Output-feedback model-reference sliding mode control of uncertain multivariable systems

This note considers the robust output tracking problem using a model-reference sliding mode controller for linear multivariable systems of relative degree one. It is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties. The strategy is based on output-feedback unit vector control to generate sliding mode. The only required a priori information about the plant high frequency gain matrix K/sub p/ is the knowledge of a matrix S/sub p/ such that -K/sub p/S/sub p/ is Hurwitz which relaxes the positive definiteness requirement usually needed by other methods.     

线性不确定广义时滞系统的鲁棒无源滤波器设计

研究一类线性不确定广义时滞系统的鲁棒无源滤波器设计问题．系统中所含的不确定性假设是未知且范数有界的．利用线性矩阵不等式方法和Lyapunov函数方法相结合,给出了广义滤波增广系统时滞独立的鲁棒无源滤波器的存在条件．设计目标是对所有的不确定性,滤波增广系统是正则、稳定、无脉冲的,且满足所提的无源滤波性能指标．所提的滤波器设计问题可转化为标准的线性矩阵不等式的求解问题,并可推广到多时滞情况．数值例子验证了设计方法的可行性．     

Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations

This paper studies the robust fuzzy control problem of uncertain discrete-time nonlinear Markovian jump systems without mode observations. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a discrete-time nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. As a result, an uncertain Markovian jump fuzzy system (MJFS) is obtained. A stochastic fuzzy Lyapunov function (FLF) is employed to analyze the robust stability of the uncertain MJFS, which not only is dependent on the operation modes of the system, but also directly includes the membership functions. Then, based on this stochastic FLF and a non-parallel distributed compensation (non-PDC) scheme, a mode-independent state-feedback control design is developed to guarantee that the closed-loop MJFS is stochastically stable for all admissible parameter uncertainties. The proposed sufficient conditions for the robust stability and mode-independent robust stabilization are formulated as a set of coupled linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, it is also demonstrated, via a simulation example, that the proposed design method is effective.     

基于扰动补偿的无微分模型参考自适应控制系统设计

针对一类含有参数不确定性和未知非线性扰动的系统,本文提出一种基于扰动补偿的无微分模型参考自适应控制方法,实现系统输出对参考模型输出信号的高精度跟踪.首先,利用被控对象模型信息设计扰动估计器,对系统非线性扰动进行在线估计;其次,基于非线性扰动估计值设计参考模型和无微分参数更新律,构建无微分模型参考自适应控制器,建立基于扰动补偿和状态反馈的自适应控制律,以消除参数不确定性和非线性扰动对系统输出的影响,保证系统输出对参考模型输出的准确跟踪;然后,给出闭环系统误差信号收敛条件和控制器参数整定方法;最后,通过数值仿真验证所提方法的有效性和优越性.     

Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds

A feedback control-design problem involving structured plant parameter uncertainties is considered. Two robust control-design issues are addressed. The Robust Stability Problem involves deterministic bounded structured parameter variations, while the Robust Performance Problem includes, in addition, a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations. The optimal projection approach to fixed-order, dynamic compensation is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design. The principle result is a sufficient condition for characterizing dynamic controllers of fixed dimension which are guaranteed to provide both robust stability and performance. The sufficient conditions involve a system of modified Riccati and Lyapunov equations coupled by an oblique projection and the uncertainty bounds. The full-order result involves a system of two modified Riccati equations and two modified Lyapunov equations coupled by the uncertainty bounds. The coupling illustrates the breakdown of the separation principle for LQG control with structured plant parameter variations. Supported in part by the Air Force Office of Scientific Research under Contract F49620-86-C-0002.     

A globally stable saturated desired compensation adaptive robust control for linear motor systems with comparative experiments

The recently proposed saturated adaptive robust controller is integrated with desired trajectory compensation to achieve global stability with much improved tracking performance. The algorithm is tested on a linear motor drive system which has limited control effort and is subject to parametric uncertainties, unmodeled nonlinearities, and external disturbances. Global stability is achieved by employing back-stepping design with bounded (virtual) control input in each step. A guaranteed transient performance and final tracking accuracy is achieved by incorporating the well-developed adaptive robust controller with effective parameter identifier. Signal noise that affects the adaptation function is alleviated by replacing the noisy velocity signal with the cleaner position feedback. Furthermore, asymptotic output tracking can be achieved when only parametric uncertainties are present.     

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.     

广义离散系统的状态反馈鲁棒H∞控制及仿真

针对一类范数有界参数不确定性的广义离散线性系统,研究了该系统的状态反馈鲁棒H∞控制问题.利用线性矩阵不等式(LMI)的方法,得到了问题可解的条件,并给出了相应的状态反馈控制律.在一定条件下,所得的状态反馈鲁棒H∞控制律使广义离散线性系统对所有容许的不确定性参数,能够保证闭环系统正则、具有因果关系并且渐进稳定,同时其传递函数矩阵能够满足给定的H∞性能指标.正常离散线性系统的相对应结果可作为论文结果的特殊形式.仿真例子验证了该方法的正确性.     

一类欠驱动机械系统的全局鲁棒控制

针对具有质心参数不确定性的Acrobot系统,提出一种全局的鲁棒控制方法.首先,给出系统具有质心参数不确定的系统模型;其次在摇起区,分析系统不确定性条件下的能量变化情况,基于能量不断增加的思想设计出摇起控制器;在平衡区,把系统的不确定性转化为模型状态矩阵的不确定性,引入H标准设计方法,得出存在H状态反馈控制器的充要条件,通过求解线性矩阵不等式使系统有效地克服不确定性的影响实现二次稳定;最后通过仿真实验验证了所提方法的有效性.     

Robust energy-to-peak filter design for stochastic time-delay systems

This paper considers the robust energy-to-peak filtering problem for uncertain stochastic time-delay systems. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time-varying. Attention is focused on the design of full-order and reduced-order filters guaranteeing a prescribed energy-to-peak performance for the filtering error system. Sufficient conditions are formulated in terms of linear matrix inequalities (LMIs), and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. In addition, the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters. The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, have been taken into consideration, with convex optimization problems obtained for the design of desired robust energy-to-peak filters.     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.     

Robust tracking enhancement of robot systems including motordynamics: a fuzzy-based dynamic game approach

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance     

On robust stabilization of Markovian jump systems with uncertain switching probabilities

This brief paper is concerned with the robust stabilization problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix. First, a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities. Then, a sufficient condition is proposed for the design of robust state-feedback controllers. A globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively. Finally, a numerical simulation is used to illustrate the developed theory.     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with °- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper.     

Robust fault detection for networked control systems with nonlinear disturbances and imperfect measurements

In this article, the robust fault detection (FD) problem is investigated for networked control systems with nonlinear disturbances and imperfect measurements. Under the consideration of packet-dropout compensation, a new measurement model is proposed to take the time-varying delay, random packet dropout and quantisation effect into account simultaneously. After properly augmenting the states of the original system and the FD filter, the robust FD problem is formulated as an auxiliary H _∞ filtering problem for a stochastic parameter system with time-varying delays and uncertainties. A sufficient condition for the existence of the robust FD filter is derived in terms of linear matrix inequalities, which depends on both the network status and the quantisation density. A numerical example is provided to illustrate the effectiveness of the proposed method.