Robust H2 estimation and control

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with normbounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities ( LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared tothe existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.     

不确定广义系统的输出反馈鲁棒预测控制

针对一类具有范数有界不确定性的广义系统,当系统状态不可测时,提出了一种基于输出反馈的鲁棒预测控制器综合算法．采用ＬＭＩ方法以及变量变换思想,将无限时域“最小最大”优化问题转化为线性规划问题．确定出一组分段连续的输出反馈控制序列,给出了输出反馈控制律存在的充分条件,证明了优化问题在初始时刻的可行解可以保证广义闭环系统是渐近稳定且正则无脉冲的．仿真实例验证了所提出方法的有效性．     

Robust H∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers

The problems of robust stability and robust stabilization of uncertain linear systems with distributed delay occurring in the state variables are studied in this paper. The essential requirement for the uncertainties is that they are norm-bounded with known bounds. Conditions for the robust stability of distributed time delay systems are given and a design method for the robust stabilizing control law of the uncertain systems is presented. The proposed method is applied to the stabilization of combustion in the chamber of a liquid monopropellant rocket motor. It is found that the combustion can be robustly stabilized when the two parameters pressure exponent γ and maximal time lag r vary in specified intervals, respectively.     

Robust optimal control of bilinear DC-DC converters

This paper addresses the control problem of dc-dc converters. The control law synthesis considered here exploits the potential of LMI-based control approaches, which allow to cope with model uncertainty, disturbances and bilinearities to synthesize simple state-feedback controllers with a priori guarantee of stability in a large domain of initial and operating conditions. The aim of the paper is to contribute with a robust control framework to deal with the common requirements of regulated dc-dc converters. The correctness of the results has been verified both with numerical simulations and with experimental measurements from a laboratory prototype.     

Robust control of continuous-time Markov jump linear systems

This paper is concerned with the problem of designing robust H₂ state-feedback controllers for continuous-time Markov jump linear systems subject to polytopic-type parameter uncertainty. Based on the parameter-dependent Lyapunov function approach, a new method for designing robust H₂ controllers is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed design method.     

参数不确定性广义周期时变系统的鲁棒稳定性分析

基于广义周期时变系统允许的充分必要条件,提出了参数不确定性广义周期时交系统鲁棒稳定的概念,并得到了该类系统鲁棒稳定的充分必要条件．研究在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法．引入广义周期时变系统二次稳定的概念,讨论了二次稳定性与鲁棒稳定性的关系．最后通过数值算例说明了所得的主要结果,     

Robust adaptive control for uncertain systems with discrete and distributed delays

In this paper, a robust adaptive control scheme is proposed for the stabilization of uncertain linear systems with discrete and distributed delays and bounded perturbations. The uncertainty is assumed to be an unknown continuous function with norm-bounded restriction. The perturbation is sector-bounded. Combining with the liner matrix inequality method, neural networks and adaptive control, the control scheme ensures the exponential stability of the closed-loop system for any admissible uncertainty.     

Robust state estimation for a class of uncertain time-delay systems

This paper considers a robust state estimation problem for a class of uncertain time-delay systems. In this problem, the noise and uncertainty are modelled deterministically via an integral quadratic constraint. The robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint. This set is found to be an ellipsoid which is constructed via a linear state estimator.     

一类基于观测器的网络控制系统鲁棒控制器设计

研究一类基于状态观测器的网络控制系统鲁棒稳定性和鲁棒控制器设计问题.考虑传感器时钟驱动、控制器和执行器事件驱动以及小于等于一个采样周期的不确定时延,建立了基于状态观测器的网络控制系统增广模型.利用线性矩阵不等式方法推导出该系统鲁棒稳定的条件,进一步给出了鲁棒控制律和状态观测器设计方法.数值仿真算例证明了分析方法和结果的有效性.     

Robust filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions

This paper addresses the design of robust filters for linear continuous-time systems subject to parameter uncertainty in the state-space model. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. Two methods based on parameter-dependent Lyapunov functions are proposed for designing linear stationary asymptotically stable filters that assure asymptotic stability and a guaranteed performance, irrespective of the uncertain parameters. The proposed filter designs are given in terms of linear matrix inequalities which depend on a scalar parameter that should be searched for in order to optimize the filter performance.     

Robust stabilization of Markovian delay systems with delay-dependent exponential estimates

A sufficient condition for the exponential estimates of a class of Markovian systems with time delay is established for the first time in terms of the linear matrix inequality (LMI) technique. The estimating procedure is implemented by solving an LMI. The proposed condition is also extended to the uncertain case. Moreover, a state feedback stabilizing controller which makes the closed-loop system exponentially stable with a prescribed lower bound of decay rate is designed. Numerical examples are provided to illustrate the effectiveness of the theoretical results.     

On Robust H2 Estimation

The problem of state estimation for uncertain systems has attracted a recurring interest in the past decade. In this paper, we shall give an overview on some of the recent development in the area by focusing on the robust H2 (Kalman) filtering of uncertain discrete-time systems. The robust H2 estimation is concerned with the design of a fixed estimator for a family of plants under consideration such that the estimation error covariance is of a minimal upper bound. The uncertainty under consideration includes norm-bounded uncertainty and polytopic uncertainty. In the finite horizon case, we shall discuss a parameterized difference Riccati equation approach for systems with norm-bounded uncertainty and pinpoint the difference of state estimation between systems without uncertaintyand those with uncertainty. In the infinite horizon case, we shall deal with both the norm-bounded and polytopic uncertainties using a linear matrix inequality (LMI) approach. In particular, we shalldemonstrate how the conservatism of design can be improved using a slack variable technique. We also propose an iterative algorithm to refine a designed estimator. An example will be given to compareestimators designed using various techniques.     

Sensor-network-based robust distributed control and estimation

This paper proposes a novel distributed estimation and control method for uncertain plants. It is of application in the case of large-scale systems, where each control unit is assumed to have access only to a subset of the plant outputs, and possibly controls a restricted subset of input channels. A constrained communication topology between nodes is considered so the units can benefit from estimates of neighboring nodes to build their own estimates. The paper proposes a methodology to design a distributed control structure so that the system is asymptotically driven to equilibrium with L₂-gain disturbance rejection capabilities. A difficulty that arises is that the separation principle does not hold, as every single unit ignores the control action that other units might be applying. To overcome this, a two-stage design is proposed: firstly, the distributed controllers are obtained to robustly stabilize the plant despite the observation errors in the controlled output. At the second stage, the distributed observers are designed aiming to minimize the effects of the communication noise in the observation error. Both stages are formulated in terms of linear matrix inequalities. The performance is shown on a level-control real plant.     

Robust analysis and control for a class of uncertain nonlinear discrete-time systems

This paper deals with the problem of robust analysis and control of a class of nonlinear discrete-time systems with (constant) uncertain parameters. For the analysis problem we use a polynomial Lyapunov function and we generalize, for nonlinear systems, the “extended stability” notion proposed by Oliveira et al. (1999) in the context of linear discrete-time uncertain systems. As a result, we propose an LMI optimization problem to maximize an estimate of the domain of attraction, and also extend this approach to the synthesis problem by considering parameter-dependent Lyapunov functions and nonlinear multipliers. Numerical examples illustrate the approach and show its potential for solving analysis and control problems of nonlinear discrete-time systems.     

Design of state estimators for uncertain linear systems using quadratic boundedness

The notion of quadratic boundedness, which allows one to address the stability of a dynamic system in the presence of bounded disturbances, is applied to the design of state estimators for discrete-time linear systems with polytopic uncertainties. Necessary and sufficient stability conditions are stated and upper bounding sequences on the estimation error are derived. For the purpose of design, such conditions can be expressed in terms of linear matrix inequalities (LMIs), thus guaranteeing the numerical tractability. Simulation results are reported to show the effectiveness of the approach.     

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 control and estimation of clutch-to-clutch shifts

Clutch-to-clutch shifts are ubiquitous in automatic transmissions, motivating the need for formal and robust methods for controlling these shifts. Limited sensing in production transmissions poses a severe hurdle for feedback control of these gearshifts. In the current study, nonlinear estimation methods are developed to compensate for limited sensing, and enable model-based closed loop control of the torque and inertia phases of shifts by manipulation of clutch pressures. During the torque phase, the offgoing clutch is controlled to emulate a one-way clutch, which ensures smooth coordination of the two clutches and reduced overall variation in the output shaft torque during the gearshift. During the inertia phase, the oncoming clutch is controlled to ensure smooth engagement at lock-up, resulting in reduction of shock and subsequent driveline oscillations. Controller performance is evaluated through numerical simulation of the proposed observer based controller on an experimentally validated high order model of a stepped production automatic transmission. The results show that shift control objectives were met by the proposed estimation and control strategy in the presence of appreciable model uncertainty and speed sensor noise, thus validating the robustness and practical effectiveness of the controller. Also, the proposed model-based controller was shown to be effective in controlling gearshifts at different power-levels (at different throttle openings), which establishes effectiveness of the same over a wide range of operating conditions.