Nonlinear Switched Systems Research Articles

Passivity-Based Adaptive Fuzzy Control for Stochastic Nonlinear Switched Systems via T–S Fuzzy Modeling

In this paper, state-estimator-based adaptive control is under consideration for a sort of nonlinear stochastic switched systems by Takagi-Sugeno (T-S) fuzzy modeling and sliding mode technique. A new fuzzy sliding surface is established by a reformed state estimator, and a novel adaptive fuzzy reaching motion controller synthesis is carried out to force the state trajectories onto the designated sliding surface in limited moments. A new mean-square exponential stability of the resultant plant with passivity is ensured under the average dwell time method and stochastic stability theory. The key challenge overcome here is that one conditional assumption involved in the previous sliding mode control-based strategies for the considered systems is no longer required despite the unavailable states, unknown perturbations and specified switching signal. At last, a practical data communication network model (DCNM) with simulation is offered to verify the feasibility of the theoretical result.

Nussbaum‐based robust adaptive control for nonlinear switching systems with switching unknown control coefficients

AbstractThis paper develops a robust adaptive dynamic surface control (DSC) design approach for switching strict feedback nonlinear systems with multiple switching control gains and unknown control directions. To capture the multiple unknown control directions, we design multiple Nussbaum‐type gains for every subsystem. Based on this Nussbaum‐type gain design, we construct a common Lyapunov function for all subsystems via backstepping technique, which can ensure the system stability under the existence of random switches. Meanwhile, the problem of multiple switching control gains is resolved by this means. To obviate repeated differentiation and decrease computation complexity, the dynamic surface control technique is introduced. Finally, two simulation examples are provided to validate the effectiveness of the developed method.

SMC for Discrete-Time Nonlinear Semi-Markovian Switching Systems With Partly Unknown Semi-Markov Kernel

This article is devoted to the discrete-time sliding mode control (DSMC) for nonlinear semi-Markovian switching systems (S-MSSs). Motivated by the fact that the complete information of the semi-Markov Kernel is difficult to be obtained in practical applications, it is recognized to be partly unknown as the most common mean. By utilizing the prior information of the sojourn-time upper bound for each switching mode, sufficient conditions under the equivalent DSMC law are proposed for the mean square stability. Moreover, the designed DSMC law realizes the finite-time reachability of the sliding region, and makes the sliding dynamics converge to the predesignated sliding region in a finite time. In the end, a numerical example and an electronic throttle model are given to validate the proposed control strategy.

Adaptive fuzzy fixed‐time control for non‐triangular structural stochastic switching nonlinear systems

AbstractIn this article, the problem of adaptive fixed‐time tracking control is addressed for non‐triangular structural stochastic switching nonlinear systems. Fuzzy logic systems are used to compensate for unknown nonlinearities, and in the meantime, to avoid the algebraic loop problem, which exists in traditional backstepping controller design processes for non‐triangular structural nonlinear systems. The unknown control gain problem is addressed by the construction of proper Lyapunov function candidates. By employing Lyapunov stability theorem, all the closed‐loop signals can be ensured to be semi‐globally practical fixed‐time stable, the output signal can track the desired signal, and the tracking error can converge to a small zone around the origin. The effectiveness of the developed control approach is verified through simulation results.

Adaptive Event-Triggered Neural Network Control for Switching Nonlinear Systems With Time Delays.

The adaptive event-triggered-based neural network control is explored for switching nonlinear systems with nonstrict-feedback structure and time-varying delays in this article. First, the switching observer is designed to estimate the unmeasurable states. Due to the existence of time-varying input delay, a compensation system is introduced. The average dwell-time (ADT) scheme and the event-triggered controller are established. Furthermore, the semiglobal uniform ultimate boundedness (SGUUB) of all the variables in the closed-loop system is achieved and the Zeno behavior is avoided. Finally, the numerical simulation shows that our proposed control approach is effective.

Dynamic Event-triggered Adaptive Control for Uncertain Nonlinear Switched Systems Based on MDADT Method

Dynamic Event-triggered Adaptive Control for Uncertain Nonlinear Switched Systems Based on MDADT Method

Stability Analysis of Impulsive Switched Nonlinear Systems With Double State-Dependent Delays

This brief addresses the problem of global asymptotic stability for impulsive switched nonlinear systems (ISNSs) with double state-dependent delays (DSDDs), where the state-dependent delays exist in both subsystem functions and impulsive functions. The innovations of our results are that: 1) Due to the ubiquitous asynchronous phenomenon between the switches and impulses in many practical systems, we investigate the asynchronous phenomenon for ISNSs with DSDDs. 2) Meanwhile, the stabilizing and destabilizing effects of state-dependent delays impulses are fully considered. 3) By utilizing multiple Lyapunov functions, the switching strategy and the impulsive strategy, based on the asynchronous phenomenon, some stability criteria on global asymptotic stability are presented for ISNSs with DSDDs. As a result, the existing results are improved and can be regarded as a special case of the stability criteria in this brief. A simulation example is provided to verify the effectiveness of the developed methods.

Adaptive Tracking for Uncertain Switched Nonlinear Systems With Prescribed Performance Under Slow Switching

This article considers the problem of adaptive prescribed performance tracking control via slow switching for a general class of uncertain switched nonlinear systems (SNSs) with unmodeled dynamics (UDs) and nonstrict-feedback structure. The UDs are not in their form of the input-to-state practical stability and their state information is unmeasurable. By reassigning the function variables, the coupling effects between UDs and the prescribed performance function are eliminated through the iterative process. In virtue of the neural networks (NNs) approximation capability, a novel adaptive backstepping procedure is proposed without adding extra first-order filters. By choosing an appropriate slow switching law, all the signals of the closed-loop system are bounded, and the system output tracks the reference signal with a prescribed performance level (PPL).

Sigmoid Function Model and Dynamic Characteristics Analysis for Inductive Wireless Power Transmission Control System

In this article, an inductive wireless power transmission (IWPT) system is a high-order nonlinear switching system with multiple operating modes. It is challenging to analyze the dynamic characteristics of such a system using the extended describing function, generalized state-space averaging, or other existing modeling methods. To address this challenge, this study proposes a modeling and dynamic characteristics analysis method for a closed-loop IWPT control system based on a sigmoid function model. A sigmoid function with a large steepness factor is adopted to approximate the switching process of the switch and a unified smooth continuous dynamic model is established for a phase-shift controlled IWPT system. Because this model is infinitely differentiable, a stability theory of continuous systems, such as the Floquet theory, can be directly applied to analyze the bifurcation type of the system and stability of periodic solutions. Analysis results reveal the transition of the phase-shift-controlled IWPT system from periodic behavior to chaotic behavior through saddle-node bifurcation and Neimark–Sacker bifurcation. A stable domain in the two-parameter space of the controller proportional coefficient and load is also obtained. Both simulation and experimental results validate the accuracy of the proposed model and theoretical analysis method, which can significantly reduce the difficulty of analyzing IWPT system dynamics.

Adaptive neural network control for uncertain dual switching nonlinear systems

Dual switching system is a special hybrid system that contains both deterministic and stochastic switching subsystems. Due to its complex switching mechanism, few studies have been conducted for dual switching systems, especially for systems with uncertainty. Usually, the stochastic subsystems are described as Markov jump systems. Based upon the upstanding identity of RBF neural network on approaching nonlinear data, the tracking models for uncertain subsystems are constructed and the neural network adaptive controller is designed. The global asymptotic stability almost surely (GAS a.s.) and almost surely exponential stability (ES a.s.) of dual switching nonlinear error systems are investigated by using the energy attenuation theory and Lyapunov function method. An uncertain dual switching system with two subsystems, each with two modes, is studied. The uncertain functions of the subsystems are approximated well, and the approximation error is controlled to be below 0.05. Under the control of the designed adaptive controller and switching rules, the error system can obtain a good convergence rate. The tracking error is quite small compared with the original uncertain dual switching system.

Quantized asynchronous extended dissipative observer-based sliding mode control for Markovian jump TS fuzzy systems

This article is dedicated to the issue of asynchronous adaptive observer-based sliding mode control for a class of nonlinear stochastic switching systems with Markovian switching. The system under examination is subject to matched uncertainties, external disturbances, and quantized outputs and is described by a TS fuzzy stochastic switching model with a Markovian process. A quantized sliding mode observer is designed, as are two modes-dependent fuzzy switching surfaces for the error and estimated systems, based on a mode dependent logarithmic quantizer. The Lyapunov approach is employed to establish sufficient conditions for sliding mode dynamics to be robust mean square stable with extended dissipativity. Moreover, with the decoupling matrix procedure, a new linear matrix inequality-based criterion is investigated to synthesize the controller and observer gains. The adaptive control technique is used to synthesize asynchronous sliding mode controllers for error and SMO systems, respectively, so as to ensure that the pre-designed sliding surfaces can be reached, and the closed-loop system can perform robustly despite uncertainties and signal quantization error.Finally, simulation results on a one-link arm robot system are provided to show potential applications as well as validate the effectiveness of the proposed scheme.

Finite-Time Stability of Switched Nonlinear Systems With State Jumps: A Dwell-Time Method

This article investigates the finite-time stability (FTS) of switched nonlinear systems (SNSs) with state jumps. Our main concerns are twofold. One is that the SNS only consists of FTS subsystems. The other is that the SNS has both FTS subsystems and exponentially stable (ES) subsystems. Due to the switches and state jumps, the main challenge of the study comes from the estimation of settling time and the synthesis of different Lyapunov functions for FTS/ES subsystems. Based on the analytical-inductive method and the initial-value-dependent dwell-time approach, several FTS criteria for the SNSs are established. Then, we provide the estimation of settling time which is explicitly dependent on the dwell time and initial value. Our results can be applied to the finite-time control problem of switched systems with/without state jumps, even when some subsystems can only be exponentially stabilized through linear feedback control and others are finite-time stabilized by discontinuous/nonlinear controls. Finally, three examples are given to illustrate the proposed results. The finite-time stabilization of a continuous stirred tank reactor and the finite-time consensus of a multiagent system are both adopted as potential applications.

Hybrid Q-learning for data-based optimal control of non-linear switching system

In this paper, the optimal control of non-linear switching system is investigated without knowing the system dynamics. First, the Hamilton-Jacobi-Bellman (HJB) equation is derived with the consideration of hybrid action space. Then, a novel data-based hybrid Q-Iearning (HQL) algorithm is proposed to find the optimal solution in an iterative manner. In addition, the theoretical analysis is provided to illustrate the convergence and optimality of the proposed algorithm. Finally, the algorithm is implemented with the actor-critic (AC) structure, and two linear-in-parameter neural networks are utilized to approximate the functions. Simulation results validate the effectiveness of the data-driven method.

Non-fragile Robust Stabilization of Nonlinear Uncertain Switched Systems with Actuator Saturation

Non-fragile Robust Stabilization of Nonlinear Uncertain Switched Systems with Actuator Saturation

Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application.

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

Adaptive Event-Triggered Output Feedback Control for Nonlinear Switched Systems Based on Full State Constraints

Aiming at the research content of tracking control for a class of nonlinear uncertain switched systems including full state constraints, a novel event-triggered adaptive fuzzy output feedback control scheme is given. The systems studied need to use the approximation principle of fuzzy logic systems (FLSs) to solve the nonlinear smooth function with unknown terms. For ensuring that all states of the systems are within the time-varying constraint limits, the stability of the switched systems is verified by utilizing tangent barrier Lyapunov function (Tan-BLF). Based on the potential barrier Lyapunov function (BLF) and backstepping recursive construction method, the adaptive law, controller and event-triggered mechanism of the subsystem are designed. The proposed method will make that the signal is bounded. Moreover, the tracking error can be adjusted to the neighborhood closed to the origin. Simulation examples indicate the feasibility of the method.

Intelligent Control of Performance Constrained Switched Nonlinear Systems With Random Noises and Its Application: An Event-Driven Approach

In this paper, the adaptive fuzzy control of switched stochastic nonlinear systems with set-time prescribed performance based on event-driven mechanism is studied. The creative part of this paper is that based on the set-time performance function, a modified event-triggered strategy that considers asynchronous switching to deteriorate system performance without strict assumptions is presented, which avoids Zeno behavior and saves communication resources. Then, by using backstepping recursive design technique, It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat {o}$ </tex-math></inline-formula> ’s differential lemma and mode-dependent average dwell time (MDADT) method, a novel adaptive performance control scheme is proposed, which can ensure that all the variables in the system are semiglobally uniformly ultimately bounded (SGUUB) in probability and the tracking error gets into prescribed boundary no later than an arbitrarily adjusted setting time. Finally, the proposed algorithm is applied to a RLC circuit and its practicability is verified via simulation results.

Input–Output Finite-Time Asynchronous SMC for Nonlinear Semi-Markov Switching Systems With Application

This article investigates the input–output finite-time stability (IO-FTS) for nonlinear hidden semi-Markov switching systems (S-MSSs) via the asynchronous sliding mode control (SMC) approach. Under the assumption that a detector is set up to estimate the mode value, the mode of the original system is not directly accessible. The asynchrony between the system and controller is described as a hidden semi-Markov model (HSMM). Many practical factors, such as semi-Markov switching parameters, finite-time interval, asynchronous phenomenon, uncertain parameters, and nonlinearity, are taking into account during the SMC design process. We aim to design an efficient finite-time asynchronous SMC scheme under a hidden semi-Markov switching effect. A novel sliding switching surface (SSS) is constructed, in which the SMC law rises asynchronously with original S-MSSs. Then, by means of finite-time stability, an asynchronous SMC law is synthesized to guarantee that the associated hidden S-MSSs fulfill the reaching condition within a finite time. Furthermore, sufficient conditions are derived in view of the IO-FTS of sliding mode dynamics under the framework of a novel inequality lemma. Results are given for the application of this control design method to a single-link robot arm model (SLRAM).

Stability Analysis of Switched Nonlinear Systems With Multiple Time-Varying Delays

This article addresses the stability problem of switched nonlinear systems (SNSs) with multiple time-varying delays (MTVDs) whose subsystems are all unstable. By utilizing a multiple Lyapunov&#x2013;Krasovskii functionals technique, some stability criteria for SNSs with MTVDs are obtained. To tackle the challenge of finding appropriate Lyapunov functions, we introduce Takagi and Sugeno (T&#x2013;S) fuzzy models and present stability criteria for switched T&#x2013;S fuzzy systems with MTVDs. Moreover, a novel switching signal is developed to eliminate the effect of the increment energy of Lyapunov functions for all unstable modes. The upshots of our result are that: 1) it allows the upper bound of the derivatives of Lyapunov functionals to be mode-dependent functions which can be positive or negative and 2) it also improves upon the existing results by removing several restrictive conditions. Finally, the effectiveness of our method is validated through numerical simulations.

Stability Analysis and Trajectory Design of a Nonlinear Switching System for Speed Sensorless Induction Motor Drive

For wide-speed range operation of speed sensorless induction motor drives (SSIMD), the stable operation at low synchronous speed range (including zero synchronous speed) is a great challenge. Virtual voltage injection method is found efficient to overcome this challenge. However, the injected virtual voltage into observer results in the estimated speed error, it is reasonable to rely upon this method only when the performance of traditional SSIMD is poor, i.e., at low speed range. At middle and high speed ranges, virtual voltage injection method cannot meet the high-accuracy requirement of speed estimation in industrial application. For wide-speed range operation of SSIMD, a necessary switching system is proposed in this article to meet the stability requirement and accuracy requirement at the same time. The input-state stability theory is adopted to verify the stability of switching method, because the switching system is a nonlinear and strong coupling system. Then the switching trajectory is optimized for smooth and fast switching transition. Finally, the effectiveness and feasibility of the proposed method are verified by experimental results.