Nonlinear Switched Systems Research Articles

Dynamic self-triggered protocol for Takagi-Sugeno fuzzy positive Markov switching systems

This study analyzes a novel dynamic self-triggered protocol for positive nonlinear stochastic switching systems, which integrates diverse key elements encompassing Markov switching parameters, Takagi-Sugeno (T-S) fuzzy, and positivity. The performance evaluation of T-S fuzzy positive Markov switching systems is conducted via a self-triggered mechanism relying solely on historical data for determining subsequent executions, thereby eliminating the requirement of continuous monitoring. A dynamic self-triggered mechanism is introduced with adjustable thresholds to further reduce the conservation of communication resources. By utilizing matrix decomposition technique and implementing an innovative optimization approach distinct from traditional linear matrix inequality method, the positivity and stochastic stability of the system are attained. The achieved results are validated through the Lotka-Volterra model.

Stability analysis and stabilization of discrete-time switched nonlinear systems with mode-dependent average dwell time under nested actuator saturation

In this paper, the stability analysis and stabilization of a class of mode-dependent mean residence time-based discrete-time switching nonlinear systems are addressed. More specifically, under the mode-dependent average dwell time (MDADT) switching mode, combined with the practical problem, the nonlinear factor of nested actuator saturation (NAS) is introduced. Firstly, in order to ensure the system stability, based on the parameter-dependent discontinuous switching Lyapunov function and several basic lemmas, a state feedback controller is designed that makes the closed-loop system (CLS) achieve local exponential stability (LES) by solving the optimal problem in terms of linear matrix inequalities (LMIs). Secondly, the system considers the maximum attraction domain that can be achieved by the NAS system under the conditions. The simulation results show the effectiveness of the proposed design method. At the same time, the efficiency of the proposed method is verified via a water tank example.

Hybrid Intelligent Optimization of Nonlinear Switched Systems With Guaranteed Feasibility

Hybrid Intelligent Optimization of Nonlinear Switched Systems With Guaranteed Feasibility

Event‐triggered adaptive neural network‐based optimal control of strictly feedback switched nonlinear systems with state constraints

AbstractIn this article, we present an innovative approach for controlling nonlinear switched systems (NSSs) with strict feedback utilizing adaptive neural networks (ANNs). Our methodology encompasses several facets, addressing key challenges inherent to these systems. To commence, we tackle the constrained nature of NSSs with strict feedback by designing a barrier Lyapunov function. This function ensures that all states within the switched systems remain within prescribed constraints. Additionally, we harness neural networks (NNs) to approximate the unknown nonlinear functions inherent to the system. Furthermore, we deploy an ANN state observer to estimate unmeasurable states. Our approach then proceeds to develop a cost function for the subsystem. Building upon this, we apply the Hamiltonian–Jacobi–Bellman (HJB) solution in conjunction with observer and behavior critic architectures, all rooted in backstepping control (BC) principles. This integration yields both a virtual optimal controller and a real optimal controller. Furthermore, we introduce a novel ANN event‐triggered control (ETC) strategy tailored explicitly for strictly feedback systems. This strategy proves highly effective in reducing the utilization of communication resources and eliminating the occurrence of Zeno behavior. Our analysis provides formal proof that all states within the closed‐loop system exhibit half‐leaf consistency and are ultimately bounded, regardless of arbitrary switching conditions. Finally, we substantiate the efficacy and viability of our control scheme through comprehensive numerical simulations.

Exponential Stability of Impulsive Switched Nonlinear Systems With Partial Unmeasurable States on Time Scales

Abstract This paper investigates the stability of a class of partially unmeasurable nonlinear impulsive switched dynamical systems on time scales. It provides sufficient conditions for ensuring exponential stability of impulsive switched systems in hybrid time domains using Gronwall's inequality, dimensionality reduction technique, and time scale theory. These conditions apply to systems where nonlinearities affect both continuous and discrete subsystems. Stable strategies involving partial unmeasurable states are obtained. Furthermore, the proposed results allow the switched system to have incomplete measurable states. The effectiveness of these results is demonstrated by several examples, which are accompanied by simulations for comparison.

Distributed Adaptive Secure Consensus Tracking Control for Asynchronous Switching Nonlinear MASs Under Sensor Attacks and Actuator Faults

A distributed adaptive secure control algorithm is proposed for asynchronous switching nonlinear multi-agent systems (MASs) in pure-feedback form while considering the sensor attacks and actuator faults, which eliminates the effect of attack signals, actuator faults and uncertainties without knowing the sign of the control gain functions. Since the system states measured by the sensors are corrupted by the malicious attacker, only the post-attack system states can be obtained. Thus, an improved coordinate transformation is constructed by using the post-attack system states and a backstepping method based on the improved coordinate transformation is developed to solve the consensus tracking control problem of the researched systems under sensor attacks. The common Lyapunov function is designed to ensure the stability of all asynchronous switching subsystems of each agent. In the end, a simulation example is presented to illustrate the theoretical results’ validity. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper deal with the distributed adaptive secure consensus tracking control problem for asynchronous switching nonlinear MASs, whose models can describe many phenomena in nature such as biological processes, robot team formation and sensor networks. It is extremely challenging to achieve the tracking control problem of the researched asynchronous switching nonlinear system in an unsafe network environment, where the unknown sensor attacks signals, actuator faults coefficients, and randomly switched non-affine nonlinearities exist together for the followers. Furthermore, the control design and stability analysis of the researched system is based on the common Lyapunov approach, which makes the developed approach more engineering oriented.

Master–Slave Synchronization of Switched Nonlinear Systems Based on Quantization and Switching Event-Triggered Strategy

Master–Slave Synchronization of Switched Nonlinear Systems Based on Quantization and Switching Event-Triggered Strategy

Robust Fault-tolerant Control with Dynamic Event-triggered Mechanism Based on Observer for Nonlinear Switched Systems

Robust Fault-tolerant Control with Dynamic Event-triggered Mechanism Based on Observer for Nonlinear Switched Systems

Characterizations and Stability Criteria for the 2-Mode Markovian Switched Nonlinear Systems

Characterizations and Stability Criteria for the 2-Mode Markovian Switched Nonlinear Systems

Design of a Novel Switched State Observer for Lipschitz Nonlinear Switched Systems with Finite-Time Boundedness Concept and Application to CSTR Systems

Design of a Novel Switched State Observer for Lipschitz Nonlinear Switched Systems with Finite-Time Boundedness Concept and Application to CSTR Systems

Stability analysis of switching systems with all modes unstable based on a $ \Phi $-dependent max-minimum dwell time method

&lt;abstract&gt;&lt;p&gt;This paper applies stable and unstable switching instants to study switching systems with unstable modes under time-dependent switching signals. A new Lyapunov function is proposed to study the properties of switching instant using different $ \Phi $-dependent max-minimum dwell time methods. After that, the global exponential stability conditions for nonlinear and linear switching systems are derived and stable switching is used to compensate for unstable switching and unstable modes. The relevant results are extended to the controller design of linear switching systems. Finally, a simulation verifies the effectiveness of the results of this paper.&lt;/p&gt;&lt;/abstract&gt;

Fuzzy Adaptive Finite-Time Resilient Control Against Unknown False Data Injection Attacks for MIMO Nonlinear Switched Systems With Unknown Dead Zone.

This article studies the finite-time adaptive resilient control problem for MIMO nonlinear switched systems with the unknown dead zone. The sensors of the controlled systems suffer from unknown false data injection (FDI) attacks so that all states cannot be directly applied to the design process of the controller. To address this negative impact of FDI attacks, a new coordinate transformation is designed in control design. Moreover, the Nussbaum gain technique is introduced to deal with the difficulty of unknown time-varying weights caused by FDI attacks. Based on the common Lyapunov function method, a finite-time resilient control algorithm is designed by employing compromised state variables, which ensures that all signals of the closed-loop systems are bounded under arbitrary switching rules even in the presence of unknown FDI attacks. Compared with the existing results, the proposed control algorithm not only enables the controlled systems to reach an equilibrium state in a finite time but also removes the assumption that the sign of the attack weights is positive. In the end, a practical simulation example proves that the designed control method is valid.

Observer-Based Adaptive NN Security Control for Switched Nonlinear Systems Against DoS Attacks: An ADT Approach.

In this article, a novel switched observer-based neural network (NN) adaptive control algorithm is established, which addresses the security control problem of switched nonlinear systems (SNSs) under denial-of-service (DoS) attacks. The considered SNSs are described in lower triangular form with external disturbances and unmodeled dynamics. Note that when an attack is launched in the sensor-controller channel, the controller will not receive any message, which makes the standard backstepping controller not workable. To tackle the challenge, a set of NN adaptive observers are designed under two different situations, which can switch adaptively depending on the DoS attack on/off. Further, an NN adaptive controller is constructed and the dynamic surface control method is borrowed to surmount the complexity explosion phenomenon. To eliminate double damage from DoS attacks and switches, a set of switching laws with average dwell time are designed via the multiple Lyapunov function method, which in combination with the proposed controllers, guarantees that all the signals in the closed-loop system are bounded. Finally, an illustrative example is offered to verify the availability of the proposed control algorithm.

Hybrid Reinforcement Learning for Optimal Control of Non-Linear Switching System.

Based on the reinforcement learning mechanism, a data-based scheme is proposed to address the optimal control problem of discrete-time non-linear switching systems. In contrast to conventional systems, in the switching systems, the control signal consists of the active mode (discrete) and the control inputs (continuous). First, the Hamilton-Jacobi-Bellman equation of the hybrid action space is derived, and a two-stage value iteration method is proposed to learn the optimal solution. In addition, a neural network structure is designed by decomposing the Q-function into the value function and the normalized advantage value function, which is quadratic with respect to the continuous control of subsystems. In this way, the Q-function and the continuous policy can be simultaneously updated at each iteration step so that the training of hybrid policies is simplified to a one-step manner. Moreover, the convergence analysis of the proposed algorithm with consideration of approximation error is provided. Finally, the algorithm is applied evaluated on three different simulation examples. Compared to the related work, the results demonstrate the potential of our method.

The finite-time boundedness and control analysis of switched nonlinear time-varying delay systems based on auxiliary matrices

This paper explores the finite-time boundedness and controller problem of switching nonlinear delay systems. The time delay is considered as time-varying delay rather than constant delay. First of all, an appropriate Lyapunov–Krasovskii functional (LKF) which contains three integral terms is selected. The upper and lower bounds of these integral terms are given by segmenting the time delay interval. Meanwhile, the auxiliary matrix method is used to separate the Lyapunov matrix from the system matrix. Moreover, a new state-dependent switching law is designed to switch between subsystems according to the change of the magnitude of the LKF. Based on the above methods, the first step is to research the finite-time bounded analysis of delayed system without control input. Then, a sufficient condition is obtained to ensure the finite-time boundedness of switched systems with control input. Further, by designing an observer-based H∞ controller, the closed-loop system with time-varying delay is bounded and has H∞ performance index ν by using the Finsler’s Lemma and Singular Value Decomposition (SVD). Simultaneously, the controller and observer gains are designed. Finally, two simulations are used to verify the effectiveness and feasibility of the proposed methods.

Finite-time Incremental Stability Analysis for Nonlinear Switched Systems With Unstable Subsystems

Finite-time Incremental Stability Analysis for Nonlinear Switched Systems With Unstable Subsystems

Adaptive Output Feedback Fuzzy Event-Triggered Control for Fractional-Order Nonlinear Switched Systems

This study examined the control problem triggered by an adaptive fuzzy event for uncertain fractional-order switched systems. First, an observer was designed to estimate unknown system states, and fuzzy logic systems were introduced to approximate unknown nonlinear functions. Further, the dynamic surface technique is employed to solve complex differential problems of fractional-order switched systems. This paper proposes a threshold-based event-triggered control scheme that avoids Zeno behavior to decrease the waste of communication resources. An event-triggered mechanism updates the control signal only when necessary to ensure system performance. The proposed control strategy enables all signals of a closed-loop system to be uniformly bounded and the tracking error of output has good convergence performance near the origin under an arbitrary switching mechanism. Finally, a numerical example is presented that demonstrates the effectiveness of the designed scheme.

Discrete-Time Switching Systems as Difference Inclusions: Deducing Converse Lyapunov Results for the Former From Those for the Latter

Nonlinear discrete-time switching systems under mode-dependent switching and dwell-time constraints are modeled by difference inclusions. Novel proofs of converse Lyapunov results are obtained for the switching systems as consequences of a converse Lyapunov result for a difference inclusion.

Active Disturbance Rejection Control for Networked Switched Nonlinear Systems With Decentralized Event-Triggered Communication

Active Disturbance Rejection Control for Networked Switched Nonlinear Systems With Decentralized Event-Triggered Communication

Adaptive neural network prescribed performance control for dual switching nonlinear time-delay system

This paper investigates the adaptive neural network prescribed performance control problem for a class of dual switching nonlinear systems with time-delay. By using the approximation of neural networks (NNs), an adaptive controller is designed to achieve tracking performance. Another research point of this paper is tracking performance constraints which can solve the performance degradation in practical systems. Therefore, an adaptive NNs output feedback tracking scheme is studied by combining the prescribed performance control (PPC) and backstepping method. With the designed controller and the switching rule, all signals of the closed-loop system are bounded, and the tracking performance satisfies the prescribed performance.