Observer-based finite-time H∞ control of Itô-type stochastic nonlinear systems

This paper investigates the finite-time $H_{\infty }$ control of Itô-type stochastic nonlinear systems. Considering the transient performance and anti-interference ability within a given limited time interval, the control strategy of stochastic nonlinear systems is researched. A new sufficient condition for mean-square finite-time boundedness for stochastic nonlinear system is developed. Due to the state components are not available, a state observer is designed. Based on the estimated state, an $H_{\infty }$ controller is proposed and Linear Matrix Inequality (LMI) conditions are given, which not only guarantee the mean-square finite-time boundedness but also satisfy the corresponding $H_{\infty }$ performance. Finally, two examples are given to demonstrate the effectiveness of the results.     

Dynamic event-triggered H∞$$ {H}_{\infty } $$ control for continuous-time singular system with cyber attacks

This essay discusses the $H_{\infty }$ control for continuous-time singular systems with two types of stochastic cyber attacks and dynamic event-triggered scheme. So as to economize network resources and reduce communication burden, the novel dynamic event-triggered mechanism is given. Cyber attacks occur randomly during network information transmission, especially the denial of service (DoS) attacks and the deception attacks. By using Lyapunov–Krasovskii functional, some novel sufficient conditions for the impulse free, regular, and asymptotically stable of the studied system are obtained, and a corresponding controller is devised. In addition, a desired controller gain is received through resolving linear matrix inequalities. Eventually, a few numerical examples are supplied to certify the usefulness of provided design ways and results.     

An improved output feedback controller design for linear discrete-time systems using a matrix decomposition method

This paper presents the design of output feedback controllers for discrete-time (DT) linear systems. New sufficient LMI conditions are derived for designing static $H_2$ and $H_{\infty }$ controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback $H_{\infty }$ controller is designed for a quarter-car suspension system. Simulation results are provided to show the efficacy of the proposed design method.     

Event-triggered H∞ control of discrete-time switched linear systems with delays

This paper studies the $H_{\infty }$ control problem of discrete-time delayed switched systems with average dwell time switching signals using event-triggered mechanism. The event-triggered mechanism can reduce redundant information transmission. First, employing state-feedback controller, two sufficient conditions are proposed to guaranteeing (i) exponential stability of the disturbance-free closed-loop system and (ii) $H_{\infty }$ performance of the closed-loop system with disturbance. Moreover, the controller gain is explicitly computed by solving a set of linear matrix inequalities. Second, results obtained for state-feedback controller are extended to those for observer-based state-feedback controller, and both the controller and observer gains are explicitly computed. All conditions are derived by utilizing a properly constructed decay-rate-dependent Lyapunov functional. Finally, a numerical example illustrates the validity of the obtained theoretical results.     

Adaptive neural network fixed-time control of p$$ p $$-normal systems with asymmetric output constraints

This paper studies the problem of fixed-time $H_{\infty }$ control for a class of nonlinear $p$-normal systems with asymmetric output constraints and external disturbances. Compared with the existing fixed-time control schemes, the smooth switching functions are designed to avoid the singularity problem. Then, a time-varying nonlinear transformation function (NTF) is introduced, blue and a unified tool to deal with the symmetric, asymmetric, and even unconstrained problems simultaneously. Moreover, by adding blue one power integration technology, the $H_{\infty }$ controller is designed, which can inhibit the influence of external disturbances on the system. According to Lyapunov stability analysis, the presented fixed-time $H_{\infty }$ blue control method ensures that all signals are bounded in a fixed time. In the end, two simulation examples demonstrate the effectiveness of the proposed scheme.     

Adaptive neural network dynamic event-triggered control for strong interconnected stochastic nonlinear systems with output constraint

This paper proposes a dynamic event-triggered mechanism based command filtered adaptive neural network (NN) tracking control scheme for strong interconnected stochastic nonlinear systems with time-varying output constraints. By designing a state observer, the unmeasured states of the systems can be estimated. The NNs are utilized to handle the unknown intermediate functions. In the controller design process, the asymmetric time-varying barrier Lyapunov functions are used to guarantee that the systems outputs do not violate the constraint regions. By integrating the command filter with variable separation technique, the controller design process is more simple, and the problem of algebraic-loop can be solved which caused by interconnected functions. According to the Lyapunov stability theory, it can be ensured that all signals of the systems are bounded in probability. Finally, the availability of the developed control scheme can be showed by the simulation example.     

Interval estimation and fault detection for switched nonlinear systems based on zonotope method

This paper investigates the state interval estimation and fault detection (FD) problems for a Lipschitz nonlinear switched system based on the combination of the $H_{\infty }$ observer and the zonotope method. To begin with, an $H_{\infty }$ observer that is robust to the disturbance is designed, and the stability of the observer error dynamic system is analyzed under the average dwell time (ADT) concept. After this, the zonotope theory is applied on the $H_{\infty }$ observer error dynamic system such that the interval state estimation can be calculated iteratively when the system suffers from no fault. Furthermore, for FD purpose, a residual is constructed based on the $H_{\infty }$ observer. Because the constructed residual contains disturbance, it cannot be used for FD directly. To overcome this drawback, the interval estimation method of the residual is proposed by using the zonotope method, and a residual-based FD scheme is developed. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

Fuzzy-model-based robust control of Markov jump nonlinear systems with incomplete transition probabilities and uncertain packet dropouts

Interval type-2 fuzzy Markov jump systems (IT2FMJSs) have received much attention because they can well describe complex nonlinear systems with uncertainties and stochastic system mode switching. However, the transition probabilities of fuzzy MJSs (FMJSs) have been assumed to be completely known, limiting real-world applications of existing results. Different from the previous studies, transition probabilities between system modes switching are partially unknown, and packet dropouts of data transmission are uncertain in this study. Compared with the previous studies, the main advantages of this work are as follows: (1) To analyze stochastic stability and reduce conservatism of existing approaches, a novel Lyapunov function that depends on both system mode and fuzzy basis function is constructed; (2) the existence of a mode-dependent and fuzzy-basis-dependent state feedback controller is revealed; (3) stochastic stability of closed-loop system with a desired $H_{\infty }$ performance is established, and the problem of incomplete transition probabilities and uncertain packet dropouts has been completely addressed. An illustrative example of a robot arm is used to demonstrate the effectiveness and practicality of the proposed control strategy. By virtue of the proposed strategy, the effects of incomplete transition probabilities and uncertain packet dropouts on IT2FMJSs have been completely alleviated.     

Finite-time boundedness and control design of uncertain switched systems with time-varying delay under new switching rules

In this article, the finite-time boundedness and control problem for time-delay switched systems with uncertainties are studied. The delay is considered as time-varying delay rather than constant delay, which is more suitable for practical engineering. First, the property of finite time boundedness for uncertain switched system without control input is researched by constructing a proper Lyapunov–Krasovskii functional (LKF) with three integral terms and the minimum LKF switching rules. Then, a state feedback controller with switching is designed. By utilizing Finsler's Lemma and singular value decomposition (SVD), sufficient conditions for finite-time boundedness of time-delay switched systems with control input and controller gain are presented. Additionally, a filter system is designed. The finite time boundedness and filter parameters of the closed-loop error system are obtained by using the auxiliary matrix method. Finally, the feasibility of the proposed methods and the significance of switching rule are demonstrated through two numerical examples.     

Observer-based event-triggered distributed model predictive control for a class of nonlinear interconnected systems

In this paper, an observer-based event-triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event-triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event-triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed-loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.     

Distributed observer design for interconnected nonlinear systems with faults and disturbances based on dynamic event conditions

This study investigated the observer design schemes for interconnected nonlinear systems with actuator faults, sensor faults, external disturbances, and limited measured resources. A novel effective distributed estimation scheme is presented for the interconnected nonlinear system to estimate the states, faults, and lumped disturbances, simultaneously. To save communication resources and to improve information utilization, an adaptive event condition is designed in the sensor channel, and the triggered values are utilized to design the observer. Especially, to handle the sensor fault, the output is separated into two parts, and the estimation is realized with the help of a normal one. In the first part of this study, a class of interconnected nonlinear systems with partial loss of effectiveness of sensor fault is considered, and an event-based distributed estimation scheme is established. In the second part, a class of more universal feedback interconnected nonlinear with both partial loss sensor fault and bias sensor fault is investigated. An augment system is formulated by an augmented vector composed of state and sensor faults. And then the estimation scheme is realized by utilizing the presented event-based distributed observer. The convergence abilities of both the two conditions are proved and, finally, the estimation performances of the presented observer are verified by a numerical simulation system and an inverted pendulum system.     

不确定非线性系统自适应动态事件触发输出反馈镇定

本文研究了一类不确定非线性系统的动态事件触发输出反馈镇定问题. 显著不同的是系统具有依赖于不可测状态的增长且增长率为输出的未知多项式. 尽管已有一些连续自适应控制器, 但需要巧妙融合非线性状态观测器、系统未知性的动态补偿以及非线性的抵御, 因此这些控制器具有一定的脆弱性, 不能平凡地拓展到不连续情形 (采样误差导致). 为此, 首先通过引入动态高增益和基于高增益的观测器来分别抵御未知增长率和重构系统不可测状态. 进而, 意识到静态事件触发机制的无效性, 通过引入动态事件触发机制, 成功设计出了事件触发输出反馈控制器, 确保了系统状态的全局有界性和收敛性. 数值仿真验证了所设计控制器的有效性.     

Observer-based path following control for autonomous vehicles with localization errors and tire slip effects

This paper investigates the problem of path following control for an autonomous vehicle subject to the localization errors and the tire slip effects. First, by analyzing the effects of localization errors, a loss-of-effectiveness actuator model is formulated, and a new chain form model is constructed for path following system of the vehicle. Then, the polytopic model is proposed to characterize the nonlinearity of the system, and an observer-based path following controller is designed by satisfying both the $H_{\infty }$ criterion and $L_1$ criterion. Finally, the path following controller design problem is converted into an optimization problem, which can be solved readily through convex optimization techniques. The effectiveness of the proposed control strategy is verified by simulation results.     

H∞ consensus for Markov jump multi-agent systems with partly unknown transition probabilities and multiplicative noise

This paper focuses on the $H_{\infty }$ consensus control problem about Markov jump multi-agent systems with partly unknown transition probabilities and multiplicative noise. The transition probabilities of the Markov jumps are considered to be partly unknown, which are more applicable than the traditional assumption in Markov jump systems that all of them must be completely known. Sufficient conditions for $H_{\infty }$ consensus control problem are derived by using less linear matrix inequalities. Finally, a simulation example is provided to show the validity of our results.     

动态事件触发机制下二阶多智能体系统完全分布式控制

本文研究了无向通信拓扑下二阶多智能体系统的一致性问题, 分别针对有领导者和无领导者的情形, 设计 了一类基于辅助动态变量的完全分布式事件触发控制策略, 该策略具有参数较少且易调等特点. 智能体自身的触 发函数满足条件时才向邻居广播自身的状态信息, 有效避免了连续通信, 减少了系统能量耗散. 每个智能体的控制 协议和触发函数都只用到自身的状态和邻居触发时刻的状态, 不涉及邻居的实时状态信息, 也不依赖通信拓扑网络 的任何全局信息. 利用代数图论以及Lyapunov稳定性理论, 证明在所提出的控制策略下, 二阶多智能体系统能够实 现渐近一致性, 且不存在Zeno行为. 仿真示例进一步验证了理论结果的有效性.     

Finite-horizon Q-learning for discrete-time zero-sum games with application to H∞$$ {H}_{\infty } $$ control

In this paper, we investigate the optimal control strategies for model-free zero-sum games involving the $H_{\infty }$ control. The key contribution is the development of a Q-learning algorithm for linear quadratic games without knowing the system dynamics. The finite-horizon setting is more practical than the infinite-horizon setting, but it is difficult to solve the time-varying Riccati equation associated with the finite-horizon setting directly. The proposed algorithm is shown to solve the time-varying Riccati equation iteratively without the use of models, and numerical experiments on aircraft dynamics demonstrate the algorithm's efficiency.