Robust H∞ control for uncertain discrete stochastic time-delay systems

This paper deals with the problems of robust stabilization and robust H_∞ control for discrete stochastic systems with time-varying delays and time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed-loop system for all admissible uncertainties, while for the robust H_∞ control problem, a state feedback controller is designed such that, in addition to the requirement of the robust stochastic stability, a prescribed H_∞ performance level is also required to be satisfied. A linear matrix inequality (LMI) approach is developed to solve these problems, and delay-dependent conditions for the solvability are obtained. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. An example is provided to demonstrate the effectiveness of the proposed approach.     

A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems

This paper investigates the robust H_∞ control and non-fragile control problems for Takagi-Sugeno (T-S) fuzzy systems with linear fractional parametric uncertainties. The robust H_∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H_∞ performance of the resulting closed-loop system is ensured. And the non-fragile H_∞ control problem is to design a state feedback controller with parameter uncertainties. Based on the linear matrix inequality (LMI) approach, new sufficient conditions for the solvability of the two problems are obtained. It is shown that the desired state feedback fuzzy controller can be constructed by solving a set of LMIs. Numerical examples are also provided to demonstrate the effectiveness of the proposed design method.     

Modeling and robust force control of constrained one-link flexible arms

In this article modeling and robust force control of constrained flexible one-link arms on the basis of a distributed parameter model are discussed. Since the tip of the flexible arm contacts a given constraint surface, a constraint condition should be satisfied. By using the Lagrange multiplier method and the Hamilton's principle, we derive dynamic equations of the joint angle, the vibration of the flexible arm, and the constraint force. The boundary condition of the derived distributed parameter system is related to the contact force and is nonhomogeneous. We introduce a change of variables to derive a homogeneous boundary condition. On the basis of a finite-dimensional modal model of the distributed parameter system, we analyze the stability of the force feedback by using the root locus technique and the compliance control. To compensate the spillover instability an optimal controller with low-pass property and a robust H_∞ controller are constructed. Experiments have been carried out and results confirm that the controllers perform remarkably well. © 1998 John Wiley & Sons, Inc.     

Delay-dependent robust stabilization and H ∞ control for uncertain stochastic T-S fuzzy systems with discrete interval and distributed time-varying delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno (T-S) fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities (LMIs) and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.     

Finite Frequency Vibration Suppression for Space Flexible Structures in Tip Position Control

This paper presents a novel control strategy for the tip position and vibration control of a class of space flexible structures. The proposed control algorithm consists of finite frequency H_∞ vibration control technique and fractional-order PD ^v control technique. More specially, a new finite frequency H_∞ controller working in the inner feedback loop is proposed to suppress vibration modes and external disturbances, and a new fractional-order PD ^v controller is developed in the outer feedback loop to guarantee the desired position tracking performance. Compared with conventional methods, the proposed one could achieve better control results. Finally, an illustrative example is presented to demonstrate the robustness and effectiveness of the proposed composite control strategy.     

输入有界的自由漂浮柔性空间机器人轨迹跟踪控制

针对自由漂浮柔性空间机器人轨迹跟踪控制问题, 首先利用拉格朗日和假设模态法建立了动力学模型. 分析系统动力学模型, 综合考虑欠驱动、柔性振动等特点, 将其简化为一种带有柔性振动扰动完全可控的动力学模型; 在此基础上, 考虑控制输入受限, 提出一种自适应状态反馈控制策略. 该策略采用自适应技术实时在线学习柔性振动扰动参数, 从而保证控制律对柔性振动扰动具有良好的鲁棒性; 最后, 基于Lyapunov方法证明了该控制策略能够实现关节期望轨迹的跟踪. 仿真验证了该控制策略对控制输入受限系统轨迹跟踪控制的有效性和可靠性.     

Robust stabilization of nonlinear systems by H∞ state feedback

This paper is concerned with robust stabilization of nonlinear systems with unstructured uncertainty via state feedback. First, a robust stability condition is given for a closed loop system which is composed of a nonlinear nominal system and an unstructured uncertainty. Second, based on the obtained robust stability condition, a sufficient condition for robust stabilization by state feedback is given in terms of the solvability of some H_∞ state feedback control.     

A new calculation method of feedback controller gain for bilinear paper-making process with disturbance

This paper presents a new method to calculate the feedback control gain for a class of multivariable bilinear system, and also applied this method on the control of two sections of paper-making process with disturbance. The robust H∞ control problem is to design a state feedback controller such that the robust stability and a prescribed H∞ performance of the resulting closed-loop system are ensured. The controller turns out to be robust with respect to the disturbance in the plant. Utilizing the Schur complement and some variable transformations, the stability conditions of the multivariable bilinear systems are formulated in terms of Lyapunov function via the form of linear matrix inequality (LMI). The gain of controller will be calculated via LMI. Finally, the application examples of a headbox section and a dryer section of paper-making process are used to illustrate the applicability of the proposed method.     

Intelligent fault-tolerant system of vibration control for flexible structures

This paper describes an intelligent fault-tolerant control method for vibration control of flexible structures. We consider a case where the fault phenomena of the control system for flexible structures can be treated as a change of system parameters. Therefore, the adaptive control method can be applied to a vibration control system for flexible structures with a fault. In this paper, a neural network (NN) adaptive control system is used to compensate for the change in the parameters of a plant with a fault. When the characteristics of the plant and of a nominal model have been agreed by a NN adaptive control system, the control method designed for the nominal model, such as decoupling feedback control or linearizing feedback control, can be used even if the change in the system parameters has been caused by a fault. To confirm the effectiveness of the proposed fault-tolerant control method, the simulational results from a 5-link robotic arm are shown at the end of the paper. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

H∞ control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions

This paper presents the issue of robust disturbance attenuation and robust asymptotic stability problem for finite-dimensional linear parameter-dependent state-delayed systems. The use of polynomial parameter-dependent quadratic Lyapunov functions and linear matrix inequalities (LMIs) formulations for robust H _∞ control are considered. It is shown that the state feedback control can be determined to guarantee the stability of the closed-loop system independently of the time-delay. We present an illustrative example to demonstrate the applicability of the proposed design approach.     

A robust H ∞ control approach for a class of networked control systems with sampling jitter and packet-dropout

This paper is concerned with the robust H _∞ control problem for a class of networked control systems (NCSs) with sampling jitter, short time-varying delays and packet-dropouts. By considering state feedback controller, the close-loop NCS is described as a discrete-time linear switched system model with uncertainties. Based on the linear matrix inequality (LMI) approach, a robust H _∞ condition is proposed to solve the H _∞ stability and stabilization problems for the considered NCS. An illustrative example is provided to demonstrate the effectiveness of the proposed theoretical results.     

Dynamics and Noncollocated Model‐Free Position Control for a Space Robot with Multi‐Link Flexible Manipulators

In this paper, both the dynamics and noncollocated model‐free position control (NMPC) for a space robot with multi‐link flexible manipulators are developed. Using assumed modes approach to describe the flexible deformation, the dynamic model of the flexible space robotic system is derived with Lagrangian method to represent the system dynamic behaviors. Based on Lyapunov's direct method, the robust model‐free position control with noncollocated feedback is designed for position regulation of the space robot and vibration suppression of the flexible manipulators. The closed‐loop stability of the space robotic system can be guaranteed and the guideline of choosing noncollocated feedback is analyzed. The proposed control is easily implementable for flexible space robot with both uncertain complicated dynamic model and unknown system parameters, and all the control signals can be measured by sensors directly or obtained by a backward difference algorithm. Numerical simulations on a two‐link flexible space robot are provided to demonstrate the effectiveness of the proposed control.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

Nonlinear control design for linear differential inclusions via convex hull of quadratics

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions (LDIs). A recently introduced non-quadratic Lyapunov function, the convex hull of quadratics, will be used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least L₂ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Numerical examples demonstrate the advantages of using nonlinear feedback control over linear feedback control for LDIs. It is also observed through numerical computation that nonlinear control strategies help to reduce control effort substantially.     

带有超大型挠性网状天线航天器姿控系统的参数化多目标设计

本文研究了带有超大型挠性附件的卫星的姿态控制问题.关于挠性航天器振动抑制与姿态控制,绝大多数已有的控制方法都是针对某一单一指标提出的.然而工程上要同时兼顾精度、快速性、平稳性、挠性部件的振动抑制以及各种鲁棒性,因此挠性航天器的姿态控制系统设计实际上是一个典型的多目标设计问题.本文针对具有超大挠性网状天线卫星的俯仰通道姿态系统,提出了一种基于输出反馈的鲁棒极点配置的参数化多目标设计方法.首先给出了系统能控与能观的充分必要条件,然后给出了动态补偿器以及特征向量矩阵的参数化表达,并在此基础上进一步对自由参向量进行了多目标优化,使得控制系统具有:1)配置到期望区域的极点; 2)较低的特征值灵敏度;3)较强的高阶未建模动态抑制能力; 4)尽可能小的控制增益.最后,本文根据卫星工程参数进行了控制器设计与仿真验证,仿真结果表明本文提出的方法可以在动态响应、高阶未建模动态抑制能力、控制量峰值等方面优于传统的PID控制器.     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity

This brief proposes a robust control algorithm for stabilization of a three-axis stabilized flexible spacecraft in the presence of parametric uncertainty, external disturbances and control input nonlinearity/dead-zone. The designed controller based on adaptive variable structure output feedback control satisfies the global reaching condition of sliding mode and ensures that the system state globally converges to the sliding mode. A modified version of the proposed control law is also designed for adapting the unknown upper bounds of the lumped uncertainties and perturbations. The stability of the system under the modified control law is established. Numerical simulations show that the precise attitude pointing and vibration suppression can be accomplished using the derived robust or adaptive controller.     

Decentralized robust H<Subscript>∞</Subscript> output feedback control for value bounded uncertain large-scale interconnected systems

In this paper, decentralized robust H_∞ output feedback control problem for large-scale interconnected system with value bounded uncertainties in the state, control input and interconnection matrices is investigated. A new bounded real lemma for the large-scale interconnected systems is derived by Lyapunov stability theory and linear matrix inequality method. Based on the new bounded real lemma, a sufficient condition expressed as matrix inequalities for the existence of a decentralized robust H_∞ output feedback controller is obtained. The controller which enables the closed-loop large-scale system robust stable and satisfies the given H_∞ performance is designed through a homotopy iterative method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Structural synthesis of multivariable controllers

In this paper the problem of achieving a desired transfer function matrix H_d(s) between external inputs and controlled outputs in a linear multivariable system by connecting proper, stabilizing controllers between measured outputs and control inputs is solved in both transfer function and state space settings. The class H_d of achievable transfer functions is directly and constructively characterized via the theory of transfer function valuations. For each H_d(s)ϵH_d, the class of synthesizing controllers is determined. Similar valuation conditions are given for the asymptotic tracking and disturbance rejection problem in which H_d(s) is only partially specified. These results extend and complement earlier results. The state space geometric solution of the problem of achieving a desired H_d(s) is obtained by formulating it as an equivalent output feedback disturbance rejection problem. A constructive solvability condition in terms of a pair of measurement and control invariant subspaces is given. This requires a nontrivial generalization of the notion of (C, A, B) pairs. An H_d(s) is shown to be admissible if and only if it induces an appropriate pair of invariant subspaces. The signal flow structure and certain factorizability conditions for a robust synthesis of the output feedback disturbance rejection problem are also given which extend earlier results on robust state feedback disturbance rejection. It is shown that every compensator corresponds to a state feedback control law implemented by an unknown input observer. The results of this paper are expected to be useful in the development of parameter optimization or other computer aided design algorithms where response specifications are to be traded against other design criteria such as sensitivity or stability margins since they explicitly characterize the algebraic variety H_d in which the response transfer function may lie.