In this paper, we study the identification of two challenging benchmark problems using neural networks. Two different global optimization approaches are used to train a recurrent neural network to identify two challenging nonlinear models, the cascaded tanks, and the Bouc-Wen system. The first approach, quotient gradient system (QGS), uses the trajectories of the nonlinear dynamical system to find the local minima of the optimization problem. The second approach, dynamical trajectory-based methodology, uses two different nonlinear dynamical systems to find the connected components of the feasible region and then searches the regions for local minima of the optimization problem. Simulation results show that both approaches effectively identify the model of the cascade tanks and the Bouc-Wen model.

In this study we introduce a new approach to train a fully recurrent artificial neural network by solving a constraint satisfaction problem using the quotient gradient method. The quotient gradient method is a trajectory based methodology for global optimization that does not suffer from the problem of local minima encountered in Newton based methods. Simulation results show that the network trained with the quotient gradient method perform better than traditional error backpropagation. The method is also easier to implement in comparison to other global optimization techniques such as genetic algorithms.

Although many sufficient conditions for the stability of Takagi-Sugeno-Kang (TSK) fuzzy systems are known, no sufficient instability conditions are available. This paper introduces four sufficient instability tests for type-1 and type-2 TSK fuzzy systems. The first test is developed using a common Lyapunov function. The second test is derived using the Variable Gradient method. The third test is based on the comparison principle with a non-differentiable Lyapunov function candidate and the upper right hand derivative. Finally, the fourth test is obtained using Chetaev's theorem. We provide numerical examples to demonstrate and compare our instability testing.

We present a networked control system for nonlinear plants with unknown dynamics using a wavelet neural network (WNN) with feedforward component and generalized predictive controller (GPC). The WNN with feedforward term is used to adaptively model the nonlinear plant using its input and output history. The WNN uses the traditional back propagation algorithm and the feedforward term uses the recursive least-squares error algorithm for training. The model predictive controller predicts the optimal plant input in the presence of sensor and actuator delay. We apply our approach to the control of an unmanned autonomous vehicle and demonstrate its efficacy in the presence of fixed and random network delays. Simulation results show that adding the feedforward component to WNN drastically reduces the number of hidden layer nodes of the WNN and makes it more suited to online identification and control.

This paper proposes a new observer design methodology for type-1 and type-2 Takagi-Sugeno-Kang fuzzy systems. The design methodology does not require a common Lyapunov function and is, therefore, applicable to systems with nondetectable consequents. Our observers include fuzzy observers as well as constant gain observers. The observers are exponentially stable, and the designer can specify the rate of exponential convergence. The observer designs can be tested using linear matrix inequalities. The observers can be combined with a fuzzy controller for observer state feedback. The observer design methodology is demonstrated using the TORA system, and the observer state feedback is applied to the control of the inverted pendulum. The results show that the observer design provides good estimates of the state and can be used in a control system design even if the system has nondetectable consequents. Comparison to results from the literature shows that the new design can provide stable observer state feedback, where other observer designs fail.

Positive systems play an important role in many fields including biology, chemistry, and economics, among others. This paper discusses the stability of interval type-2 discrete-time positive Takagi-Sugeno-Kang (TSK) fuzzy systems. It discusses positive TSK systems and their nonzero equilibrium point. It then provides sufficient conditions for their exponential stability and instability. All the proposed stability and instability conditions can be tested using linear matrix inequalities. The stability and instability tests are demonstrated through application to a TSK model of the electric power market under a variety of market conditions.

This paper introduces a new stability test and control design methodology for type-1 and type-2 continuous-time (CT) Takagi-Sugeno-Kang systems. Unlike methods based on a common Lyapunov function, our stability results apply for systems with unstable consequents, and our controllers can be designed for systems with unstabilizable consequents. The stability results are derived using the comparison principle with a discontinuous function and the upper right-hand derivative. The control results include CT fuzzy proportional controllers and fuzzy proportional-integral controllers that can be obtained by solving linear matrix inequalities. We provide several examples to demonstrate our stability testing and controller design and compare our results to available methods in the literature. Our results compare favorably with results available in the literature and provide stability tests and controllers where earlier approaches fail.

A new method of speed sensorless instantaneous power control (IPC) of induction motor drives using an extended Kalman filter (EKF) is presented. The proposed algorithm is based on control of the flow of instantaneous real and reactive powers into the induction motor. The sensorless control method uses EKF-based speed estimation. Unlike the similar methods using the stator or rotor fluxes, the air gap flux is employed to calculate the reference powers needed for IPC. The effectiveness of the proposed control method was verified through computer simulations.

Fuzzy systems are excellent approximators of known functions or for the dynamic response of a physical system. We propose a new approach to approximate any known function by a Takagi-Sugeno-Kang fuzzy system with a guaranteed upper bound on the approximation error. The new approach is also used to approximately represent the behavior of a dynamic system from its input-output pairs using experimental data with known error bounds. We provide sufficient conditions for this class of fuzzy systems to be universal approximators with specified error bounds. The new conditions require a smaller number of membership functions than all previously published conditions. We illustrate the new results and compare them to published error bounds through numerical examples.

This paper introduces sufficient conditions for the exponential stability of type-1 and type-2 Takagi–Sugeno–Kang (TSK) fuzzy systems. A major advantage of the new conditions is that they do not require the existence of a common Lyapunov function and are, therefore, applicable to systems with unstable consequents. In addition, our results include two classes of type-2 TSK systems with type-1 consequents for which no stability tests are available. The use of the conditions in stability testing is demonstrated using simple numerical examples that include cases where methods that are based on a common Lyapunov function fail. The application of the stability test to develop new controller design methodologies is presented in a separate paper (i.e., Part II).

This paper proposes a new control system design methodology for type-1 and type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems that are based on new stability conditions. The stability conditions are discussed in a companion paper (Part I) and are used in the proofs of our main results. A major advantage of the new methodology is that it does not require a common Lyapunov function and is therefore applicable to systems with nonstabilizable consequents. Our controllers include fuzzy type-1 proportional and proportional-integral (PI) controllers, as well as constant state feedback for the same systems. The controller results in an exponentially stable system, and the designer can specify the rate of exponential convergence. The controller designs can be tested by the usage of linear matrix inequalities (LMIs). The design methodology is demonstrated by the usage of simple examples where methods that are based on a common Lyapunov function fail and physical systems where the new methodology provides better performance.

Type-2 fuzzy systems provide good models for uncertain fuzzy systems. This paper introduces three sufficient stability conditions for Takagi-Sugeno-Kang (TSK) type-2 fuzzy systems. The main advantage of the new conditions is that they do not require the existence of a common Lyapunov function and are therefore applicable to systems with unstable consequents. Conditions are derived for stability in the sense of Lyapunov and for asymptotic stability. The use of each condition in stability testing is demonstrated using simple numerical examples where methods based on a common Lyapunov function fail.

Automated control and management of large-scale physical systems is a challenging problem in a wide variety of applications including: power grids, transportation networks, and telecommunication networks. Such systems require (i) data collection, (ii) secure data transfer to processing centers, (iii) data processing, and (iv) timely decision making and control actions. These tasks are complicated by the vast amount of data, the distributed sources of data, and the need for efficient data communication. In addition, large physical systems are often subdivided into separately owned subsystems. This multi-owner structure imposes physical, economic, market, and political constraints on the data transfer. These divisions make systems vulnerable to potential coordinated attacks. Defending against such attacks requires the infrastructures to be more automated and self-healing. Motivated by the challenge of a more efficient, secure and robust power grid, which is less vulnerable to blackouts due to cascaded events, this paper discusses some of the fundamental problems in designing future cyber-physical systems.

We propose a new approach for the stability analysis of discrete Sugeno types II and III fuzzy systems. The approach does not require the existence of a common Lyapunov function. We introduce the concept of fuzzy positive definite and fuzzy negative definite functions. This new concept is used to replace classical positive and negative definite functions in arguments similar to those of traditional Lyapunov stability theory. We obtain the equivalent fuzzy system for a cascade of two Type II/III fuzzy systems. We use the cascade of a system and a fuzzy Lyapunov function candidate to derive new conditions for stability and asymptotic stability for discrete type II and type III fuzzy systems. To demonstrate the new approach, we apply it to numerical examples where no common Lyapunov function exists

We propose a new approach for the stability analysis of continuous Sugeno Types II and III dynamic fuzzy systems. We introduce the concept of fuzzy positive definite and fuzzy negative definite systems and use them in arguments similar to those of traditional Lyapunov stability theory to derive new conditions for stability and asymptotic stability for continuous Type II/III dynamic fuzzy systems. To demonstrate the new approach, we apply it to numerical examples.

Quality of service (QoS) in the Internet depends on queuing and sophisticated scheduling in routers. In this paper, we address the issue of managing traffic flows with different priorities. In our reference model, incoming packets are first classified based on their priority, placed into different queues with different capacities, and then multiplexed onto one router link. The fuzzy nature of the information on Internet traffic makes this problem particularly suited to fuzzy methodologies. We propose a new solution that employs a fuzzy inference system to dynamically and efficiently schedule these priority queues. The fuzzy rules are derived to minimize the selected Lyapunov function. Simulation experiments show that the proposed fuzzy scheduling algorithm outperforms the popular weighted round Robin (WRR) queue scheduling mechanism

Several approaches have appeared in the literature for the design of controller/observer combinations for Takagi-Sugeno-Kang (TSK) systems. These approaches did not exploit the fact that lower order systems can be obtained for estimating the control from output measurements. We propose a new approach for the feedback stabilization of TSK system using an observer of the control vector. We obtain stability conditions for the new observer/controller and show that it can provide a more efficient solution than the results published earlier. We demonstrate our results through a numerical example where the order of the observers with the functional observers if half that of the reduced order observers

We quantify why, as designers, we should prefer clique-based hypercubes (K-cubes) over traditional hypercubes based on cycles (C-cubes). Reaping fresh analytic results, we find that K-cubes minimize the wirecount and, simultaneously, the latency of hypercube architectures that tolerate failure of any f nodes. Refining the graph model of Hayes (1976), we pose the feasibility of configuration as a problem in multivariate optimization: What (f+1)-connected n-vertex graphs with fewest edges [n(f+1)/2] minimize the maximum a) radius or b) diameter of subgraphs (i.e., quorums) induced by deleting up to f vertices? We solve (1) for f that is superlogarithmic but sublinear in n and, in the process, prove: 1) the fault tolerance of K-cubes is proportionally greater than that of C-cubes; 2) quorums formed from K-cubes have a diameter that is asymptotically convergent to the Moore Bound on radius; 3) under any conditions of scaling, by contrast, C-cubes diverge from the Moore Bound. Thus, K-cubes are optimal, while C-cubes are suboptimal. Our exposition furthermore: 4) counterexamples, corrects, and generalizes a mistaken claim by Armstrong and Gray (1981) concerning binary cubes; 5) proves that K-cubes and certain of their quorums are the only graphs which can be labeled such that the edge distance between any two vertices equals the Hamming distance between their labels; and 6) extends our results to K-cube-connected cycles and edges. We illustrate and motivate our work with applications to the synthesis of multicomputer architectures for deep space missions.

We reduce stability robustness analysis for linear, time-invariant, discrete-time systems to a search problem and attack the problem using genetic algorithms. We describe the problem framework and the modifications that needed to be made to the canonical genetic algorithm for successful application to robustness analysis. Our results show that genetic algorithms can successfully test a sufficient condition for instability in uncertain linear systems with nonlinear polynomial structures. Three illustrative examples demonstrate the new approach.

This paper presents a method of nonlinear system identification using a new Gabor/Hopfield network. The network can identify nonlinear discrete-time models that are affine linear in the control. The system need not be asymptotically stable but must be bounded-input-bounded-output (BIBO) stable for the identification results to be valid in a large input-output range. The network is a considerable improvement over earlier work using Gabor basis functions (GBF's) with a back-propagation neural network. Properties of the Gabor model and guidelines for achieving a global error minimum are derived. The new network and its use in system identification are investigated through computer simulation. Practical problems such as local minima, the effects of input and initial conditions, the model sensitivity to noise, the sensitivity of the mean square error (MSE) to the number of basis functions and the order of approximation, and the choice of forcing function for training data generation are considered.

A modeling methodology that combines ideas from IDEF0 and from data flow and data structured system design is reported. The approach allows the development of hierarchical models for large-scale systems that can be used for documentation as well as for decision-making. The approach is described and applied to the modeling of a manufacturing system. With little modification, the methodology is also recommended for any large system whose structure and operation are not easily determined. Potential applications include biological, physiological, ecological and economic planning and general management systems.>

A class of large-scale decision systems is described, and a multilevel, multi-intelligence information/knowledge/control structure is defined. The description is in a form that features the various levels of signal processing, data fusion, autonomous fuzzy logic and pattern recognition (via neural networks), system knowledge base, and personal expert system, and the way in which these processors are integrated so as to form an operational model for the overall decision system.>

Recent research on fast exact maneuvering strategies for manipulators has employed acceleration commands as control variables. The forces and torques can then be synthesized, either in software or with dedicated hard-wired interfaces. Among the difficulties that occur when such maneuver techniques are employed is the fact that actuator saturation constraints are related to acceleration bounds in a state-dependent way. Recent work in the literature relies on generating a correction to the acceleration inputs, by pointwise constrained acceleration error minimization. This technique works best for infinite time horizons and highly coupled manipulator geometries, but not for terminal control or when the forces and torques enter the dynamics multiplied by a diagonal control influence matrix. An alternative technique discussed in the present paper consists of running actuators at saturation levels between sampling instants, then re-initializing an exact optimal regulator algorithm whenever the inputs drop below saturation range. Examples of such a maneuver strategy are given, both for asymptotic regulation and terminal control.