新型有限时间收敛滑模扩张状态观测器研究

针对一类具有量测噪声的非线性不确定系统,设计了基于新型滑模扩张状态观测器的Terminal滑模控制方案．首先对系统进行两次状态扩张,然后设计一种新型滑模扩张状态观测器,通过采用特殊的滑模面保证观测误差在有限时间内收敛到零．在此基础上,设计Terminal滑模控制器,使系统状态也能在有限时间内收敛到零．严格的理论证明和仿真结果均证明了所设计新型滑模观测器及闭环控制方案的有效性和快速性．     

非线性不确定系统的鲁棒滑模观测器设计

对非线性不确定性系统,提出一种鲁棒滑模观测器.所提出的鲁棒滑模观测器通过滑模与相应的控制策略来实现,设计参数的选取不需要求解大量方程,同时能保证对系统的非线性不确定项具有鲁棒性.通过设计滑模,可以调整观测器跟踪系统状态的收敛速度,使状态估计达到预期的指标.仿真结果验证了提出方法的有效性.     

Decentralized Sliding Mode Control for Multi‐Input Complex Interconnected Systems Subject to non‐smooth Nonlinearities

Many modern control systems become gradually more complicated and, consequently, the approach to control design approaches is both difficulty and complex. Moreover, if such a complex interconnected system is subjected to non‐smooth nonlinearities in the actuator, then unexpected difficulties, degradation or, even worse, instability will arise in the system performance. Therefore, a new decentralized sliding mode control (DSMC) approach for such a class of complex interconnected systems subjected to non‐smooth (deadzone) nonlinearities is proposed in this paper. Based on sliding mode control (SMC) theory, the proposed DSMC laws guarantee the global reaching condition of the sliding mode in uncertain complex interconnected systems with deadzone nonlinearities, that is, they can ensure that the sliding mode is reached in finite time and with prescribed transient behavior. In the sliding mode, the investigated uncertain complex interconnected system with deadzone nonlinearities in the actuator still are insensitive to system uncertainties and external disturbances. The proposed DSMC laws can work effectively for uncertain complex interconnected systems either with or without deadzone nonlinearities in the actuator. However, this cannot be guaranteed by the traditional DSMC design for systems without input deadzone nonlinearities. Furthermore, the sliding motion can be controlled to converge within a specified exponential speed. Finally, two illustrative examples with a series of computer simulations are presented to demonstrate the effectiveness of the proposed DSMC laws.     

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.     

A multitask sliding mode control for mismatched uncertain large-scale systems

A new sliding mode control (SMC) approach, output variables only, single phase only and chattering phenomenon free, is presented for a class of mismatched uncertain large-scale systems. For a new multitask SMC, it is not required that the system states are available. Moreover, the sliding function in this study just depends on output variables. Using an exponential type sliding surface, the system states are always in the sliding mode at the beginning time t = 0. Using a newly appropriate linear matrix inequality stability conditions by the Lyapunov method are derived such that each subsystem in the new sliding mode is completely invariant to matched uncertainties. As a result, robustness of the mismatched uncertain large-scale systems can be assured throughout an entire response of the system starting from the initial time t = 0. In every subsystem, a scheme of decentralised control using only output states is proposed. In addition, a continuous controller is finally designed for chattering removal. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.     

Sliding mode observer–controller design for uncertain Markovian jump systems with time delays

This paper proposes a sliding mode observer–controller design method for uncertain Markovian jump systems with time delays and uncertain switching probabilities. Both the structures of a sliding mode observer and a sliding mode controller are given. By the mode‐dependent Lyapunov functional approach, a sufficient condition for the stochastic stability of the closed‐loop system is given, which can be converted into a convex optimization problem. The reachability of the sliding surfaces in both the estimation error space and the state estimate space can be ensured by the presented control scheme. Finally, the effectiveness of the proposed design method is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd.     

DESIGN MODIFICATION OF SLIDING MODE OBSERVERS FOR UNCERTAIN MIMO SYSTEMS WITHOUT AND WITH TIME‐DELAY

In this paper, the sliding mode observers design techniques for MIMO and as a simple example for SISO systems are systematically advanced as a first purpose. Design parameters are selected such that on the defined switching surface always is generated asymptotically stable sliding mode. Moreover, observer state error dynamics is globally robustly asymptotically stable. Then, advanced design techniques are generalized to the design of a new modification of sliding mode observers for uncertain MIMO systems with time‐delay. Robust sliding and global asymptotic stability conditions are derived by using Lyapunov‐Krasovskii V‐functional method. By these conditions observer parameters are designed such that an asymptotically stable sliding mode always is generated in observer and observer state error dynamics is robustly globally asymptotically stable. The main results are formulated in terms of Lyapunov matrix equations and inequalities. Design example for AV‐8A Harrier VTOL aircraft with simulation results using MATLAB‐Simulink show the effectiveness of proposed design approaches.     

Fixed-time sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems

This paper investigates a fixed-time convergence issue using the sliding mode observer-based controller for a class of uncertain nonlinear double integrator systems. This observer-based controller is designed assuming that only the first state measurement is available and there is no information about external disturbances and modeling uncertainties. A new form of sliding mode observer in combination with a sliding mode controller is designed to estimate unmeasured state and unknown disturbances and uncertainties as well as provide the estimated data in the control law. A novel form of sliding surfaces for the robust observer-based controller is proposed for which fixed-time convergence is guaranteed to achieve trajectory tracking. In the proposed fixed-time scheme, the bound on the settling time is user-defined using design parameters regardless of the system's initial conditions. The control law and observer law are designed such that the chattering issue is alleviated in the control signal. The stability analysis of the closed-loop system using the observer-based controller is established via the Lyapunov theory. The validity of the controller design is tested by applying and simulating an example of a robot manipulator in Simulink/MATLAB. The superiority of the proposed method is demonstrated by comparing it with two other methods from the relevant literature.     

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.     

Design of decentralised adaptive sliding mode controllers for large-scale systems with mismatched perturbations

Based on the Lyapunov stability theorem, a methodology for designing a decentralised adaptive sliding mode control scheme is proposed in this paper. This scheme is implemented for a class of large-scale systems with both matched and mismatched perturbations. The perturbations and the interconnection terms are assumed to be norm bounded under certain mild conditions. The decentralised sliding surfaces with adaptive mechanisms embedded are specially designed for each subsystem, so that when each subsystem enters the sliding mode, the mismatched perturbations and the effects of interconnections can be effectively overcome and achieve asymptotic stability. The decentralised controller with embedded adaptive mechanisms is capable of driving the controlled state trajectories into the designated sliding surface in finite time. This is also achieved without the knowledge of upper bounds of the perturbations except those of the uncertainties in the input channels. A numerical example is included to demonstrate the feasibility of the proposed control scheme.     

An adaptive solution for robust control based on integral high‐order sliding mode concept

A new high‐order sliding mode controller is proposed. The main features are gain adaptivity and the use of integral sliding mode concept. The gain adaptation allows a reduction of the chattering and gives a solution to control uncertain nonlinear systems whose the uncertainties/perturbations have unknown bounds. The concept of real high‐order sliding mode detector is introduced given that it plays a key role in the adaptation law of the gain. This new control approach is applied by simulation to an academic example to evaluate its efficiency. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

High order sliding mode observer for linear systems with unbounded unknown inputs

A global observer is designed for strongly detectable systems with unbounded unknown inputs. The design of the observer is based on three steps. First, the system is extended taking the unknown inputs (and possibly some of their derivatives) as a new state; then, using a global high-order sliding mode differentiator, a new output of the system is generated in order to fulfil, what we will call, the Hautus condition, which finally allows decomposing the system, in new coordinates, into two subsystems; the first one being unaffected directly by the unknown inputs, and the state vector of the second subsystem is obtained directly from the original system output. Such decomposition permits designing of a Luenberger observer for the first subsystem, which satisfies the Hautus condition, i.e. all the outputs have relative degree one w.r.t. the unknown inputs. This procedure enables one to estimate the state and the unknown inputs using the least number of differentiations possible. Simulations are given in order to show the effectiveness of the proposed observer.     

滞后中立型关联控制系统的滑动模变结构控制*

本文设计了滞后中立型非线性关联系统的滑动曲面和分菜滑动模型控制器，每个子系统的控制器仅用到其局部状态信息，在滑动曲面和分散滑动模控制器可实现的条件下，在子上Ｒｉｃｃａｔｉ方程的描述和到了可实现滑动模控制器的一个充分条件，该条件等价于由分散和状态反馈镇定的条件，从而本文的结果比以前的工作更合适，且可实现减少设计的保守性。     

基于高增益鲁棒滑模观测器的故障检测和隔离

针对一类同时具有执行器和传感器故障的不确定线性系统,讨论了基于观测器的故障检测和隔离方法.首先,通过引入增维向量,使得在构造的增维系统中,故障向量包含了原系统的执行器故障和传感器故障.通过构造辅助输出使增维系统的观测器匹配条件得以满足,同时设计高增益滑模观测器对辅助输出进行估计.然后,对增维系统构造鲁棒滑模观测器并用作故障检测观测器,通过滑模控制项来抑制干扰,使观测器具有鲁棒性.在此基础上,结合多观测器故障隔离思想,提出了可以同时对执行器故障和传感器故障进行检测和隔离的方法. 最后,通过对一个五阶飞行器模型进行仿真,证明了所提方法的有效性.     

Adaptive Observer‐Based Global Sliding Mode Control for Uncertain Discrete‐Time Nonlinear Systems with Time‐Delays and Input Nonlinearity

A new discrete‐time adaptive global sliding mode control (SMC) scheme combined with a state observer is proposed for the robust stabilization of uncertain nonlinear systems with mismatched time delays and input nonlinearity. A state observer is developed to estimate the unmeasured system states. By using Lyapunov stability theorem and linear matrix inequality (LMI), the condition for the existence of quasi‐sliding mode is derived and the stability of the overall closed‐loop system is guaranteed. Finally, simulation results are presented to demonstrate the validity of the proposed scheme.     

Decentralized sliding mode control for a class of nonlinear interconnected systems by static state feedback

In this paper, a class of interconnected systems is considered, where the nominal isolated systems are fully nonlinear. A robust decentralized sliding mode control based on static state feedback is developed. By local coordinate transformation and feedback linearization, the interconnected system is transformed to a new regular form. A composite sliding surface which is a function of the system state variables is proposed and the stability of the corresponding sliding mode dynamics is analyzed. A new reachability condition is proposed and a robust decentralized sliding mode control is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. Both uncertainties and interconnections are allowed to be unmatched and are assumed to be bounded by nonlinear functions. The bounds on the uncertainties and interconnections have more general forms when compared with existing work. A MATLAB simulation example is used to demonstrate the effectiveness of the proposed method.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive sliding mode observer‐based synchronization for uncertain chaotic systems

This paper investigates the synchronization problem for a class of uncertain chaotic systems. Only partial information of the system states is known. An adaptive sliding mode observer‐based slave system is designed to synchronize a given chaotic master system with unknown parameters and external disturbances. Based on the Lyapunov stability theorem, the global synchronization between the master and slave systems is ensured. Furthermore, the structure of the slave system is simple and the proposed adaptive sliding mode observer‐based synchronization scheme can be implemented without requiring a priori knowledge of upper bounds on the norm of the uncertainties and external disturbances. Simulation results demonstrate the effectiveness and robustness of the proposed scheme. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society