This article explores the observer-based feedback control problem for a nonlinear hyperbolic partial differential equations (PDEs) system. Initially, the polynomial fuzzy hyperbolic PDEs (PFHPDEs) model is established through the utilization of the fuzzy identification approach, derived from the nonlinear hyperbolic PDEs model. Various types of state estimation and controller design problems for the polynomial fuzzy PDEs system are discussed concerning the state estimation problem. To investigate the relaxed stability problem, Euler's homogeneous theorem, Lyapunov-Krasovskii functional with polynomial matrices (LKFPM), and the sum-of-squares (SOSs) approach are adopted. The exponential stabilization condition is formulated in terms of the spatial-derivative-SOSs (SD-SOSs). Additionally, a segmental algorithm is developed to find the feasible solution for the SD-SOS condition. Finally, a hyperbolic PDEs system and several numerical examples are provided to illustrate the validity and effectiveness of the proposed results.

This article presents a novel path-following-method-based polynomial fuzzy control design. By examining the stabilization problem, the nonconvex stabilization criterion represented in terms of bilinear sum-of-squares (SOS) constraints is proposed to complement the existing convex stabilization criteria. Based on the polynomial Lyapunov function and considering the operation domain, the stabilization control is designed with a systematic region of attraction (ROA) analysis method. Since the proposed stabilization criterion remains in nonconvex form, the conservativeness caused by the transformation from nonconvex (bilinear SOS) constraints into convex (SOS) constraints can be avoided. Moreover, the restriction on the Lyapunov function candidates for the convex transformation in the literature does not exist in the proposed nonconvex stabilization criterion. The stabilization analysis for polynomial fuzzy control systems is concerned with the double fuzzy summation problem that can be treated as the copositivity problem. Therefore, the SOS-based copositive relaxation technique is applied for the proposed stabilization criterion. Since the proposed nonconvex stabilization criterion is represented in terms of bilinear SOS constraints, the path-following method is employed for solving the bilinear SOS problem. Finally, design examples are provided to demonstrate that the proposed nonconvex stabilization criterion complements the existing convex stabilization criteria.

Web API/service technology has been attracting considerable attention and the REST (REpresentational State Transfer) architecture is now widely accepted as mainstream technology. Nonetheless, developing the means by which to discover RESTful Web APIs/services is crucial to the further development of this technology. Unfortunately, existing search engines for RESTful Web APIs/services provide only keyword-based or tag-based search functions. A failure to take into account the semantics and/or characteristics (e.g., their interface compatibility) greatly hampers the ability to find suitable APIs/services. In this study, we propose a novel approach to the discovery of RESTful Web API/services, referred to as Test-Oriented API Search with Semantic Interface Compatibility (TASSIC). This scheme involves expanding the terms of Web API/service documents based on DBpedia and WordNet. Unsuitable APIs/services are then filtered out using a systematic process, as follows: 1) calculation of semantic similarity between a set of candidate APIs/services and a user query, 2) analysis of interface compatibility between candidate APIs/services using the Hungarian Algorithm, 3) invocation of candidate APIs/services to verify functionality and availability, and 4) analysis of similarity between the actual response of the candidate services and the expected response specified in the user query. The proposed TASSIC increases the likelihood of matching APIs/services that are semantically equivalent or similar to user queries. Unit test and acceptance test are used to verify that a set of candidate APIs/services are actually available and that they actually meets user requirements. Experiment results demonstrate the efficacy of TASSIC, the accuracy of which is superior to that of existing methods.

This study aims to develop a robust monitoring system for advanced control and compensation of the overlay errors based on E-insensitive support vector regression (SVR), considering metrology delay. The proposed E-insensitive SVR control system has the ability to solve quadratic optimization problems in real settings. To investigate the consistency and reliability of the proposed algorithm, a simulation study based on empirical data was conducted to validate the solution quality enhancement by the proposed approach. The stability of the system under metrology delay was investigated when Lyapunov stability function takes place as the kernel function of the E-insensitive SVR optimization system. For sensitivity analysis, we compared and analyzed the effect of noise and time-varying metrology delay, within an online process with a simulation study based on empirical data. This approach can effectively reduce the misalignment of the overlay errors through the self-tuning process of E-insensitive SVR and provide real-time decision aid for process engineers.

The study designs a deep-learning-based facial classifier by applying the minimum spanning tree algorithm. A new data format is developed by adding the 3D information into 2D color images. This new type of data can magnificently raise the classifier's accuracy. This data can also recognize the target even in the bad situation. Firstly, the 3D features are extracted from Kinect sensor. After that, some of the extracted features are chosen to compose the minimum spanning tree (MST). The data represented by the minimum spanning tree is then put into the color image to form the new data. The new data will be trained by a deep-learning neural network to create the facial classifier. Comparing with the methods of image-only data with support vector machine (SVM), MST-image data with SVM and image-only data with deep-learning neural network (DLNN), the proposed method of MST-image data with DLNN has the highest identifying accuracy.

This paper deals with a sum-of-squares (SOS)-based control Lyapunov function (CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models, which are known as universal approximators. Next, global stabilization conditions represented in terms of SOS are provided in the framework of the CLF design, i.e., a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying Sontag's control law, once a CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions. Both global and semiglobal stabilization problems are formulated as SOS optimization problems, which reduce to numerical feasibility problems. Five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and SOS approaches.

This paper presents a new sum-of-squares (SOS, for brevity) design framework for robust control of polynomial fuzzy systems with uncertainties. Two kinds of robust stabilization conditions are derived in terms of SOS. One is global SOS robust stabilization conditions that guarantee the global and asymptotical stability of polynomial fuzzy control systems. The other is semiglobal SOS robust stabilization conditions. The latter is available for very complicated systems that are difficult to guarantee the global and asymptotical stability of polynomial fuzzy control systems. The main feature of all the SOS robust stabilization conditions derived in this paper are to be expressed as nonconvex formulations with respect to polynomial Lyapunov function parameters and polynomial feedback gains. Since a typical transformation from nonconvex SOS design conditions to convex SOS design conditions often results in some conservative issues, the new design framework presented in this paper gives key ideas to avoid the conservative issues. The first key idea is that we directly solve nonconvex SOS design conditions without applying the typical transformation. The second key idea is that we bring a so-called copositivity concept. These ideas provide some advantages in addition to relaxations. To solve our SOS robust stabilization conditions efficiently, we introduce a gradient algorithm formulated as a minimizing optimization problem of the upper bound of the time derivative of an SOS polynomial that can be regarded as a candidate of polynomial Lyapunov functions. Three design examples are provided to illustrate the validity and applicability of the proposed design framework. The examples demonstrate advantages of our new SOS design framework for the existing linear matrix inequality approaches and the existing convex SOS approach.

This paper proposes sum-of-squares (SOS) methodologies for stability analysis and region-of-attraction (ROA) estimation for nonlinear systems represented by polynomial fuzzy models via piecewise polynomial Lyapunov functions (PPLFs). At first, two SOS-based global stability criteria are proposed by applying maximum-type and minimum-type PPLFs, respectively. It is known that less-conservative results can be obtained by reducing global stability to local stability, since it is usually the case for nonlinear systems that the stability cannot be reached globally. Therefore, based on the two types of PPLFs, two local stability criteria are further proposed with the algorithms that enlarge the estimated ROA as much as possible. The constraints for checking (global and local) stability and enlarging the estimated ROA are represented in terms of bilinear SOS problems. Hence, the path-following method is applied to solve the bilinear SOS problems in the proposed methodologies. Finally, some examples are provided to illustrate the utility of the proposed methodologies.

This paper presents a sum-of-squares (SOS) based methodology to obtain inner bounds on the region-of-attraction (ROA) for nonlinear systems represented by polynomial fuzzy systems. The methodology searches a polynomial Lyapunov function to guarantee the local stability and the invariant subset of the ROA is presented as the level set of the polynomial Lyapunov function. At first the methodology checks whether the considered system can be guaranteed to be locally asymptotically stable. After confirming that the system is guaranteed to be locally asymptotically stable, the methodology enlarges the invariant subset of the ROA as much as possible. The constraints for both of checking stability and enlarging contractively invariant set are represented in terms of bilinear SOS optimization problems. The path-following method is applied to solve the bilinear SOS optimization problems in the methodology.

This paper presents a novel method for stabilization analysis of the single-input polynomial fuzzy systems using a sum of squares (SOS) approach to construct control Lyapunov functions (CLFs) for the systems. First, we represent a nonlinear system as a polynomial fuzzy system. Then, sufficient conditions in SOS terms for a positive definite function to become a CLF is presented. We solve the sufficient conditions using SOS optimization technique to construct the CLF. Finally, after a CLF is constructed, the controller for the system is designed using Sontag's formula. To illustrate the validity of the proposed approach, a design example is provided.

As semiconductor manufacturing reaching nanotechnology, to obtain high resolution and alignment accuracy via minimizing overlay errors within the tolerance is crucial. To address the needs of changing production and process conditions, this study aims to propose a novel dynamically adjusted proportional-integral (DAPI) run-to-run (R2R) controller to adapt equipment parameters to enhance the overlay control performance. This study evaluates the performance of controllers via the variation of each overlay factor and the variation of maximum overlay errors in real settings. To validate the effectiveness of the proposed approach, an empirical study was conducted in a leading semiconductor company in Taiwan and the results showed practical viability of the proposed DAPI controller to reduce overlay errors effectively than conventional exponentially weighted moving average controller used in this company.

This paper proposes the minimum-type piecewise-Lyapunov-function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie et al. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov functions as the Lyapunov function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov function as the Lyapunov function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.

This paper presents a polynomial fuzzy observer design for a wider class of polynomial fuzzy systems via a sum of squares (SOS, for brevity) approach. The proposed SOS-based framework provides a number of innovations and improvements over the existing LMI-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results for a class of polynomial fuzzy systems that is more general representation of the well-known T-S fuzzy system. Next, we propose a polynomial fuzzy observer to estimate states in a wider class of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions is that they realize the so-called separation principle, that is, that a polynomial fuzzy controller and observer for this class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state estimation error (via the observer) to zero. The design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recent developed SOSTOOLS and a semidefinite program (SDP) solver, respectively. To illustrate the validity and applicability of the proposed approach, a design example is provided. The example demonstrates advantages of the SOS-based approach for the existing LMI approaches to T-S fuzzy observer designs.

In this study, the conditions of fuzzy model based H∞stabilization are presented to stabilize the generalized Lorenz chaotic systems in finite time T and with pre-specified exponential convergence rate. Let the fuzzy state feedback controller be the form of parallel distributed compensation (PDC) and be designed to achieve the finite-time stability for the closed-loop system. The concept of Lyapunov theory, finite-time stability, H∞control and LMI-based approach are employed to derive the main result. Finally, the simulation results have been shown the validity of the proposed method.

Based on the piecewise Lyapunov function, this study proposes a switching fuzzy controller, which switches depending on the Lyapunov function, to get relaxed stabilization conditions for the continuous T-S fuzzy system. The relaxed conditions are bilinear with the s-procedure parameters, therefore the particle swarm optimization (PSO) algorithm is utilized with the LMI tool to solve the relaxed conditions. Two simulation examples are given to show the relaxation and effectiveness of the proposed method.

This paper studies the problem of guaranteed cost control for a Takagi-Sugeno (T-S) fuzzy system by descriptor system method. The redundancy property of a T-S descriptor system is utilized to simplify the control design issue. Furthermore, a linear quadratic cost function is considered as the performance index of the T-S fuzzy control system. According to the redundancy property, the control design of a descriptor system often leads to fewer stability conditions. Consequently, the T-S fuzzy system herein is presented as the descriptor system form. Then, the guaranteed cost fuzzy control for the descriptor subsystem is synthesized by parallel distributed compensation (PDC). Based on the Lyapunov stability criterion and linear matrix inequalities (LMIs) method, some sufficient conditions are derived to obtain the local state feedback gains of the PDC such that the whole fuzzy descriptor system is not only asymptotically stable but also cost guaranteed. Finally, a practical example is given to illustrate the effectiveness of the proposed criterion.

In this paper, two new relaxed stabilization criteria for discrete-time T-S fuzzy systems are proposed. In the beginning, the operation state space is divided into several subregions, and then, the T-S fuzzy system is transformed to an equivalent switching fuzzy system corresponding to each subregion. Consequently, based on the piecewise Lyapunov function, the stabilization criteria of the switching fuzzy system are derived. The criteria have two features: 1) the behavior of the two successive states of the system is considered in the inequalities and 2) the interactions among the fuzzy subsystems in each subregion Sj are presented by one matrix Xj. Due to the above two features, the feasible solutions of the inequalities in the criteria are much easier to be found. In other words, the criteria are much more relaxed than the existing criteria proposed in other literature. The proposed conditions in the criteria and the fuzzy control design can be solved and achieved by means of linear matrix inequality tools. Two examples are given to present the superiority of the proposed criteria and the effectiveness of the fuzzy controller's design, respectively.

The purpose of this paper deals with the decentralized stabilization problem for a large-scale system in which the system is composed of several T-S fuzzy subsystems with nonlinear interconnections. The decentralized parallel distributed compensation (PDC) fuzzy control in each subsystem is designed to stabilize the whole system. Based on Lyapunov criteria, the stabilization theorem is proposed. Moreover, in the theorem, the positive definite matrices Piand PDC gain Kilcan be obtained by linear matrix inequalities (LMI) toolbox of Matlab. Finally, we give a numerical example to illustrate the control design and effectiveness.

In this paper a new relaxed stabilization criterion for discrete-time T-S fuzzy systems are proposed. First the operation state space is divided into several subregions and then the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Consequently, based on the piecewise Lyapunov function, the stabilization criterion of the switching fuzzy system is derived. The main novelties of the criterion are as follows. (1) The positive definite matrix Plcorresponding to the subregion Siinstead of the traditional common P is found to satisfy the inequalities, (2) the successive two states of the system are considered in the inequalities. Due to the above two novelties, the criterion can be more relaxed. The proposed conditions in the criterion can be solved by means of linear matrix inequalities (LMIs) tools. An example is given to illustrate the advantage of the proposed criterion.