consumption. A combined convex optimization and weight-product tracking method (CCO-WPT) is proposed in this paper. The proposed method utilizes the convex optimization method (CO) for accurate location estimations and the weight-product tracking method (WPT) to reduce the number of computations. The CCO-WPT method can decrease the computational time/complexity and, at the same time, guarantee a good level of accuracy so that the implemented locating system can serve as many MSs as possible. An optimal schedule is also derived to assign the number of MSs to be located by CO and WPT individually. The advantage of this method is that the combined scheme can provide a trade-off between accuracy and complexity, which makes it possible to deal with the variant number of MSs required be served.

In this paper, we consider the problem of a robust mean-square-error (MSE) equalizer design for wireless multi-input multi-output (MIMO) communication systems subject to channel matrix uncertainties. Our goal is to find the equalizer minimizing the MSE of the error symbol vectors under the worst channel uncertainty. As we show, the optimal minimax MSE equalizer can be formulated as a solution to a semidefinite programming problem (SDP). In addition, we derive a suboptimal solution for the problem, which may save computational cost as well as have comparable MSE performance, since the amount of computations in the SDP may grow rapidly as the MIMO dimension increases. We further partition the MIMO channel uncertainty range into finite Markov-transitioned channel uncertain states. On this basis, a feasible equalizer can be obtained from a weighted combination of either multiple quasi-optimal minimax MSE equalizers or multiple quasi-suboptimal minimax MSE equalizers, each of which is designed with respect to a channel uncertain state. Simulation results show that a weighted combination of a moderate number of quasi-suboptimal minimax MSE equalizers can achieve robust equalization with satisfactory MSE performance as well as with superior bit-error-rate performance.

MOTIVATION: Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology. RESULTS: A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi-Sugeno (T-S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method. AVAILABILITY: http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdf.

In this paper, a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems (NPDSs). Based on Galerkin's method, a Takagi-Sugeno (T-S) fuzzy PDS is first proposed to model an NPDS. Then, the T-S fuzzy PDS can be represented by a finite-dimensional T-S fuzzy subsystem in controlled mode and a coupled infinite-dimensional T-S fuzzy subsystem in residual mode. Therefore, the NPDS can be partitioned into a finite-dimensional T-S fuzzy slow state-space subsystem to be controlled and a coupled infinite-dimensional fast residual subsystem to be tolerated. Based on the small-gain theorem, a robust fuzzy observer-based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the NPDS. Furthermore, based on the dissipative theory, an Hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of NPDSs. The MATLAB linear matrix inequality toolbox can be employed to efficiently solve the optimal Hinfin fuzzy observer-based control design problem of NPDSs. Finally, a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer-based control method for the perturbative NPDSs.

A new technique using an adaptive fuzzy algorithm to obtain the solutions to a class of partial differential equations (PDEs) is presented. The design objective is to find a fuzzy solution to satisfy precisely the PDEs with boundary conditions. According to the adaptive scheme of fuzzy logic systems, a fuzzy solution with adjustable parameters for the PDE is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been derived. Furthermore, the convergence of error equations in mesh points is also discussed from the energy perspective. In this paper, we show that the proposed method can solve a variety of PDEs encountered in engineering. Comparisons are also made with solutions obtained by the finite-element method.

To date, nonlinearlinfin-gaincontrol problems have not been solved by the conventional control methods for nonlinear discrete-time systems with persistent bounded disturbances. This study introduces fuzzy observer-based fuzzy control design, where the premise variables depend on the state variables estimated by a fuzzy observer, to deal with the nonlinearlinfin-gaincontrol problem. The fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables depend on the state variables. First, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear discrete-time system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to minimize the upper bound oflinfin-gainof the closed-loop system under some nonlinear matrix inequality (non-LMI) constraints. A novel decoupled method is proposed in this study to transform the non-LMI conditions into some linear matrix inequality (LMI) forms. By the proposed decoupled method and the genetic algorithm, thelinfin-gainfuzzy observer-based fuzzy control problem for the nonlinear discrete-time systems can be easily solved by an LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of perturbation due to persistent bounded disturbances, extend thelinfin-gaincontrol problems from linear discrete-time systems to nonlinear discrete-time systems. A simulation example is given to illustrate the design procedures and to confirm thelinfin-gainperformance of the proposed method.

In this study, we propose a combined scheme for mobile location estimation in urban areas. First, the proposed scheme employs particle filters to estimate the unobstructed distances traveled by light between base stations (BSs) and the mobile station (MS). Next, according to those estimations of unobstructed distances, which are usually non-Euclidean due to Non-Line of Sight (NLOS) radio propagations, the locating problem is formulated as a non-convex and unconstrained optimization problem with the proposed mixed Manhattan/Euclidean norm. The solution to such a non-convex and unconstrained optimization problem serves as a more accurate estimation of the location of MS. The advantage of the proposed mobile location estimation method is that this method can be applied to both LOS and NLOS propagations and there is no need to reconstruct the Euclidean distances between BSs and the MS from mostly non-Euclidean distances so that the reconstruction error can be avoided and a more accurate mobile location estimation can be achieved. Finally, a convex and constrained optimization problem is introduced to approximate the non-convex and unconstrained optimization problem since the convex optimization problems can be solved very efficiently nowadays.

A robust model matching control of immune response is proposed for therapeutic enhancement to match a prescribed immune response under uncertain initial states and environmental disturbances, including continuous intrusion of exogenous pathogens. The worst-case effect of all possible environmental disturbances and uncertain initial states on the matching for a desired immune response is minimized for the enhanced immune system, i.e. a robust control is designed to track a prescribed immune model response from the minimax matching perspective. This minimax matching problem could be transformed to an equivalent dynamic game problem. The exogenous pathogen and environmental disturbances are considered as a player to maximize (worsen) the matching error when the therapeutic control agents are considered as another player to minimize the matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust model matching control problem by the nonlinear dynamic game method directly. A fuzzy model is proposed to interpolate several linearized immune systems at different operation points to approximate the innate immune system via smooth fuzzy membership functions. With the help of fuzzy approximation method, the minimax matching control problem of immune systems could be easily solved by the proposed fuzzy dynamic game method via the linear matrix inequality (LMI) technique with the help of robust control toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed method.

A novel prediction scheme is proposed for real-time MPEG video to predict the burst and long-range dependent traffic. The trend and periodic characteristics of MPEG video traffic are fully captured by a proposed stochastic state-space dynamic model. Then a recursive Hinfinfiltering algorithm is proposed to estimate traffic for long-range prediction. Simulation results based on real MPEG traffic data show that the proposed scheme has superior performance and lower complexity than some adaptive neural network methods, such as TDNN, NARX, and Elman neural networks.

Molecular noises in gene networks come from intrinsic fluctuations, transmitted noise from upstream genes, and the global noise affecting all genes. Knowledge of molecular noise filtering in gene networks is crucial to understand the signal processing in gene networks and to design noise-tolerant gene circuits for synthetic biology. A nonlinear stochastic dynamic model is proposed in describing a gene network under intrinsic molecular fluctuations and extrinsic molecular noises. The stochastic molecular-noise-processing scheme of gene regulatory networks for attenuating these molecular noises is investigated from the nonlinear robust stabilization and filtering perspective. In order to improve the robust stability and noise filtering, a robust gene circuit design for gene networks is proposed based on the nonlinear robust H infinity stochastic stabilization and filtering scheme, which needs to solve a nonlinear Hamilton-Jacobi inequality. However, in order to avoid solving these complicated nonlinear stabilization and filtering problems, a fuzzy approximation method is employed to interpolate several linear stochastic gene networks at different operation points via fuzzy bases to approximate the nonlinear stochastic gene network. In this situation, the method of linear matrix inequality technique could be employed to simplify the gene circuit design problems to improve robust stability and molecular-noise-filtering ability of gene networks to overcome intrinsic molecular fluctuations and extrinsic molecular noises.

An adaptive two-loop power tracking control scheme is proposed for direct sequence code-division multiple-access (DS-CDMA) cellular systems in a wireless network. The scheme includes an outer-loop controller and an inner-loop controller. An adaptive searching algorithm is designed for determining an optimal target signal to interference and noise ratio (SINR) for each user in the outer loop. The utility optimization can be achieved by using the adaptive algorithm through the net utility function based on the quality of service (QoS) for the purpose of resource management of wireless communication networks. A prediction control is designed to compensate for the effect of round-trip time-delay, channel fading, multiple access interference (MAI), and noise in the inner loop. The optimal target SINR tracking can be achieved by using the prediction control through a robust pole placement. Combining these two controllers in the outer loop and inner loop, utility optimization and target SINR tracking can be achieved at the same time. The stability and convergence of the proposed scheme are discussed. Several simulation results are given to confirm the performance of the proposed method.

In this study, the authors propose a novel full-diversity combination algorithm to significantly improve the performance of the network Kalman-based blind equalizers. Based on the weighted Gaussian sum (WGS) technique and the network of extended Kalman filters (NEKF), the proposed full-diversity blind equalizer can employ the prediction errors of network of Kalman filters to achieve the maximum likelihood (ML) detection. In the first initial condition, the proposed full-diversity blind equalizer requires an initial training sequence in order to estimate the initial channel coefficients. For symbol detection, the proposed full-diversity blind equalizer demonstrates a significant improvement over the conventional WGS-IMM(Interacting Multiple Model) blind equalizer in the bit error rate (BER) performance. Besides, from the trade-off between performance and computational complexity, the proposed modified 2-Diversity blind equalizer is shown to be a best choice for the WGS-based blind equalizer.

BACKGROUND: Eukaryotic cells have developed mechanisms to respond to external environmental or physiological changes (stresses). In order to increase the activities of stress-protection functions in response to an environmental change, the internal cell mechanisms need to induce certain specific gene expression patterns and pathways by changing the expression levels of specific transcription factors (TFs). The conventional methods to find these specific TFs and their interactivities are slow and laborious. In this study, a novel efficient method is proposed to detect the TFs and their interactivities that regulate yeast genes that respond to any specific environment change. RESULTS: For each gene expressed in a specific environmental condition, a dynamic regulatory model is constructed in which the coefficients of the model represent the transcriptional activities and interactivities of the corresponding TFs. The proposed method requires only microarray data and information of all TFs that bind to the gene but it has superior resolution than the current methods. Our method not only can find stress-specific TFs but also can predict their regulatory strengths and interactivities. Moreover, TFs can be ranked, so that we can identify the major TFs to a stress. Similarly, it can rank the interactions between TFs and identify the major cooperative TF pairs. In addition, the cross-talks and interactivities among different stress-induced pathways are specified by the proposed scheme to gain much insight into protective mechanisms of yeast under different environmental stresses. CONCLUSION: In this study, we find significant stress-specific and cell cycle-controlled TFs via constructing a transcriptional dynamic model to regulate the expression profiles of genes under different environmental conditions through microarray data. We have applied this TF activity and interactivity detection method to many stress conditions, including hyper- and hypo- osmotic shock, heat shock, hydrogen peroxide and cell cycle, because the available expression time profiles for these conditions are long enough. Especially, we find significant TFs and cooperative TFs responding to environmental changes. Our method may also be applicable to other stresses if the gene expression profiles have been examined for a sufficiently long time.

BACKGROUND: ChIP-chip data, which indicate binding of transcription factors (TFs) to DNA regions in vivo, are widely used to reconstruct transcriptional regulatory networks. However, the binding of a TF to a gene does not necessarily imply regulation. Thus, it is important to develop methods to identify regulatory targets of TFs from ChIP-chip data. RESULTS: We developed a method, called Temporal Relationship Identification Algorithm (TRIA), which uses gene expression data to identify a TF's regulatory targets among its binding targets inferred from ChIP-chip data. We applied TRIA to yeast cell cycle microarray data and identified many plausible regulatory targets of cell cycle TFs. We validated our predictions by checking the enrichments for functional annotation and known cell cycle genes. Moreover, we showed that TRIA performs better than two published methods (MA-Network and MFA). It is known that co-regulated genes may not be co-expressed. TRIA has the ability to identify subsets of highly co-expressed genes among the regulatory targets of a TF. Different functional roles are found for different subsets, indicating the diverse functions a TF could have. Finally, for a control, we showed that TRIA also performs well for cell-cycle irrelevant TFs. CONCLUSION: Finding the regulatory targets of TFs is important for understanding how cells change their transcription program to adapt to environmental stimuli. Our algorithm TRIA is helpful for achieving this purpose.

Multicarrier code-division multiple access (MC-CDMA) combines multicarrier transmission with direct-sequence (DS) spread spectrum techniques. In this study, several possible channel models of MC-CDMA systems are considered as a multi-state switching Markov process to match the time-varying multipath fading channel. A novel multiple channel estimator, which consists of several possible channel models and can be self-adjusted to fit different channel uncertain conditions, is proposed for MC-CDMA systems to effectively estimate channel coefficients in the frequency domain over time-varying multipath fading channels. Based on the proposed channel estimation, an enhanced minimum mean-square error (MMSE) equalizer is employed for symbol detection of MC-CDMA systems. Simulation results demonstrate that the proposed multiple channel estimator can track the channel more accurately than the conventional channel estimators. With the consideration of channel estimation error as a channel noise to improve symbol detection, the enhanced equalizer based on the proposed multiple channel estimator performs much better than those based on the conventional channel estimators in bit error rate (BER).

In this paper, we consider the channel tracking problem for a direct-sequence code division multiple-access (DS-CDMA) communication under Gaussian noise. This problem is important in the design of a receiver over multipath time-varying fading channels. The main contribution of this paper is two-fold. The first one is a multiple-model framework for modeling the channel, composed of a set of known first- and second-order auto-regressive models (AR(i), i = 1,2) with the transitions between models obeying a Markov chain. Each AR model assumes a velocity sub-range of mobile users, and the set covers the range of possible dynamics of the time-varying fading channel. The second contribution is the adaptation of the known interacting multiple-model (EMM) estimation algorithm for channel tracking based on the above modeling framework. This tracking solution in combination with Kalman-based symbol detector leads to a feasible receiver architecture for attaining satisfactory performance

This study introduces a fuzzy control design to deal with the nonlinear Hinfincontrol problem subject to actuator saturation. For the Hinfinrobust control scheme, however, the high gain problem is inevitable. Often, very large control inputs in the transiency are required for the Hinfincontrol scheme. In practice, physical capacity of the actuator is limited and the actuator saturation may severely degrade the performance of the closed-loop systems, lead to a large overshoot, induce a limit cycle and even make the otherwise stable closed-loop system unstable. In the proposed Hinfinfuzzy control design, first, the Takagi and Sugeno (T-S) fuzzy model is employed to approximate a nonlinear dynamic system. Next, based on the fuzzy model, an Hinfinfuzzy controller subject to actuator saturation can be obtained under some linear matrix inequality (LMI) constraints.

In this study, we propose a novel robust diversity combination algorithm for a blind equalizer, which takes advantage of the multipath diversity to significantly improve the performance of the conventional blind equalizers. The proposed robust blind equalizer based on the weighted Gaussian sum (WGS) technique and the network of extended Kalman filters, can effectively estimate both the channel coefficients and the transmitted symbols over the fast time-varying inter-symbol interference (ISI) fading channels. Simulation results illustrate that the proposed blind equalizer based on the robust diversity combination algorithm can track the fast time-varying fading channel more accurately than the conventional blind equalizers. For symbol detection, the proposed robust blind equalizer shows a significant improvement compared with the conventional blind equalizers in the bit error rate (BER) performance.

Multicarrier code-division multiple access (MC-CDMA) combines multicarrier transmission with direct-sequence (DS) spread spectrum techniques. In this study, a novel multiple channel estimator, which consists of several possible channel models and can be self-adjusted to fit different channel uncertain conditions, is proposed for MC-CDMA systems to effectively estimate channel coefficients in the frequency domain over time-varying multipath fading channels. Based on the proposed channel estimation, an enhanced minimum mean-square error (MMSE) equalizer is employed for symbol detection of MC-CDMA systems. Simulation results demonstrate that the proposed multiple channel estimator can track the channel more accurately than the conventional channel estimators. With the consideration of channel estimation error, the enhanced equalizer based on the proposed multiple channel estimator performs much better than those based on the conventional channel estimators in bit error rate (BER).

How to design a robust gene network to tolerate intrinsic kinetic parameter variations and to attenuate extrinsic environmental noises to a desired altering level will be an important topic in metabolic engineering for biotechnological purpose or drug design for therapeutic purpose. At present, there is still no good systematic design method to achieve the robust gene network design. In this study, a gene network suffering from intrinsic kinetic parameter fluctuations and extrinsic environmental noises is modeled as Langevin equation with state-dependent stochastic noises. Based on the nonlinear stochastic filtering theory, a systematic gene circuit design method is proposed to achieve robust stability to tolerate intrinsic noises and to attenuate extrinsic noises to a prescribed filtering level. Computational simulations of a gene network are performed to illustrate the systematic design procedure and to confirm the performance of the proposed robust filtering circuit design in gene networks. The robust gene network design principles have not only yielded a comprehensive design theory of robust gene networks, but also gained valuable insights into the molecular noise filtering of gene networks. The proposed design method could precede the experimental biotechnological method to allow objective numerical improvement strategies for robust gene circuit designs.

MOTIVATION: Transcription factor binding sites are known to co-occur in the same gene owing to cooperativity of the transcription factors (TFs) that bind to them. Genome-wide location data can help us understand how an individual TF regulates its target gene. Nevertheless, how TFs cooperate to regulate their target genes still needs further study. In this study, genome-wide location data and expression profiles are integrated to reveal how TFs cooperate to regulate their target genes from the stochastic system perspective. RESULTS: Based on a stochastic dynamic model, a new measurement of TF cooperativity is developed according to the regulatory abilities of cooperative TF pairs and the number of their occurrences. Our method is employed to the yeast cell cycle and reveals successfully many cooperative TF pairs confirmed by previous experiments, e.g. Swi4-Swi6 in G1/S phase and Ndd1-Fkh2 in G2/M phase. Other TF pairs with potential cooperativity mentioned in our results can provide new directions for future experiments. Finally, a cooperative TF network of cell cycle is constructed from significant cooperative TF pairs. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: http://www.ee.nthu.edu.tw/~bschen/cooperativity/

BACKGROUND: Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale. At present, no good theory exists for identifying all possible mechanisms of genetic regulatory networks to attenuate the molecular noise to achieve regulatory ability or to amplify the molecular noise to randomize outcomes to the advantage of diversity. Therefore, the noise filtering of genetic regulatory network is an important topic for gene networks under intrinsic fluctuation and extrinsic noise. RESULTS: Based on stochastic dynamic regulation equation, the intrinsic fluctuation in reaction rates is modeled as a state-dependent stochastic process, which will influence the stability of gene regulatory network, especially, with low concentrations of reacting species. Then the mechanisms of genetic regulatory network to attenuate or amplify extrinsic fluctuation are revealed from the nonlinear stochastic filtering point of view. Furthermore, a simple measure of attenuation level or amplification level of extrinsic noise for genetic regulatory networks is also introduced by nonlinear robust filtering method. Based on the global linearization scheme, a convenient method is introduced to measure noise attenuation or amplification for each gene of the nonlinear stochastic regulatory network by solving a set of filtering problems, which correspond to a set of linearized stochastic regulatory networks. Finally, by the proposed methods, several simulation examples of genetic regulatory networks are given to measure their robust stability under intrinsic fluctuations, and to estimate the genes' attenuation and amplification levels under extrinsic noises. CONCLUSION: In this study, a stochastic nonlinear dynamic model is developed for genetic regulatory networks under intrinsic fluctuation and extrinsic noise. By the method we proposed, we could determine the robust stability under intrinsic fluctuations and identify the genes that are significantly affected by extrinsic noises, which we call the weak structure of the network. This method will be potential for robust gene circuit design in future, on which a drug design could be based.

BACKGROUND: A transcriptional regulatory module (TRM) is a set of genes that is regulated by a common set of transcription factors (TFs). By organizing the genome into TRMs, a living cell can coordinate the activities of many genes and carry out complex functions. Therefore, identifying TRMs is helpful for understanding gene regulation. RESULTS: Integrating gene expression and ChIP-chip data, we develop a method, called MOdule Finding Algorithm (MOFA), for reconstructing TRMs of the yeast cell cycle. MOFA identified 87 TRMs, which together contain 336 distinct genes regulated by 40 TFs. Using various kinds of data, we validated the biological relevance of the identified TRMs. Our analysis shows that different combinations of a fairly small number of TFs are responsible for regulating a large number of genes involved in different cell cycle phases and that there may exist crosstalk between the cell cycle and other cellular processes. MOFA is capable of finding many novel TF-target gene relationships and can determine whether a TF is an activator or/and a repressor. Finally, MOFA refines some clusters proposed by previous studies and provides a better understanding of how the complex expression program of the cell cycle is regulated. CONCLUSION: MOFA was developed to reconstruct TRMs of the yeast cell cycle. Many of these TRMs are in agreement with previous studies. Further, MOFA inferred many interesting modules and novel TF combinations. We believe that computational analysis of multiple types of data will be a powerful approach to studying complex biological systems when more and more genomic resources such as genome-wide protein activity data and protein-protein interaction data become available.

In direct-sequence code division multiple access (DS-CDMA) cellular radio systems, power control is an important means to achieve higher communication link quality and larger system capacity. In order to track a desired signal-to-interference-plus-noise ratio (SINR) under round-trip delay, multiple access interference (MAI), channel fading, and noise, a robust state feedback control via a desired pole (eigenvalue) placement and an l1optimal prediction is proposed for power control of CDMA systems. The l1predictor is used to predict the tracking error to compensate for the effect of round-trip delay, such that the peak of prediction error due to the uncertainties of channel fading, interference, and noise is as small as possible. Then the optimal l1predictor design problem is transformed to a suboptimal prediction problem by minimizing the upper bound of the l1norm of SINR tracking error and solving the eigenvalue problem (EVP) under some linear matrix inequality (LMI) constraints. Under the proposed framework, the global information of the channel gains of all users in the CDMA system is not required

A Kalman-based interacting multiple model (IMM) smoother is proposed for mobile location estimation with the time of arrival (TOA) measurement data in cellular networks to meet the Federal Communications Commission (FCC) requirement for phase 2. In this study, the line-of-sight (LOS) and non-line-of-sight (NLOS) conditions in cellular networks are considered as a Markov process with two interactive modes. Then we propose a Kalman-based IMM smoother to accurately estimate smooth range between the corresponding base station (BS) and mobile station (MS) in cellular networks. It is shown that the proposed mobile location estimator can efficiently mitigate the NLOS effects of the measurement range error even when the corresponding BS changes the condition between LOS and NLOS. Simulation results demonstrate that the performance of the proposed Kalman-based IMM smoother is improved significantly over the FCC target in both fixed LOS/NLOS and LOS/NLOS transition conditions

A robust Kalman filter-based adaptive multiuser receiver is proposed for channel estimation and multiuser detection of ultra wideband (UWB) systems in a realistic indoor channel. A state space stochastic model is developed to describe the dynamics of the UWB multiuser transmission systems. A robust Kalman filter is employed to estimate the channel parameters. In the tracking mode with consideration of channel estimation errors, the proposed robust Kalman filter-based adaptive multiuser decision-feedback equalizer can significantly reduce effects of the multiple access interference (MAI) from the other users and the inter-symbol interference (ISI) in the UWB channel. Simulation results illustrate that performance of the proposed robust adaptive channel estimation works well in a realistic UWB channel. Using the proposed robust channel estimator, the performance of the proposed UWB multiuser detector almost achieves the same bit error rate (BER) as that with actual UWB channel cases, and outplay than that of the conventional RAKE receiver and single-stage parallel interference cancellation (PIC) detector for UWB systems.

MOTIVATION: The robustness of a biochemical network is defined as the tolerance of variations in kinetic parameters with respect to the maintenance of steady state. Robustness also plays an important role in the fail-safe mechanism in the evolutionary process of biochemical networks. The purposes of this paper are to use the synergism and saturation system (S-system) representation to describe a biochemical network and to develop a robustness measure of a biochemical network subject to variations in kinetic parameters. Since most biochemical networks in nature operate close to the steady state, we consider only the robustness measurement of a biochemical network at the steady state. RESULTS: We show that the upper bound of the tolerated parameter variations is related to the system matrix of a biochemical network at the steady state. Using this upper bound, we can calculate the tolerance (robustness) of a biochemical network without testing many parametric perturbations. We find that a biochemical network with a large tolerance can also better attenuate the effects of variations in rate parameters and environments. Compensatory parameter variations and network redundancy are found to be important mechanisms for the robustness of biochemical networks. Finally, four biochemical networks, such as a cascaded biochemical network, the glycolytic-glycogenolytic pathway in a perfused rat liver, the tricarboxylic acid cycle in Dictyostelium discoideum and the cAMP oscillation network in bacterial chemotaxis, are used to illustrate the usefulness of the proposed robustness measure.

BACKGROUND: The cellular signaling pathway (network) is one of the main topics of organismic investigations. The intracellular interactions between genes in a signaling pathway are considered as the foundation of functional genomics. Thus, what genes and how much they influence each other through transcriptional binding or physical interactions are essential problems. Under the synchronous measures of gene expression via a microarray chip, an amount of dynamic information is embedded and remains to be discovered. Using a systematically dynamic modeling approach, we explore the causal relationship among genes in cellular signaling pathways from the system biology approach. RESULTS: In this study, a second-order dynamic model is developed to describe the regulatory mechanism of a target gene from the upstream causality point of view. From the expression profile and dynamic model of a target gene, we can estimate its upstream regulatory function. According to this upstream regulatory function, we would deduce the upstream regulatory genes with their regulatory abilities and activation delays, and then link up a regulatory pathway. Iteratively, these regulatory genes are considered as target genes to trace back their upstream regulatory genes. Then we could construct the regulatory pathway (or network) to the genome wide. In short, we can infer the genetic regulatory pathways from gene-expression profiles quantitatively, which can confirm some doubted paths or seek some unknown paths in a regulatory pathway (network). Finally, the proposed approach is validated by randomly reshuffling the time order of microarray data. CONCLUSION: We focus our algorithm on the inference of regulatory abilities of the identified causal genes, and how much delay before they regulate the downstream genes. With this information, a regulatory pathway would be built up using microarray data. In the present study, two signaling pathways, i.e. circadian regulatory pathway in Arabidopsis thaliana and metabolic shift pathway from fermentation to respiration in yeast Saccharomyces cerevisiae, are reconstructed using microarray data to evaluate the performance of our proposed method. In the circadian regulatory pathway, we identified mainly the interactions between the biological clock and the photoperiodic genes consistent with the known regulatory mechanisms. We also discovered the now less-known regulations between crytochrome and phytochrome. In the metabolic shift pathway, the casual relationship of enzymatic genes could be detected properly.

BACKGROUND: Gene expression programs depend on recognition of cis elements in promoter region of target genes by transcription factors (TFs), but how TFs regulate gene expression via recognition of cis elements is still not clear. To study this issue, we define the cis-regulatory circuit of a gene as a system that consists of its cis elements and the interactions among their recognizing TFs and develop a dynamic model to study the functional architecture and dynamics of the circuit. This is in contrast to traditional approaches where a cis-regulatory circuit is constructed by a mutagenesis or motif-deletion scheme. We estimate the regulatory functions of cis-regulatory circuits using microarray data. RESULTS: A novel cross-gene identification scheme is proposed to infer how multiple TFs coordinate to regulate gene transcription in the yeast cell cycle and to uncover hidden regulatory functions of a cis-regulatory circuit. Some advantages of this approach over most current methods are that it is based on data obtained from intact cis-regulatory circuits and that a dynamic model can quantitatively characterize the regulatory function of each TF and the interactions among the TFs. Our method may also be applicable to other genes if their expression profiles have been examined for a sufficiently long time. CONCLUSION: In this study, we have developed a dynamic model to reconstruct cis-regulatory circuits and a cross-gene identification scheme to estimate the regulatory functions of the TFs that control the regulation of the genes under study. We have applied this method to cell cycle genes because the available expression profiles for these genes are long enough. Our method not only can quantify the regulatory strengths and synergy of the TFs but also can predict the expression profile of any gene having a subset of the cis elements studied.

Intelligent robust tracking control designs are proposed in this paper for both uncertain holonomic and nonholonomic mechanical systems. A unified and systematic procedure, that is based on an adaptive fuzzy (or neural network) system and a linear observer, is employed to derive the controllers for these two constrained mechanical systems. Adaptive fuzzy-based (or neural network-based) position feedback tracking controllers can be constructed such that all the states and signals of the closed-loop systems are bounded and the tracking error locally converges to a small region around zero. Only position measurements are required for feedback. The implementation of the fuzzy (or neural network) basis functions depends only on the desired reference information and so once a set of desired trajectories is given, the required basis functions can be explicitly preassigned. Consequently, the intelligent robust position feedback tracking controllers developed here possess the properties of computational simplicity and easy implementation. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed control algorithms.

In orthogonal frequency division multiplexing (OFDM) systems, time-varying multipath fading leads to the loss of subcarrier orthogonality and the occurrence of intercarrier interference (ICI). In this study, an efficient ICI suppression with less noise enhancement for multicarrier equalization is presented by using a parallel canceling scheme via frequency-domain equalization techniques, with the assumption that the channel impulse response (CIR) varies linearly during a block period. In order to avoid performance deterioration due to unreliable initial estimations in the parallel cancellation scheme, a cost function with proper weighting factor is introduced to improve the performance of the proposed equalizer. The proposed equalizer consists of a set of prefilters and a set of ICI cancellation filters, with two stages to perform different functions to achieve minimum mean square error (MMSE) equalization. The prefilters compensate for the multiplicative distortion at the first stage, and the ICI cancellation filters remove the effects of ICI by a parallel cancellation scheme at the second stage. Finally, the performance of the proposed equalizer is analyzed and compared with that of other equalizers, indicating significant performance improvement.

Identification of a T-S fuzzy ARMAX model is addressed in this paper. From the fuzzy ARMAX model, a fuzzy one-step ahead prediction model is developed. A recursive least square algorithm is then proposed to identify the parameters in the consequent part of a T-S fuzzy ARMAX system. Properties of the parameter estimates are rigorously derived. This work is an extension of the results of identification of stochastic linear systems.

To date, nonlinear L/sub /spl infin// - gain control problems have not been solved by the conventional control methods for nonlinear dynamic systems with persistent bounded disturbances. This study introduces a fuzzy control design to deal with the nonlinear L/sub /spl infin// - gain control problem. First, the Takagi and Sugeno (T-S) fuzzy model is employed to approximate the nonlinear dynamic system. Next, based on the fuzzy model, the upper bound of L/sub /spl infin// - gain of the closed-loop system can be obtained under some linear matrix inequality constraints. Therefore, the nonlinear L/sub /spl infin// - gain control problem is transformed into a suboptimal control problem, i.e., to minimize the upper bound of the L/sub /spl infin// - gain of the closed-loop system subject to some LMI constraints. In this situation, the nonlinear L/sub /spl infin// - gain control problem can be easily solved by LMI-based optimization method. The proposed methods, which efficiently attenuate the peak of error signal due to persistent bounded external disturbances, extend the L/sub /spl infin// - gain control problems from linear dynamic systems to nonlinear dynamic systems.

MOTIVATION: Genome-wide gene expression programs have been monitored and analyzed in the yeast Saccharomyces cerevisiae, but how cells regulate global gene expression programs in response to environmental changes is still far from being understood. We present a systematic approach to quantitatively characterize the transcriptional regulatory network of the yeast cell cycle. For the interpretative purpose, 20 target genes were selected because their expression patterns fluctuated in a periodic manner concurrent with the cell cycle and peaked at different phases. In addition to the most significant five possible regulators of each specific target gene, the expression pattern of each target gene affected by synergy of the regulators during the cell cycle was characterized. Our first step includes modeling the dynamics of gene expression and extracting the transcription rate from a time-course microarray data. The second step embraces finding the regulators that possess a high correlation with the transcription rate of the target gene, and quantifying the regulatory abilities of the identified regulators. RESULTS: Our network discerns not only the role of the activator or repressor for each specific regulator, but also the regulatory ability of the regulator to the transcription rate of the target gene. The highly coordinated regulatory network has identified a group of significant regulators responsible for the gene expression program through the cell cycle progress. This approach may be useful for computing the regulatory ability of the transcriptional regulatory networks in more diverse conditions and in more complex eukaryotes. SUPPLEMENTARY INFORMATION: Matlab code and test data are available at http://www.ee.nthu.edu.tw/~bschen/quantitative/regulatory_network.htm

How to develop a novel missile guidance law that can act effectively against very high speed incoming targets, such as ballistic missiles, has been a major concern in the defense technique. It has been unveiled recently in the literature that the most effective way for a lower speed interceptor to successfully engage an incoming target with very high speed is to limit the aspect angle between the missile and target flight path to within 180/spl deg/ plus or minus few degrees. On the basis of this requirement, a new integrated fuzzy guidance law is developed in this paper against very high-speed maneuverable targets on three-dimensional space. An integrated fuzzy type guidance law is explored for midcourse and terminal phases. It is shown that the integrated guidance scheme offers excellent tracking performance as well as performance sensitivity with respect to some parametric variations.

In this paper, a robust Smith prediction filter is proposed for power control design of direct-sequence code-division multiple-access cellular mobile radio systems. Due to the type-I (integrator) structure in the close loop, we first show that zero steady-state tracking error of the averaged received signal-to-noise plus interference ratio (SINR) with respect to a constant target SINR can be ensured. Next, with the Smith predictor to compensate round trip delay, a fixed-order robust H/sub /spl infin// loop filter is developed by using the genetic algorithm to minimize the worst-case variance of the received SINR from the minimax perspective. Using the proposed robust control approach, the statistics of the fading and interference are not needed in the design procedure. To confirm the performance of the proposed method, several simulation results are given in comparison with other methods.

An adaptive fuzzy mixed H/sub 2//H/sub /spl infin// lateral control of nonlinear missile systems with uncertain disturbances considered is proposed to achieve H/sub 2/ quadratic tracking with H/sub /spl infin// disturbance rejection. This approach can be applied to control the lateral directional dynamics of the missiles at high angle of attack or generate moments on missile operating in flight regimes where the effectiveness of conventional aerodynamic surfaces is reduced. Using an adaptive fuzzy approximation method, the uncertain nonlinear model of the missile system is estimated. Then, by a mixed H/sub 2//H/sub /spl infin// control design, the effects of external disturbance and fuzzy approximation error as well as consumed energy of the controller is minimized. By the skew symmetric property of the missile system and adequate choice of state variable transformation, this problem can be reduced to solve two algebraic Riccati-like equations. Furthermore, a closed-form solution to these two algebraic equations can be obtained with very simple form for the preceding control design.

Direct-sequence Code-division multiple-access (DS-CDMA) has merged as proper format for wireless communication systems. As a result of multiple-access interference (MAI), inter-symbol interference (ISI), narrowband interference (NBI) and nonlinearities in channels, DS-CDMA systems can suffer deterioration in performance. In practical application, it is difficult to design optimal equalizer for nonlinear DS-CDMA systems. Here, we use fuzzy models as the nonlinear interpolation of several linear channels. Based on fuzzy linear interpolation channel, a robust suboptimal fuzzy equalizer is proposed to efficiently compensate the nonlinear channel, MAI, ISI and channel noise to reconstruct the transmitted signals for each user. The robust suboptimal equalization design problem is transformed to a linear matrix inequality problem, which can be efficiently solved convex optimization technique.

In general, it is a difficult work to design an efficient filter for nonlinear systems. This paper studies fuzzy filtering design for nonlinear discrete-time systems. First, the Takagi and Sugeno fuzzy model is proposed to approximate a nonlinear discrete-time system. Next, based on the fuzzy model, the fuzzy estimation for nonlinear discrete-time systems is studied. Using a suboptimal approach, the minimum variance fuzzy estimation problems are characterized in terms of an eigenvalue problem (EVP) by minimizing the upper bound on the variance of the estimation error. The EVP can be solved very efficiently using convex optimization techniques.

This paper considers the signal reconstruction problem under unknown parameters and nature missing data. The solution is divided into two stages. At the first stage, the parameter estimation of autoregressive moving average (ARMA) model with nature missing data is studied. In the second stage, a robust Kalman filter to reconstruct the input signal is developed. The missing data model is based on a probabilistic structure with unknown. In this situation, the estimation becomes a highly nonlinear optimization problem with many local minima. In this paper, we combine the global search method of genetic algorithm and simulated annealing (GA/SA) to achieve a global optimal solution with fast convergent rate. After the system parameters are exactly estimated in the first stage, the problem of reconstructing the missing signal can be handled elegantly using the proposed robust Kalman filter in the second stage.

In general, fuzzy control design for stochastic nonlinear systems is still difficult since the fuzzy bases are stochastic so as to increase the difficulty and complexity of the fuzzy tracking control design. In this study, a fuzzy stochastic moving-average model with control input (fuzzy ARMAX model) is introduced to describe nonlinear stochastic systems. From the fuzzy ARMAX model, a fuzzy one-step ahead prediction model is developed. Based on a fuzzy one-step ahead prediction stochastic model, optimal design algorithms are proposed to achieve the optimal tracking of nonlinear stochastic systems. In this study, the minimum variance tracking control, generalized minimum variance tracking control, and the optimal model reference tracking control are developed for stochastic fuzzy systems. We construct some basic stability conditions for general stochastic fuzzy systems and use these conditions to verify the stability of the fuzzy tracking control systems. Finally, two simulation examples are given to indicate the performance of the proposed methods.

Generally, it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises. In this paper, we propose the H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization/detection of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the signal transmission system is described as a state-space model and the input signal is embedded in the state vector such that the signal reconstruction (estimation) design becomes a nonlinear state estimation problem. Then, the Takagi-Sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions. Since the statistics of noises are unknown, the fuzzy H/sub /spl infin// equalizer is proposed to treat the state estimation problem from the worst case (robust) point of view. When the statistics of noises are uncertain but with some nominal (or average) information available, the mixed H/sub 2//H/sub /spl infin// equalizer is employed to take the advantage of both H/sub 2/ optimal performance with nominal statistics of noises and the H/sub /spl infin// robustness performance against the statistical uncertainty of noises. Using the LMI approach, the fuzzy H/sub 2//H/sub /spl infin// equalizer/detector design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.

In order to exploit the nonlinear time-varying property of network traffic, the traffic flow from controlled sources is described by a fuzzy autoregressive moving-average model with auxiliary input (fuzzy ARMAX process), with the traffic flow from uncontrolled sources (i.e., cross traffic) being described as external disturbances. In order to overcome the difficulty of the transmission delay in the design of congestion control, the fuzzy traffic model is translated to an equivalent fuzzy predictive traffic model. A fuzzy adaptive flow control scheme is proposed to avoid congestion at high utilization while maintaining good quality of service. By use of fuzzy adaptive prediction technique, the difficulties in congestion control design due to nonlinearity, time-varying characteristics, and large propagation delay can be overcome by the proposed adaptive traffic control method. A comparative evaluation is also given to show the superiority of the proposed method.

A fuzzy differential game theory is proposed to solve the n-person (or n-player) nonlinear differential noncooperative game and cooperative game (team) problems, which are not easily tackled by the conventional methods. In the paper, both noncooperative and cooperative quadratic differential games are considered. First, the nonlinear stochastic system is approximated by a fuzzy model. Based on the fuzzy model, a fuzzy controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or with the cooperative game in the sense of Pareto-optimal strategies. Using a suboptimal approach, the outcomes of the fuzzy differential games for both the noncooperative and the cooperative cases are parameterized in terms of an eigenvalue problem. Since the state variables are usually unavailable, a suboptimal fuzzy observer is also proposed in this study to estimate the states for these differential game problems. Finally, simulation examples are given to illustrate the design procedures and to indicate the performance of the proposed methods.

For original paper see ibid., vol. 6, p.1-11 (1998). In this correspondence, we show that the rule base implemented in the aforementioned paper cannot act as a universal approximator. Furthermore, we show by simulation that the robot example reported in the paper can be effectively controlled without need for the fuzzy component.

An adaptive fuzzy control approach based on solving Hamilton-Jacobi partial differential inequality (HJPDI) is proposed for the nonlinear H/sub /spl infin// control problem, which is commonly encountered in the nonlinear robust control system analysis and design. The solution of Hamilton-Jacobi partial differential inequality is approximated using adaptive fuzzy on-line learning along the dynamic trajectories of the closed-loop system.

This paper considers the problem of estimating the autoregressive moving average (ARMA) power spectral density when measurements are corrupted by noises and with missing data. The missing data model is based on an unknown probabilistic structure. In this situation, the spectral estimation becomes a highly nonlinear optimization problem with many local minima. In this paper, we use the global search method of genetic algorithm (GA) to achieve a global optimal solution of this spectral estimation problem. From the simulation results, we have found that the performance is improved significantly if the probability of data missing is considered in the spectral estimation problem.

In the presence of narrowband interference (NBI), the performance of the direct-sequence code-division multiple access communication system can be improved by using various interference cancellation schemes. In this paper, a scheme of parallel interference cancellers (PICs), which includes a set of NBI cancellation filters and a set of multiple access interference (MAI) cancellation filters, is developed to improve the signal-to-interference ratio (SIR) and handle the MAI effect. In order to avoid performance deterioration due to unreliable initial detection, a robust coefficient /spl gamma/ is introduced in our proposed design criterion. A recursive least-square algorithm is employed to update the tap coefficients of the PICs. In other words, no training or retraining period is needed in our proposed PICs. Finally, the SIR performance of the proposed detector is analyzed and compared to that of the conventional linear detector.

In general, due to the interactions among subsystems, it is difficult to design an H/sub /spl infin// decentralized controller for nonlinear interconnected systems. The model reference tracking control problem of nonlinear interconnected systems is studied via H/sub /spl infin// decentralized fuzzy control method. First, the nonlinear interconnected system is represented by an equivalent Takagi-Sugeno type fuzzy model. A state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H/spl infin/ model reference tracking performance is achieved. Furthermore, the stability of the nonlinear interconnected systems is also guaranteed. If states are not all available, a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control. Consequently, a fuzzy observer-based state feedback decentralized fuzzy controller is proposed to solve the H/sub /spl infin// tracking control design problem for nonlinear interconnected systems. The problem of H/sub /spl infin// decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem (EVP). The EVP can be solved very efficiently using convex optimization techniques. Finally, simulation examples are given to illustrate the tracking performance of the proposed methods.

This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H/sub /spl infin// model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method.

A PID-type controller incorporating neural network elimination scheme and sliding-mode control action for different objectives including H/sub 2/ tracking performance, H/sub /spl infin// tracking performance, and regional pole constraints is developed in robotic systems under plant uncertainties and external disturbances. The adaptive neural networks are used to compensate the plant uncertainties. The sliding-mode control action is included to eliminate the effect of approximation error via neural network approximation. The sufficient conditions are developed for different objectives in terms of linear matrix inequality (LMI) formulations. The interesting combinations of different objectives are considered in this paper, which include H/sub /spl infin// PID tracking control design with regional pole constraints and mixed H/sub 2//H/sub /spl infin// PID tracking control design with regional pole constraints. These multiobjective PID control problems are characterized in terms of eigenvalue problem (EVP). The EVP can be efficiently solved by the LMI toolbox in Matlab. The proposed methods are simple and the PID control gain for different objectives can be obtained systematically.

This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H/sub /spl infin// model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple linear fuzzy controller is used in our approach without the complicated feedback linearization technique and adaptive scheme. Using the proposed method, the fuzzy tracking control design problem is parametrized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques.

In general, it is not easy to design a decentralized controller for nonlinear interconnected systems. In this study, the stability of nonlinear interconnected systems is studied via a fuzzy decentralized control method. First, the nonlinear interconnected systems are represented by an equivalent Takagi-Sugeno type fuzzy model. If the state variables are unavailable, a fuzzy observer-based state feedback controller is also proposed to solve the stability problem of nonlinear interconnected systems. A robust decentralized stabilization technique is proposed for each decentralized controller to override the effect of fuzzy approximation error and interconnection among subsystems. This design problem is equivalent to solving a linear matrix inequality problem.

In code-division multiple-access systems transmitting data over time-varying multipath channels, both intersymbol interference (ISI) and multiple-access interference (MAI) arise. In this paper, we address interference suppression, multipath diversity and processing gain protection for multiuser detection with less noise enhancement by using a parallel cancelling scheme. The proposed detector consists of a RAKE filter, forward filter, and feedback filter with different functions for each filter. The RAKE filter increases the signal-to-noise ratio by taking the advantage of multipath and code diversities. The forward filter is proposed, in combination with the feedback filter, to remove the effects of MAI and ISI by parallel cancellation. In order to avoid performance deterioration due to unreliable initial estimation in the parallel cancellation, a cost function with proper weighting is introduced to improve the performance of the proposed detector. In the proposed design method, a recursive least square algorithm is employed to update the tap-coefficients of all filters for MAI and ISI cancellation. Finally, the performance of the proposed detector is analyzed and compared with other detectors.

Adaptive fuzzy-based tracking control designs are proposed in the paper for both holonomic mechanical systems as well as a large class of nonholonomic mechanical systems with plant uncertainties and external disturbances. A unified and systematic procedure is employed to derive the controllers for both holonomic and nonholonomic mechanical control systems, respectively. First, a fuzzy logic system is introduced to learn the behavior of unknown (or uncertain) mechanical dynamics by using an adaptive algorithm. Next, the effect of approximation error on the tracking error must be efficiently eliminated by employing an additional robustifying algorithm. Consequently, hybrid adaptive-robust controllers can be constructed such that the resulting closed-loop mechanical systems guarantee a satisfactorily transient and asymptotic performance. Furthermore, a partitioned procedure with respect to the above developed adaptive fuzzy logic approximators is introduced such that the number of fuzzy IF-THEN rules is significantly reduced and the developed control schemes can be easily implemented from the viewpoint of practical applications. Finally, simulation examples are presented to illustrate the tracking performance of a two-link constrained robot manipulator and a vertical wheel rolling on a plane surface by the proposed adaptive fuzzy-based control algorithms.

In this study, a fuzzy autoregressive (fuzzy-AR) model is proposed to describe the traffic characteristics of high-speed networks. The fuzzy-AR model approximates a nonlinear time-variant process with a combination of several linear local AR processes using a fuzzy clustering method. We propose that the use of this fuzzy-AR model has greater potential for congestion control of packet network traffic. The parameter estimation problem in fuzzy-AR modeling is treated by a clustering algorithm developed from actual traffic data in high-speed networks. Based on the adaptive AR-prediction model and queueing theory, a simple congestion control scheme is proposed to provide an efficient traffic management for high-speed networks. Finally, using the actual Ethernet-LAN packet traffic data, several examples are given to demonstrate the validity of this proposed method for high-speed network traffic control.

This study introduces a mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H/sub 2//H/sub /spl infin// controller is developed to achieve the suboptimal H/sub 2/ control performance with a desired H/sub /spl infin// disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H/sub 2//H/sub /spl infin// control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method.

In this work, we develop an equivalent filter bank structure for the computation of the fractional Fourier transform (FrFT). The purpose of this work is to provide a unified approach to the computation of the FrFT via the filter bank approach.

This study introduces a fuzzy linear control design method for nonlinear systems with optimal H/sup /spl infin// robustness performance. First, the Takagi and Sugeno fuzzy linear model (1985) is employed to approximate a nonlinear system. Next, based on the fuzzy linear model, a fuzzy controller is developed to stabilize the nonlinear system, and at the same time the effect of external disturbance on control performance is attenuated to a minimum level. Thus based on the fuzzy linear model, H/sup /spl infin// performance design can be achieved in nonlinear control systems. In the proposed fuzzy linear control method, the fuzzy linear model provides rough control to approximate the nonlinear control system, while the H/sup /spl infin// scheme provides precise control to achieve the optimal robustness performance. Linear matrix inequality (LMI) techniques are employed to solve this robust fuzzy control problem. In the case that state variables are unavailable, a fuzzy observer-based H/sup /spl infin// control is also proposed to achieve a robust optimization design for nonlinear systems. A simulation example is given to illustrate the performance of the proposed design method.

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance.

The objective of H/sub /spl infin// disturbance attenuation problem is to attenuate the effect of disturbance to the prescribed level and achieve performance robustness. Chen, Lee and Chang (Fuzzy Syst., vol.4, p.32-43, 1996) proposed an adaptive fuzzy H/sub /spl infin// disturbance attenuation algorithm. The fuzzy approximation error, which is influenced by the control input, is taken as the disturbance signal in the proposed algorithm. The authors argue that, because of the tradeoff between the attenuation level and the control input, performance robustness cannot be achieved by the proposed algorithm. The original authors agree that the approximation error will influence the performance robustness, especially in the case without external disturbance and with very small attenuation level. However, in practical control applications, very small attenuation levels are avoided in order to prevent high-gain control.

When the samples of a critically sampled speech signal are lost, objectionable aliasing occurs and perfect recovery of the original speech becomes impossible. In this work, a multirate state-space representation of the autoregressive (AR) speech process is derived to describe the generation of regularly missing-sample speech sequences. Next, a new sample-interpolation algorithm based on the multirate Kalman reconstruction filter is proposed to reduce speech quality degradation caused by packet losses. This method is used together with packet interleaving configuration, thereby simplifying the recovery of missing packets to the interpolation of missing samples. Subjective tests indicate that the proposed Kalman-based sample-interpolation algorithm performs better than the conventional odd-even sample-interpolation procedure for mitigating the effects of random packet losses in 64 kb/s PCM codes. The tolerable packet loss rate P/sub L/, which is strictly input-speech-dependent, can be as high as 10-20% with Kalman interpolation. These observations are based on computer simulations in terms of signal-to-noise ratio (SNR) values, waveform reconstruction plots, error spectral shapes, and summaries of informal listening tests.

A fuzzy logic controller equipped with a training (adaptive) algorithm is proposed in this work to achieve H/sup /spl infin// tracking performance for a class of uncertain (model free) nonlinear single-input single-output (SISO) systems with external disturbances. An attempt is also made to create a bridge between two important control design techniques, i.e., H/sup /spl infin// control design and fuzzy control design, so as to supply H/sup /spl infin// control design with more intelligence and fuzzy control design with better performance. The perfect matching of parameters in an adaptive fuzzy logic system is generally deemed impossible. Therefore, a desired tracking performance cannot be guaranteed in the conventional adaptive fuzzy control systems. In this study, the influence of both fuzzy logic approximation error and external disturbance on the tracking error is attenuated to a prescribed level. Both indirect and direct adaptive fuzzy controllers are employed to treat this H/sup /spl infin// tracking problem. The authors' results indicate that arbitrarily small attenuation level can be achieved via the proposed adaptive fuzzy control algorithm if a weighting factor of control variable is adequately chosen. The proposed design method is also useful for the robust tracking control design of the nonlinear systems with external disturbances and a large uncertainty or unknown variation in plant parameters and structures. Furthermore, only smooth control signals are needed via the proposed control designs. Two simulation examples are given finally to illustrate the performance of the proposed methods. Computer simulation results confirm that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the proposed method.