Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics

FTC Design for Switched Fractional-Order Nonlinear Systems: An Application in a Permanent Magnet Synchronous Motor System

In this article, an adaptive fault-tolerant control (FTC) method and a fractional-order dynamic surface control (DSC) algorithm are jointly proposed to deal with the stabilization problem for a class of multiple-input-multiple-output (MIMO) switched fractional-order nonlinear systems with actuator faults and arbitrary switching. In each MIMO subsystem and each switched subsystem, the neural networks (NNs) are utilized to identify the complicated unknown nonlinearities. A fractional filter DSC technology is adopted to conquer the issue of "explosion of complexity," which may occur when some functions are repeatedly derived. The common Lyapunov function method is used to restrain arbitrary switching problems in the system, and the actuator compensation technique is introduced to tackle the failure faults and bias faults in the actuators. By combining the backstepping DSC design technique and fractional-order stability theory, a novel NN adaptive switching FTC algorithm is proposed. Under the operation of the proposed algorithm, the stability and control performance of the fractional-order systems can be guaranteed. Finally, a simulation example of a permanent magnet synchronous motor (PMSM) system reveals the feasibility and effectiveness of the developed scheme.

Adaptive Optimized Backstepping Control-Based RL Algorithm for Stochastic Nonlinear Systems With State Constraints and Its Application

This article investigates the adaptive neural-network (NN) tracking optimal control problem for stochastic nonlinear systems, which contain state constraints and uncertain dynamics. First, to avoid the violation of state constraints in achieving optimal control, the novel barrier optimal performance index functions for subsystems are developed. Second, under the framework of the identifier-actor-critic, the virtual and actual optimal controllers are presented based on the backstepping technique, in which the unknown nonlinear dynamics are learned by the NN approximators. Moreover, the quartic barrier Lyapunov functions are constructed instead of square ones to cope with the Hessian term to ensure the stability of the systems with stochastic disturbance. The proposed optimal control strategy can guarantee the boundedness of closed-loop signals, and the output can follow the given reference signal. Meanwhile, the system states are restricted within some preselected compact sets all the while. Finally, both numerical and practical systems are carried out to further illustrate the validity of the proposed optimal control approach.

Dissipativity-Based Intermittent Fault Detection and Tolerant Control for Multiple Delayed Uncertain Switched Fuzzy Stochastic Systems With Unmeasurable Premise Variables

This study focuses on dissipativity-based fault detection for multiple delayed uncertain switched Takagi-Sugeno fuzzy stochastic systems with intermittent faults and unmeasurable premise variables. Nonlinear dynamics, exogenous disturbances, and measurement noise are also considered. In contrast to the existing study works, there is a wider range of applications. An observer is explored to detect faults. A controller is studied to stabilize the considered system. A piecewise fuzzy Lyapunov function is collected to obtain delay-dependent sufficient conditions by means of linear matrix inequalities. The designed observer has less conservatism. In addition, the strict [Formula: see text]dissipativity performance is achieved in the residual dynamic. Besides, the elaborate H_∞ performance and the elaborate H_ performance are also acquired. Finally, the availability of the method in this study is verified through two simulation examples.

Asynchronous Stabilization for Two Classes of Stochastic Switching Systems with Applications on Servo Motors

This paper addresses the asynchronous stabilization problem of two typical stochastic switching systems, i.e., dual switching systems and semi-Markov jump systems. By dual switching, it means that the systems contain both deterministic and stochastic switching dynamics. New stability criteria are firstly proposed for these two switched systems, which can well handle the asynchronous phenomenon. The conditional expectation of Lyapunov functions is allowed to increase during some unmatched interval to reduce the conservatism. Next, we present numerically testable asynchronous controller design methods for the dual switching systems. The proposed method is suitable for the situation where the asynchronous modes come from both inaccurate mode detection and time varying delay. Meanwhile, the transition probabilities are both uncertain and partly accessible. Finally, novel asynchronous controller design methods are proposed for the semi-Markov jump systems. The sojourn time of the semi-Markov jump systems can have both lower and upper bounds, which could be more practical than previous scenarios. Examples are utilized to demonstrate the effectiveness of the proposed methods.

Adaptive Neural Control for Switched Nonlinear Systems With Unstable Dynamic Uncertainties: A Small Gain-Based Approach

This article concentrates on the adaptive neural control for switched nonlinear systems interconnected with unmodeled dynamics. The investigated model consists of two dynamic processes, namely, the x -system and the unmodeled z -dynamics. In this article, we focus on a scenario that the unmodeled z -dynamics do not contain input-to-state practically stable (ISpS) modes, that is, all modes are not ISpS (non-ISpS). First, we design an adaptive neural controller such that each mode of the closed-loop x -system is ISpS with respect to the state of dynamic uncertainties. Then, fast average dwell time (fast ADT) and slow average dwell time (slow ADT) are simultaneously used to limit the switching law. In this way, both the closed-loop x -system and the unmodeled z -dynamics are ISpS under switching. By assigning the ISpS gains with small-gain theorem, we can guarantee that the whole closed-loop system is semiglobal uniformly ultimately bounded (SGUUB), and meanwhile, the system output is steered to a small region of zero. Finally, simulation examples are used to verify the effectiveness of the proposed control scheme.

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H_∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example.

Novel Data and Neural Network-Based Nonlinear Adaptive Switching Control Method

We propose an adaptive nonlinear control method for a discrete-time dynamical system. First, the nonlinear term is decomposed into a previous sampling instant term and an unknown increment term, which are determined using an intelligent estimation algorithm based on adaptive fuzzy neural networks. The problem of obtaining accurate input data due to the unknown current control signal in unmodeled dynamics using conventional estimation algorithms is addressed, and the conservativeness is reduced. Furthermore, historical data of the controlled plant are leveraged, and the data in the nonlinear term containing repeated estimation information are disregarded. Then, we apply the proposed decomposition method for the nonlinear term to design nonlinear switching controllers. One linear and two nonlinear adaptive controllers are designed, all with compensation of the nonlinear term at the previous sampling instant and increment estimation. These three adaptive controllers coordinately operate the plant by switching rules to guarantee the stability of the controlled plant and to improve the system performance. The stability and convergence of the system are analyzed and verified. Finally, simulation examples are used to verify the effectiveness of the proposed method and compare it with existing methods to confirm its superior performance.

Adaptive Neural Output-Feedback Controller Design of Switched Nonlower Triangular Nonlinear Systems With Time Delays

In this article, we study the issue of adaptive neural output-feedback controller design for a class of uncertain switched time-delay nonlinear systems with nonlower triangular structure. The prominent contribution of this article is that the delay-dependent stability criterion of nonswitched nonlinear systems is successfully extended to that of switched nonlower triangular nonlinear systems. The design algorithm is listed as follows. First, a switched state observer is designed such that the error dynamic system can be generated. Second, neural networks, adaptive backstepping technique, and variable separation method are, respectively, applied to construct a common controller for all subsystems, in which the Lyapunov-Krasovskii functionals are deliberately constructed such that the average dwell-time scheme can be employed to guarantee the stability and performance of the closed-loop system, despite the existence of time delays. Third, the stability analysis process confirms in detail that all the variables of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, simulation study is given to show the validity of the proposed control approach.

Barrier Lyapunov Function-Based Adaptive Fuzzy FTC for Switched Systems and Its Applications to Resistance-Inductance-Capacitance Circuit System

In this article, the adaptive fault-tolerant control (FTC) problem is solved for a switched resistance-inductance-capacitance (RLC) circuit system. Due to the existence of faults which may lead to instability of subsystems, the innovation of this article is that the unstable subsystems are taken into account in the frame of output constraint and unmeasurable states. Obviously, there are not any unstable subsystems in unswitched systems. The unstable subsystems will involve many serious consequences and difficulties. Since the system states are unavailable, a switched state observer is designed. In addition, the fuzzy-logic systems (FLSs) are employed to approximate unknown internal dynamics in the controller design procedure. Then, the barrier Lyapunov function (BLF) is exploited to guarantee that the system output satisfy its constrained interval. Moreover, by using the average dwell-time method, all signals in the resulting systems are proofed to be bounded even when faults occur. Finally, the proposed strategy is carried out on the switched RLC circuit system to show the effectiveness and practicability.

Stackelberg-Theoretic Approach for Performance Improvement in Fuzzy Systems

This paper investigates the robust control for dynamical systems subject to uncertainty. The uncertainty is assumed to be (possibly fast) time varying and bounded. The bound is unknown but lies within a prescribed fuzzy set (hence the fuzzy dynamical system). We propose an approach for the robust control design which is implemented in two steps. First, a class of robust controls is proposed based on tunable parameters. The proposed controls are deterministic and are not conventionally IF-THEN rules based. By the Lyapunov minimax approach, we prove that the proposed controls are able to guarantee deterministic system performance, namely, uniform boundedness and ultimate uniform boundedness. Second, optima seeking from the proposed controls is considered to improve fuzzy system performance. We formulate the optima-seeking problem as a two-player (one leader and one follower) Stackelberg game by developing two cost functions, each of which is in charge of one tunable parameter (i.e., the player). Each cost function consists of an average fuzzy system performance index and the associated player's control effort. We show that the solution of the optimal design problem (i.e., the optima of the tunable parameters), which is called the Stackelberg strategy, always exists and how to obtain the backwards-induction outcome is provided. Simulation results on the walking control of a biped robot model are presented for demonstration.

Adaptive Decentralized Controller Design for a Class of Switched Interconnected Nonlinear Systems

This paper is concerned with the switched decentralized adaptive control design problem for switched interconnected nonlinear systems under arbitrary switching, where the actuator failures may occur infinite times and the control directions are allowed to be unknown. By introducing a Nussbaum-type function and an integrable auxiliary signal, a switched decentralized adaptive control scheme is developed to deal with the potentially infinite times of actuator failures and the unknown control directions. The basic idea is to design different parameter update laws and control laws for distinct switched subsystems. It is proved that the state variables of the resulting closed-loop system are asymptotically stable. Finally, a numerical simulation on a double-inverted pendulum model is given to verify the proposed control scheme.

Adaptive Neural Fault-Tolerant Control for the Yaw Control of UAV Helicopters with Input Saturation and Full-State Constraints

In this paper, an adaptive neural fault-tolerant tracking control scheme is presented for the yaw control of an unmanned-aerial-vehicle helicopter. The scheme incorporates a non-affine nonlinear system that manages actuator faults, input saturation, full-state constraints, and external disturbances. Firstly, by using a Taylor series expansion technique, the non-affine nonlinear system is transformed into an affine-form expression to facilitate the desired control design. In comparison with previous techniques, the actuator efficiency is explicit. Then, a neural network is considered to approximate unknown nonlinear functions, and a time-varying barrier Lyapunov function is employed to prevent transgression of the full-state variables using a backstepping technique. Robust adaptive control laws are designed to handle parameter uncertainties and unknown bounded disturbances to cut down the number of learning parameters and simplify the computational burden. Moreover, an auxiliary system is constructed to guarantee the pitch angle of the UAV helicopter yaw control system to satisfy the input constraint. Uniform boundedness of all signals in a closed-loop system is ensured via Lyapunov theory; the tracking error converges to a small neighborhood near zero. Finally, when the numerical simulations are applied to a yaw control of helicopter, the adaptive neural controller demonstrates the effectiveness of the proposed technique.

Variable-Structure Near-Space Vehicles with Time-Varying State Constraints Attitude Control Based on Switched Nonlinear System

This study is concerned with the attitude control problem of variable-structure near-space vehicles (VSNSVs) with time-varying state constraints based on switched nonlinear system. The full states of vehicles are constrained in the bounded sets with asymmetric time-varying boundaries. Firstly, considering modeling uncertainties and external disturbances, an extended state observer (ESO), including two distinct linear regions, is proposed with the advantage of avoiding the peaking value problem. The disturbance observer is utilized to estimate the total disturbances of the attitude angle and angular rate subsystems, which are described in switched nonlinear systems. Then, based on the estimation values, the asymmetric time-varying barrier Lyapunov function (BLF) is employed to construct the active disturbance rejection controller, which can ensure the full state constraints are not violated. Furthermore, to resolve the 'explosion of complexity' problem in backstepping control, a modified dynamic surface control is proposed. Rigorous stability analysis is given to prove that all signals of the closed-loop system are bounded. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.

Adaptive Fuzzy Control of Stochastic Nonlinear Systems With Fuzzy Dead Zones and Unmodeled Dynamics

This paper focuses on an input-to-state practical stability problem for a class of stochastic nonlinear systems with unmodeled dynamics and fuzzy dead zones. A feasible adaptive fuzzy control method is proposed for the developed stochastic system with the slope of dead zone being certain or fuzzy. Based on stochastic small-gain theorem and backstepping technique, the closed-loop system is guaranteed to be input-state-practically stable in probability. The main contributions of this paper lie in that the considered system is more general, and the modified Lemma 2 makes the presentation of the formulas in lemma consistent with their application forms. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approach.

Linguistic Pythagorean Einstein Operators and Their Application to Decision Making

Linguistic Pythagorean fuzzy (LPF) set is an efficacious technique to comprehensively represent uncertain assessment information by combining the Pythagorean fuzzy numbers and linguistic variables. In this paper, we define several novel essential operations of LPF numbers based upon Einstein operations and discuss several relations between these operations. For solving the LPF numbers fusion problem, several LPF aggregation operators, including LPF Einstein weighted averaging (LPFEWA) operator, LPF Einstein weighted geometric (LPFEWG) operator and LPF Einstein hybrid operator, are propounded; the prominent characteristics of these operators are investigated as well. Furthermore, a multi-attribute group decision making (MAGDM) approach is presented on the basis of the developed operators under an LPF environment. Ultimately, two application cases are utilized to demonstrate the practicality and feasibility of the developed decision approach and the comparison analysis is provided to manifest the merits of it.

Adaptive Fuzzy Tracking Control for Strict-Feedback Markov Jumping Nonlinear Systems With Actuator Failures and Unmodeled Dynamics

In this paper, an adaptive fuzzy tracking controller is developed for a class of strict-feedback Markovian jumping systems subjected to multisource uncertainties. The unpredictable actuator failures, the unknown nonlinearities, and the unmodeled dynamics are simultaneously taken into consideration, which evolve according to the Markov chain. It is noted that the elements in the transition rate matrix of the Markov chain are not fully available. In virtue of the norm estimation approach, the challenges caused by the complex multiple uncertainties and actuator failures are effectively handled. Furthermore, to compensate for the unavailable switching nonlinearities, the fuzzy logic systems are employed as online approximators. As a result, a novel adaptive fuzzy fault-tolerant tracking control structure is constructed. The sufficient condition is provided to guarantee that the studied system is stochastically stable. Finally, a number of illustrative examples are employed to demonstrate the effectiveness of the proposed methodology.

Robust H∞ Adaptive Fuzzy Tracking Control for MIMO Nonlinear Stochastic Poisson Jump Diffusion Systems

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 multi-output (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 strict-feedback 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.

Neural Networks-Based Adaptive Finite-Time Fault-Tolerant Control for a Class of Strict-Feedback Switched Nonlinear Systems

This paper concentrates upon the problem of finite-time fault-tolerant control for a class of switched nonlinear systems in lower-triangular form under arbitrary switching signals. Both loss of effectiveness and bias fault in actuator are taken into account. The method developed extends the traditional finite-time convergence from nonswitched lower-triangular nonlinear systems to switched version by designing appropriate controller and adaptive laws. In contrast to the previous results, it is the first time to handle the fault tolerant problem for switched system while the finite-time stability is also necessary. Meanwhile, there exist unknown internal dynamics in the switched system, which are identified by the radial basis function neural networks. It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability. Finally, an illustrative simulation on a resistor-capacitor-inductor circuit is proposed to further demonstrate the effectiveness of the theoretical result.

Small-Gain Technique-Based Adaptive NN Control for Switched Pure-Feedback Nonlinear Systems

This paper focuses on the problem of adaptive neural networks (NNs) tracking control for a class of completely nonaffine switched pure-feedback uncertain nonlinear systems with switched reference model. A sufficient and necessary condition for the control problem to be solvable is derived by exploiting the common Lyapunov function (CLF) method, backstepping, input-to-state stability analysis, and the small-gain technique. Also, a small-gain technique-based adaptive NN control scheme is provided to avoid the designed difficulty caused by the construction of an overall CLF for the switched closed-loop system, which is usually required when studying the switched pure-feedback system. Adaptive NN controllers of individual subsystems are constructed to guarantee that all of the signals in the closed-loop system are semi-globally uniformly ultimately bounded under arbitrary switchings, and the tracking error converges to a small neighborhood of the origin. Two examples, which include a continuously stirred tank reactor system, are presented to demonstrate the effectiveness of the proposed design approach.

Adaptive Fuzzy Containment Control of Nonlinear Systems With Unmeasurable States

The adaptive fuzzy containment control problem is discussed for high-order systems with unknown nonlinear dynamics and unmeasurable states guided by multiple dynamic leaders. A high gain observer is introduced to reconstruct the system states. Then, utilizing fuzzy logic systems to model followers' dynamics, an observer-based adaptive fuzzy containment control approach is presented using only the relative position of the neighbors. It is shown that the uniformly ultimately bounded containment control is realized under the condition that, each follower can obtain the information from at least one leader through a directed path. As an extension, an observer-based containment control with prescribed performance is developed, which guarantees the relative position error to be bounded by a specified bound. The obtained theoretical results are validated by simulation examples.

Adaptive Neural Tracking Control of Switched Stochastic Pure-Feedback Nonlinear Systems With Unknown Bouc-Wen Hysteresis Input

This paper aims to analyze the problem of adaptive neural network (NN) tracking control for a class of switched stochastic nonlinear pure-feedback systems with unknown direction hysteresis. In the light of recent studies on the hysteresis phenomenon in the field of nonlinear switched systems, this paper focuses on Bouc-Wen hysteresis model with unknown parameters and direction conditions. To simplify the control design, the following procedure is applied. Prior to tackling the unknown direction hysteresis problem based on the Nussbaum function and the backstepping techniques, the pure-feedback structure difficulty is governed by the mean value theorem. Furthermore, an optimized adaptation method is utilized to cope with computational burden. Universal approximation capability of radial basis function NNs and Lyapunov function method is synthesized to develop an adaptive NN tracking control scheme. It is demonstrated that under arbitrary deterministic switching, the presented controller can guarantee that all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability and the tracking error converges to a neighborhood of the origin. Finally, two simulation examples are given to illustrate the advantages of the proposed control design approach.

Robust Adaptive Fuzzy Control of a Class of Uncertain Nonlinear Systems With Unstable Dynamics and Mismatched Disturbances

This paper studies the robust stabilization problem for a class of uncertain nonlinear systems with unstable zero dynamics. The considered zero dynamic is not assumed to be input-to-state practically stable and contains nonlinear uncertainties and mismatched external disturbances. A new robust adaptive fuzzy control method is developed by combining theory with backstepping technique. First, an ideal virtual control function is designed, which can guarantee the zero dynamic asymptotically stable with a suboptimal performance. Then, based on some non-negative functions and backstepping design, the actual controller is constructed for the overall system, which ensures that the tracking error for the ideal virtual control signal converges to a priori accuracy regardless of external disturbances. In this design, an auxiliary signal is introduced to overcome the difficulties from the unavailable virtual reference signal. By exploiting the implicit function theorem, the proposed design technique is directly applied to a special case, where the zero dynamic is partially linear. A two inverted pendulums is used to illustrate the application and effectiveness of the proposed design method.

Robust Fault Detection for Switched Fuzzy Systems With Unknown Input

This paper investigates the fault detection problem for a class of switched nonlinear systems in the T-S fuzzy framework. The unknown input is considered in the systems. A novel fault detection unknown input observer design method is proposed. Based on the proposed observer, the unknown input can be removed from the fault detection residual. The weighted performance level is considered to ensure the robustness. In addition, the weighted performance level is introduced, which can increase the sensibility of the proposed detection method. To verify the proposed scheme, a numerical simulation example and an electromechanical system simulation example are provided at the end of this paper.

Robust Fuzzy Adaptive Tracking Control for Nonaffine Stochastic Nonlinear Switching Systems

This paper is concerned with the trajectory tracking control problem of a class of nonaffine stochastic nonlinear switched systems with the nonlower triangular form under arbitrary switching. Fuzzy systems are employed to tackle the problem from packaged unknown nonlinearities, and the backstepping and robust adaptive control techniques are applied to design the controller by adopting the structural characteristics of fuzzy systems and the common Lyapunov function approach. By using Lyapunov stability theory, the semiglobally uniformly ultimate boundness in the fourth-moment of all closed-loop signals is guaranteed, and the system output is ensured to converge to a small neighborhood of the given trajectory. The main advantages of this paper lie in the fact that both the completely nonaffine form and nonlower triangular structure are taken into account for the controlled systems, and the increasing property of whole state functions is removed by using the structural characteristics of fuzzy systems. The developed control method is verified through a numerical example.

Stability Analysis of Genetic Regulatory Networks With Switching Parameters and Time Delays

This paper is concerned with the exponential stability analysis of genetic regulatory networks (GRNs) with switching parameters and time delays. In this paper, a new integral inequality and an improved reciprocally convex combination inequality are considered. By using the average dwell time approach together with a novel Lyapunov-Krasovskii functional, we derived some conditions to ensure the switched GRNs with switching parameters and time delays are exponentially stable. Finally, we give two numerical examples to clarify that our derived results are effective.

Adaptive Backstepping-Based Neural Tracking Control for MIMO Nonlinear Switched Systems Subject to Input Delays

This brief proposes a new neural-network (NN)-based adaptive output tracking control scheme for a class of disturbed multiple-input multiple-output uncertain nonlinear switched systems with input delays. By combining the universal approximation ability of radial basis function NNs and adaptive backstepping recursive design with an improved multiple Lyapunov function (MLF) scheme, a novel adaptive neural output tracking controller design method is presented for the switched system. The feature of the developed design is that different coordinate transformations are adopted to overcome the conservativeness caused by adopting a common coordinate transformation for all subsystems. It is shown that all the variables of the resulting closed-loop system are semiglobally uniformly ultimately bounded under a class of switching signals in the presence of MLF and that the system output can follow the desired reference signal. To demonstrate the practicability of the obtained result, an adaptive neural output tracking controller is designed for a mass-spring-damper system.

Adaptive Fuzzy Output Constrained Control Design for Multi-Input Multioutput Stochastic Nonstrict-Feedback Nonlinear Systems

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Adaptive Neural Tracking Control for Switched High-Order Stochastic Nonlinear Systems

This paper deals with adaptive neural tracking control design for a class of switched high-order stochastic nonlinear systems with unknown uncertainties and arbitrary deterministic switching. The considered issues are: 1) completely unknown uncertainties; 2) stochastic disturbances; and 3) high-order nonstrict-feedback system structure. The considered mathematical models can represent many practical systems in the actual engineering. By adopting the approximation ability of neural networks, common stochastic Lyapunov function method together with adding an improved power integrator technique, an adaptive state feedback controller with multiple adaptive laws is systematically designed for the systems. Subsequently, a controller with only two adaptive laws is proposed to solve the problem of over parameterization. Under the designed controllers, all the signals in the closed-loop system are bounded-input bounded-output stable in probability, and the system output can almost surely track the target trajectory within a specified bounded error. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input

In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.

A Many-Objective Evolutionary Algorithm Using A One-by-One Selection Strategy

Most existing multiobjective evolutionary algorithms experience difficulties in solving many-objective optimization problems due to their incapability to balance convergence and diversity in the high-dimensional objective space. In this paper, we propose a novel many-objective evolutionary algorithm using a one-by-one selection strategy. The main idea is that in the environmental selection, offspring individuals are selected one by one based on a computationally efficient convergence indicator to increase the selection pressure toward the Pareto optimal front. In the one-by-one selection, once an individual is selected, its neighbors are de-emphasized using a niche technique to guarantee the diversity of the population, in which the similarity between individuals is evaluated by means of a distribution indicator. In addition, different methods for calculating the convergence indicator are examined and an angle-based similarity measure is adopted for effective evaluations of the distribution of solutions in the high-dimensional objective space. Moreover, corner solutions are utilized to enhance the spread of the solutions and to deal with scaled optimization problems. The proposed algorithm is empirically compared with eight state-of-the-art many-objective evolutionary algorithms on 80 instances of 16 benchmark problems. The comparative results demonstrate that the overall performance of the proposed algorithm is superior to the compared algorithms on the optimization problems studied in this paper.

Observer-Based Output-Feedback Asynchronous Control for Switched Fuzzy Systems

This paper investigates an output-feedback control design problem for a class of switched continuous-time Takagi-Sugeno (T-S) fuzzy systems. The considered fuzzy systems consist of several switching modes and each switching mode is described by T-S fuzzy models. In addition, there exists the asynchronous switching between the system switching modes and the controller switching modes. By using parallel distributed compensation design method, the output-feedback control schemes are developed based on state observers for the measurable and immeasurable premise variables cases. The sufficient conditions of ensuring the switched control system stabilization are proposed based on the theory of Lyapunov stability and average-dwell time methods. The controller and observer gains are obtained via two-step method. An illustrated numerical example is provided to show the effectiveness of the proposed control approaches.

Reliable Output Feedback Control for T-S Fuzzy Systems With Decentralized Event Triggering Communication and Actuator Failures

Due to the unavailability of full state variables in many control systems, this paper is concerned with the design of reliable observer-based output feedback controller for a class of network-based Takagi-Sugeno fuzzy systems with actuator failures. In order to better allocate network resources under the case that the sensor nodes are physically distributed, the decentralized event triggering communication scheme is adopted such that each sensor node is capable to determine the transmission of its local measurement information independently. Considering that the implementation of the controller may not be synchronized with the plant trajectories due to asynchronous premise variables with such communication mechanism, a novel piecewise fuzzy observer-based output feedback controller is developed. By applying a piecewise Lyapunov function and some techniques on matrix convexification, an approach to the design of observer and controller gain is derived for the augmented closed-loop system to be asymptotically stable with a guaranteed H_∞ performance and reduced transmission frequency. Finally, two examples are given to show the effectiveness of the developed method.

Observer-Based Fuzzy Adaptive Output-Feedback Control of Stochastic Nonlinear Multiple Time-Delay Systems

This paper is concerned with the observer-based fuzzy output-feedback control for stochastic nonlinear multiple time-delay systems. On the basis of the consistent form of virtual input signals and increasing characteristics of the system upper bound functions, a variable splitting technique is employed to surmount the difficulty occurred in the nonlower-triangular form. In the controller design procedure, a state observer is first designed, and then an adaptive fuzzy output-feedback control method is presented by combining backstepping design together with fuzzy systems' universal approximation capability. The proposed adaptive controller guarantees the semi-global boundedness of closed-loop system trajectories in terms of fourth-moment. Two simulation examples are displayed to demonstrate the feasibility of the suggested controller.

Observer-Based Non-PDC Control for Networked T-S Fuzzy Systems With an Event-Triggered Communication

This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi-Sugeno (T-S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions. First, a unified event-triggered T-S fuzzy model is provided, in which: 1) a fuzzy observer with the imperfect premise matching is constructed to estimate the unmeasurable states of the studied system; 2) a fuzzy controller is designed following the same premise as the observer; and 3) an output-based event-triggering transmission scheme is designed to economize the restricted network resources. Different from the traditional PDC method, the synchronous premise between the fuzzy observer and the T-S fuzzy system are no longer needed in this paper. Second, by use of Lyapunov theory, a stability criterion and a stabilization condition are obtained for ensuring asymptotically stable of the studied system. On account of the imperfect premise matching conditions are well considered in the derivation of the above criteria, less conservation can be expected to enhance the design flexibility. Compared with some existing emulation-based methods, the controller gains are no longer required to be known a priori. Finally, the availability of proposed non-PDC design scheme is illustrated by the backing-up control of a truck-trailer system.

Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

Adaptive Fuzzy Output-Feedback Stabilization Control for a Class of Switched Nonstrict-Feedback Nonlinear Systems

This paper proposes an fuzzy adaptive output-feedback stabilization control method for nonstrict feedback uncertain switched nonlinear systems. The controlled system contains unmeasured states and unknown nonlinearities. First, a switched state observer is constructed in order to estimate the unmeasured states. Second, a variable separation approach is introduced to solve the problem of nonstrict feedback. Third, fuzzy logic systems are utilized to identify the unknown uncertainties, and an adaptive fuzzy output feedback stabilization controller is set up by exploiting the backstepping design principle. At last, by applying the average dwell time method and Lyapunov stability theory, it is proven that all the signals in the closed-loop switched system are bounded, and the system output converges to a small neighborhood of the origin. Two examples are given to further show the effectiveness of the proposed switched control approach.

Performance-Based Adaptive Fuzzy Tracking Control for Networked Industrial Processes

In this paper, the performance-based control design problem for double-layer networked industrial processes is investigated. At the device layer, the prescribed performance functions are first given to describe the output tracking performance, and then by using backstepping technique, new adaptive fuzzy controllers are designed to guarantee the tracking performance under the effects of input dead-zone and the constraint of prescribed tracking performance functions. At operation layer, by considering the stochastic disturbance, actual index value, target index value, and index prediction simultaneously, an adaptive inverse optimal controller in discrete-time form is designed to optimize the overall performance and stabilize the overall nonlinear system. Finally, a simulation example of continuous stirred tank reactor system is presented to show the effectiveness of the proposed control method.

Robust finite-time event-triggered H∞ boundedness for network-based Markovian jump nonlinear systems

This paper investigates the problem of finite-time event-triggered H∞ boundedness for network-based Markovian jump nonlinear system. An improved model is introduced in terms of network-induced delay. By synthesizing the newly event-triggering conditions, the finite-time H∞ boundedness for networked Markovian jump nonlinear systems are guaranteed. At last, a numerical example is given to illustrate the effectiveness of proposed theoretical results.