On the stochastic finite-time stability for switched stochastic nonlinear systems

In this paper, the stochastic finite-time stability (SFTS) criteria for switched stochastic nonlinear systems (SSNS) with nonlocal Lipschitz coefficients are established. The main tools that we used here are mode-dependent limiting average dwell time (MD-LADT), stopping time technology and the stochastic analysis theory. The established criteria show that the diffusion coefficient, the drift coefficient and the switching law play crucial roles in obtaining the SFTS for the SSNS. Besides, our criteria provide some approaches on how to design the switching law to achieve the SFTS if a switched stochastic system contains SFTS subsystems and stochastic finite-time instable (SFTI) subsystems simultaneously. Finally, an example is given to illustrate the importance and usefulness of the theoretical results.     

Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method.     

Command filter-based adaptive fixed-time fault-tolerant control for stochastic nonlinear systems with actuator hysteresis

In this paper, an adaptive fault-tolerant fixed-time control problem is considered via command-filter technique for stochastic nonlinear systems with sensor fault and actuator hysteresis. With the application of command-filtering technique, a novel command-filter compensate mechanism is designed, which implies that the improved control scheme not only eliminates “the explosion of complexity” but also realizes the compensate signal is bounded within fixed-time interval. The unavailability of state variables caused by sensor fault is solved by applying parameter separation and regrouping approach. Meanwhile, an adaptive auxiliary signal is designed to cope with the backlash-like hysteresis phenomenon, which can avoid singularity, reduce chattering, and facilitate controller design. Combining backstepping technique and Lyapunov stability theorem, an adaptive fault-tolerant control approach is developed, which can guarantee all closed-loop signals remain semi-globally practical fixed-time stable (SGPFS) in probability. The validity of the proposed strategy is illustrated by simulation examples.     

非线性系统有限时间控制研究综述

近30年来,有限时间控制因其具有收敛速度快、抗扰性强、控制精度高等优点,引起了学者们的研究兴趣.据作者所知,目前鲜有文献系统地总结有限时间控制的相关研究内容.因此,本文致力于较为系统且完整地给出非线性系统有限时间控制方法的研究进展.主要内容包括如下几方面:研究意义;有限时间的定义,判据及设定时间表达式;有限时间设计方法的研究现状以及未来工作.     

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.     

Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.     

输出受限的不确定非线性系统的自适应固定时间控制

针对具有非对称输出约束和外界干扰的不确定非线性系统,提出自适应固定时间反步控制策略.首先,采用非对称障碍Lyapunov函数处理系统的输出约束问题;其次,通过构造固定时间干扰观测器估计外界干扰,设计自适应固定时间滤波器,解决传统反步控制的“计算爆炸”问题,通过自适应律估计虚拟控制输入导数的未知上界;再次,基于Lyapunov稳定性理论证明闭环系统在固定时间内有界稳定且输出保持在约束范围内;最后,通过永磁同步电机的仿真验证所设计的控制策略的有效性.     

Global finite-time stabilisation for a class of stochastic high-order time-varying nonlinear systems

In this paper, the problem of global finite-time stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with time-varying nonlinearities. Based on the generalised stochastic Lyapunov theorem on finite-time stability, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee that the closed-loop system is globally finite-time stable in probability. Finally, several simulation examples are provided to illustrate the effectiveness of the proposed method.     

Nonlinear control and synchronization of a class of nonlinear coupled dynamical systems

In this paper, a control problem for a class of nonlinear coupled dynamical systems is proposed and a continuous nonlinear feedback control law is designed using direct Lyapunov method to solve the proposed control problem. Moreover, synchronization problem for a special case of this class nonlinear coupled dynamical systems is concerned. Numerical examples show the effectiveness and advantage of the designed continuous nonlinear control law and derived synchronization result.     

随机非线性系统的输出反馈控制

针对满足线性增长条件的一类随机非线性系统, 本文研究了输出反馈镇定问题. 然而不同于现有的所有文献, 由于线性增长条件中含有不可量测的状态, 引入了一个待定的高增益观测器. 利用反推设计技术, 构造性地给出了一个输出反馈控制器的设计, 通过适当地选取高增益参数, 保证了闭环系统的零解是概率意义下全局渐近稳定的, 输出几乎处处调节于零.     

-like control for nonlinear stochastic systems

In this paper we develop a H_∞-type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L₂-gain property and the solution to a certain Hamilton–Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case-based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.     

Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain second-order affine nonlinear system with the new forms of terminal sliding mode (TSM). Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.     

Feedback control of nonlinear systems

This paper deals with the design of (memoryless) state-feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs. The purpose of the design is to obtain a (locally) internally stable closed-loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated. Two standard setups are considered: in the first one, the ratio between the energy associated with the penalty variable and that associated with the exogenous input is required to be bounded by a constant 0 < γ this setup includes (to some extent) the standard H_∞ control problem of linear system theory. In the second one, the penalty variable is required to converge to 0 as t ∞; this setup generalizes the so-called servomechanism problem of linear system theory.     

Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain second-order affine nonlinear system with the new forms of terminal sliding mode (TSM). Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.     

Robust finite-time control for a class of extended stochastic switching systems

This article proposes a new design approach for robust finite-time H _∞ control of a class of Markov jump systems with partially known information on the transition jump rates. The system under consideration involves norm-bounded parameter uncertainties and external disturbance. The problems of robust finite-time boundedness and finite-time stabilisation of the underlying systems are considered. Then, a H _∞ state feedback controller is designed. Sufficient conditions that consider only the known bounds on the transition jump rates are developed in the form of linear matrix inequalities. A numerical example is included to show the usefulness of the theoretic results obtained.     

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.     

基于事件触发非线性多智能体系统的固定时间一致性

本文研究了在有向拓扑下,带有非线性动力学多智能体系统的固定时间一致性问题.提出了一种新的基于事件触发机制的非线性控制策略,对于每个智能体给出了基于状态信息的事件触发条件,当状态误差满足所给条件时才触发事件,能有效的减小系统的能量耗散和控制器的更新频次.利用Lyapunov稳定性理论和代数图论,证明在该控制策略下,多智能体系统在固定时间能实现领导跟随一致性,且不存在Zeno行为.相较于有限时间一致性策略,采用固定时间一致性策略系统的收敛时间不再依赖于系统的初始状态.最后,仿真实例验证了理论结果的有效性.     

Adaptive finite-time control of nonlinear systems with parametric uncertainty

In this note, global finite time stabilization is investigated for a class of nonlinear systems in p normal form with parametric uncertainties. To achieve finite-time stabilization, a constructive control design approach is proposed by following backstepping methodology, and an adaptive finite-time control law is obtained in the form of continuous time-invariant feedback.     

Feedback affinization of nonlinear control systems

In this paper conditions for the nonlinear control system

to have a nonlinear feedback control

u=(x,v), vΩ′R^m′, m′m, 0Ω′

such that the nonlinear system takes a form of an affine system

are presented. All results require algebraic operations and differentiation of functions only.     

Feedback decomposition of nonlinear control systems

By using the recently developed (differential) geometric approach to nonlinear systems, a feedback decomposition for nonlinear control systems is derived.