基于隐Lyapunov 函数的软变结构控制: 一种控制策略

针对变结构控制的抖振问题,基于隐Lyapunov函数,提出一种新的控制策略:软变结构控制.首先给出软变结构控制的定义和控制器的构造方法;然后设计软变结构控制器和隐Lyapunov区域,给出了控制不受限和控制受限两种情形的软变结构控制,同时,分析了带有状态观测器的软变结构控制.软变结构控制是无滑模的变结构控制,能有效削弱抖振,保持高速调节速度和缩短趋近时间.仿真实例表明了该方法的有效性和可行性.     

随机马尔可夫跳变系统的变结构控制设计

采用滑动扇区方法,研究了不确定随机马尔可夫跳变系统的变结构控制设计问题。首先给出随机马尔可夫跳变系统滑动扇区的定义,然后基于线性矩阵不等式技术,提出一种滑动扇区及变结构控制律设计方法。经过理论证明该控制律能够确保随机马尔可夫跳变不确定系统二次稳定,并有效地抑制抖振。最后数值仿真算例验证了控制方案的有效性。     

Robust H∞ Sliding Mode Control for a Class of Singular Stochastic Nonlinear Systems

This paper concerns the problem of robust H_∞ sliding mode control for a class of singular stochastic nonlinear systems. Integral sliding mode control is developed to deal with this problem. Based on the integral sliding surface of the design and linear matrix inequality, a sufficient condition which guarantees the sliding mode dynamics is asymptotically mean square admissible and has a prescribed H_∞ performance for a class of singular stochastic nonlinear systems is proposed. Furthermore, a sliding mode control law is synthesized such that the singular stochastic nonlinear system can be driven to the sliding surface in finite time. Finally, a numerical example is proposed to illustrate the effectiveness of the given theoretical results.     

Fast smooth second-order sliding mode control for stochastic systems with enumerable coloured noises

A fast smooth second-order sliding mode control is presented for a class of stochastic systems driven by enumerable Ornstein–Uhlenbeck coloured noises with time-varying coefficients. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the control. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Then the prescribed sliding variable dynamic is presented. The sufficient condition guaranteeing its finite-time convergence is given and proved using stochastic Lyapunov-like techniques. The proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are given comparing with smooth second-order sliding mode control to validate the analysis.     

含有有色噪声的随机系统在适应稳定意义下的变结构控制

研究含吸典型环境随机噪声－Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｃｋｂｅｃｋ有色噪声的连续时间随机系统在实用稳定意义下的变结构控制,构造了变结构控制律,证明了滑动模的可达性,估计了系统运动达到滑动模的时间,证明了滑动模运动的实用稳定性和鲁棒性,文末用仿真实例验证了本文的结果。     

一类由偏微分方程描述时滞随机系统的变结构控制

研究了一类由偏微分方程描述的Ito型时变时滞随机系统的变结构控制问题．首先构造了系统的滑动流形,设计了变结构控制律;然后证明T系统的滑动模具有次可达性,并且利用Halanay不等式的方法给出了系统滑动模运动为均方稳定运动的一个充分条件．     

Adaptive H∞ sliding mode control of uncertain neutral‐type stochastic systems based on state observer

This paper is focused on the problem of adaptive sliding mode control design for uncertain neutral‐type stochastic systems under a prescribed H_∞ performance. A simplified state observer is put forward to estimate the unknown state variables, which could be properly incorporated for establishing a new linear‐type switching surface and the associated adaptive variable structure controller. By virtue of the adaptive control design, unknown matched perturbation and potential uncertainties can be counteracted, and the system trajectories are guaranteed to reach the predefined switching surface within finite moment in almost surely sense, and performance analysis of the closed‐loop dynamics during the sliding surface is carried out with a specified H_∞ performance. At last, two illustrative examples through computer simulations are provided to verify the effectiveness and applicability of the proposed scheme.     

Sliding mode control for a class of nonlinear discrete-time networked systems with multiple stochastic communication delays

In this article, a sliding mode control problem is studied for a class of uncertain nonlinear networked systems with multiple communication delays. A sequence of stochastic variables obeying Bernoulli distribution is applied in the system model to describe the randomly occurring communication delays. The discrete-time system considered is also subject to parameter uncertainties and state-dependent stochastic disturbances. A novel discrete switching function is proposed to facilitate the sliding mode controller design. The sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is robustly exponentially stable in the mean square if two LMIs with an equality constraint are feasible. A discrete-time SMC controller is designed that is capable of guaranteeing the discrete-time sliding-mode reaching condition of the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.     

Nonfragile observer‐based H ∞ sliding mode control for Itô stochastic systems with Markovian switching

The paper is devoted to investigating sliding mode control for a class of nonlinear uncertain stochastic systems with input nonlinearity and Markovian switching. A nonfragile observer subjected to the transition rates of the modes is designed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are established. The state estimation‐based sliding mode control law is derived to guarantee the reachability of the sliding surface in finite time interval. The sufficient conditions on asymptotically stochastic stability of the error system and sliding mode dynamics with a given disturbance attenuation level are derived in terms of linear matrix inequalities. Finally, an example is provided to illustrate the efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Functional observer-based sliding mode controller design for discrete-time stochastic LTI systems with unmatched uncertainty

Discrete-time sliding mode control is one of the most prominent robust control technique to stabilise systems. However, the assumption of full state feedback being available is seldom satisfied in practice. This paper presents the functional observer-based sliding mode controller (SMC) design for discrete-time stochastic systems with unmatched uncertainty. A disturbance-dependent sliding function method is proposed such that the effect of unmatched uncertainty of the system is minimised. Furthermore, SMC is calculated using the functional observer method. Finally, a simulation example is given to show the effectiveness of the proposed method.     

Sliding mode control for a class of nonlinear It ô stochastic systems with state and input delays

This paper deals with the problem of sliding mode control (SMC) for a class of nonlinear stochastic systems. The nonlinear uncertainties are unknown and unmatched. There exist state and input delays. A special switching function is designed such that the insensitivity of the system can be guaranteed throughout the entire response of the system from the initial time instance. Both the sliding surface and the sliding mode controller exist if a set of matrix inequalities is feasible. A simulation example is given to illustrate the proposed method. Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il lee. The research was partially supported by NNSF under Grant (60674015, 60674089), the Technology Innovation Key Foundation of Shanghai Municipal Education Commission (09ZZ60), Shanghai Leading Academic Discipline Project (B504), China. Yugang Niu received the Ph.D. degree in Control Theory and Control Engineering Automation from Nanjing University of Science and Technology in 2001. His research interests include nonlinear control, stochastic control systems, sliding mode control and network congestion control. Bei Chen received the B.S. degree in Automation from East China University of Science & Technology in 2008. Her current research areas are sliding mode control, and networked control systems. Xingyu Wang received the Ph.D. degree in Industrial Automation from the East China Chemical Institute in 1984. His current research areas primarily cover control theory and applications, intelligent control, and brain control with its wide range of applications.     

Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach

In this paper, a fault estimation and fault-tolerant control problem for a class of T-S fuzzy stochastic time-delay systems with actuator and sensor faults is investigated. A novel sliding mode observer is proposed, which can simultaneously estimate the system states, actuator and sensor faults with good accuracy. Based on the state and actuator fault estimation, a new sliding mode control scheme is developed, which can effectively eliminate the influence of actuator fault. Sufficient conditions for the existence of the proposed observer and fault-tolerant sliding mode controller are provided in terms of linear matrix inequality, and moreover, the reachability of the sliding mode surface can be guaranteed under the proposed control scheme. The propose sliding mode observer and fault-tolerant sliding mode controller can overcome the restrictive assumption that the input matrix of all local modes is the same. Finally, a numerical example is provided to verify the effectiveness of the proposed sliding mode observer and fault-tolerant sliding mode control technique.     

随机大系统利用变结构控制的分散镇定*

本文研究了随机大系统的变结构控制问题。并证明了所构造的滑动流形的可达性和均方渐近稳定性。     

Memoryless SMC Design Methods for Stochastic Delay Systems

Recently, the sliding mode control (SMC) method has been extended to accommodate stochastic systems. Particularly, restrictive assumption on the structure of the control systems have been removed and a practical SMC design method for stochastic systems has been presented. This paper continues this line of research and studies the SMC methods for stochastic systems with state delay in diffusion. Both delay‐independent and delay‐dependent approaches are investigated. Essentially, this paper studies SMC design methods with memoryless controllers for time delay systems, which has been a problem in the past decades.     

广义系统的变结构控制

本文研究了线性广义系统的变结构控制问题，通过引进滑动模动态补偿器，得到了系统的滑动方程及关于内外部干扰的不变性条件；并给出了综合方法；最后研究了实际滑动模的近似问题。     

关联不确定大系统的分散变结构控制

分散控制方法和变结构控制方法两者优点的结合使得分散变结构控制在大系统研 究中得到了广泛的重视.针对各个子系统均为多输入情况.研究了不确定性关联大系统的分 散变结构控制方法.基于开关平面的等价性,提出了关联大系统的分散滑动模态全局可达条 件.并针对子系统不确定性的界已知及未知两种情况,提出了分散变结构控制算法.该方法克 服了以往控制方法中需已知线性关联函数或不确定性关联的界的缺陷.     

一类具有变时滞不确定分布参数系统的滑动模控制

研究一类不确定变时滞分布参数系统的滑动模控制问题．首先设计一种无记忆功能的变结构控制器;然后分析了在滑动模切换面上滑动模控制系统关于不确定量的不变性特征;最后给出了从任意初始位置出发的轨线到达滑动模态区的时间估计．研究表明,所设计的控制器结构简单．容易实现．     

Sliding Mode Control for Nonlinear Markovian Jump Systems Under Denial-of-Service Attacks

This paper investigates the sliding mode control (SMC) problem for a class of discrete-time nonlinear networked Markovian jump systems (MJSs) in the presence of probabilistic denial-of-service (DoS) attacks. The communication network via which the data is propagated is unsafe and the malicious adversary can attack the system during state feedback. By considering random Denial-of-Service attacks, a new sliding mode variable is designed, which takes into account the distribution information of the probabilistic attacks. Then, by resorting to Lyapunov theory and stochastic analysis methods, sufficient conditions are established for the existence of the desired sliding mode controller, guaranteeing both reachability of the designed sliding surface and stability of the resulting sliding motion. Finally, a simulation example is given to demonstrate the effectiveness of the proposed sliding mode control algorithm.      

A sliding mode observer design for uncertain fractional Ito stochastic systems with state delay

This paper addresses the robust observer design problem for uncertain time-delay fractional Ito stochastic systems. A sliding surface is proposed and it is shown that state estimates converge towards it and remain there for the subsequent time. Additionally, by constructing a novel Lyapunov functional, a sufficient condition for the stability of the sliding motion of the estimated states is given in the form of Linear Matrix Inequalities (LMIs). It is demonstrated that the state estimates are stabilizable in probability provided that the LMI is feasible. Moreover, a finite-time sliding mode control law based on the estimated states is proposed. Simulation examples are given to show the validity and effectiveness of the results.