Robust receding-horizon state estimation for uncertain discrete-time linear systems

An approach to robust receding-horizon state estimation for discrete-time linear systems is presented. Estimates of the state variables can be obtained by minimizing a worst-case quadratic cost function according to a sliding-window strategy. This leads to state the estimation problem in the form of a regularized least-squares one with uncertain data. The optimal solution (involving on-line scalar minimization) together with a suitable closed-form approximation are given. The stability properties of the estimation error for both the optimal filter and the approximate one have been studied and conditions to select the design parameters are proposed. Simulation results are reported to show the effectiveness of the proposed approach.     

Robust control for linear uncertain systems via linear quadratic state feedback

By the Lyapunov stability criterion and the algebraic Riccati equation, conditions of selecting the weighting matrices in the quadratic cost function are derived so that linear quadratic state feedback can exponentially stabilize a linear uncertain system, provided the uncertainties satisfy the so-called matching conditions and within a given bounding set. Furthermore, two simple but effective algorithms are proposed for systematically selecting the weighting matrices. The main features of this approach are that the uncertain system can be exponentially stabilized with prescribed exponential rate and no precompensator is needed. Two examples are given to illustrate the results.     

Robust state estimation for uncertain linear systems with deterministic input signals

In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.     

不确定系统鲁棒LQ设计的稳定裕度分析和工程应用研究

针对不确定线性系统, 研究鲁棒LQ设计的稳定裕度分析问题. 首先提出不确定系统α_0裕度稳定鲁棒界, 针对结构和非结构不确定系统, 分别给出了鲁棒LQ控制系统的鲁棒稳定裕度性分析方法, 进一步给出对结构不确定系统优化鲁棒界的算法. 最后是造纸打浆过程实例的鲁棒稳定裕度性分析以及相应仿真结果.     

基于依参数Lyapunov函数的不确定系统鲁棒稳定控制

采用依参数Lyapunov函数方法,对一类含不确定参数的连续线性系统进行鲁棒稳定控制器设计.通过引入合适的松弛变量扩大参数寻优空间,从而降低系统设计的保守性.此外,为进一步增加系统设计的自由度,对上述松弛变量进行参数化,从而获得保守性更低的稳定条件.仿真结果表明,所提出的控制器设计方法与现有方法相比对不确定参数具有更好的鲁棒性.     

Robust controllers for uncertain linear multivariable systems

This paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems. In the first part, it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties, and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty. In the second part, in contrast with the first part, it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known. The type of plant uncertainty is the so-called “stable-factor” uncertainty, and necessary and sufficient conditions are given for robust stabilization. In the third part, the model of uncertainty is a ball in the space of rational matrices metrized by the so-called graph metric, and sufficient conditions for robust stabilization are derived.     

Robust nonfragile Kalman filtering for uncertain linear systemswith estimator gain uncertainty

The note is concerned with the problem of a robust nonfragile Kalman filter design for a class of uncertain linear systems with norm-bounded uncertainties. The designed state estimator can tolerate multiplicative uncertainties in the state estimator gain matrix. The robust nonfragile state estimator designs are given in terms of solutions to algebraic Riccati equations. The designs guarantee known upper bounds on the steady-state error covariance. A numerical example is given to illustrate the results     

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.     

Robust observer-based controller design for state constrained uncertain systems: attractive ellipsoid method

ABSTRACT

This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers.     

Robust controllability of linear stochastic uncertain systems

The paper extends the concept of robust controllability via linear state feedback to stochastic uncertain systems. We show that the controllability of a stochastic uncertain system can be characterized using solutions to a game-type differential Riccati equation.     

Robust finite-time stabilisation of uncertain linear systems

This article deals with the problem of finite-time stability and stabilisation of uncertain linear systems. For linear time-varying systems subject to norm-bounded uncertainties some conditions for finite-time stability are provided. These conditions are expressed in terms of differential linear matrix inequalities. Then the problem of controller design is tackled, both for the state feedback and for the output feedback case; in both cases the controller can be found solving a suitable set of LMIs. A typical engineering case-study is included, to illustrate the applicability of the devised conditions.     

Robust tracking for a class of uncertain linear systems

Tracking of a specified nominal output within an arbitrary error bound in the presence of uncertainties is formulated in terms of topological neighbourhoods in the function space Lκ∞ [0, ∞). It is shown that an observer-based state-feedback controller can be constructed to effect the desired robust tracking for a class of multi-input-multi-output linear systems containing uncertain parameters. The controller and the observer gains for this structure are chosen on the basis of a quantitative pole placement. This pole placement is based on an inequality arrived at by separating the uncertain effects of the true system from a nominal set of equations containing no uncertainties. The applicability of the proposed scheme is illustrated by synthesizing a controller for a second-order system.     

Robust fault estimator design for uncertain networked control systems with random time delays: An ILMI approach

This paper investigates the problem of robust fault estimation for a class of uncertain networked control systems (NCSs) with random communication network-induced delays, which are described by Markov processes. Based on the Lyapunov-Razumikhin method, the existence of a delay-dependent fault estimator is given in terms of the solvability of bilinear matrix inequalities (BMIs). An iterative algorithm is proposed to change this non-convex BMI problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. The effectiveness of the proposed design methodology is verified by an internet-based DC motor test rig.     

Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator

In this article, one linear and one nonlinear robust control strategies are proposed for uncertain nonlinear continuous‐time systems with disturbances and state delays. The approaches are based on the uncertainty and disturbance estimator (UDE) introduced in 2004. In the case of a linear controller, the terms containing the nonlinear functions and time delays are treated as additional disturbances to the system. In the case of a nonlinear controller, both known and unknown delay scenarios are considered. In the case of an unknown time delay, the terms containing the delay are treated as additional disturbances to the system. The algorithms provide excellent tracking and disturbance rejection performance. Simulations are given to show the effectiveness of the strategies, first via a simple example and second via an application to a continuous stirred tank reactor system. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust stabilization for uncertain discrete singular systems with state delay

The robust stabilization problem for uncertain discrete singular time‐delay systems is addressed in this paper. In terms of strict linear matrix inequality and a finite sum inequality, a delay‐dependent criterion for the nominal systems to be admissible is obtained. Based on the criterion, a state feedback controller, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is regular, causal and stable, is constructed. An explicit expression for the desired controller is also given. The obtained results include both delay‐independent and delay‐dependent cases. Some numerical examples are introduced to show the effectiveness of the given results. Copyright © 2008 John Wiley & Sons, Ltd.     

参数摄动系统的鲁棒H ∞状态估计

基于Shaked提出的参数依赖型有界实引理，研究具有凸多面体参数摄动系统的鲁棒H∞状态估计问题．采用线性矩阵不等式技术，推导出此类不确定系统的全阶鲁棒H∞滤波器存在的充分条件，并将滤波器的设计转化为一个凸优化的求解问题．与传统的基于二次稳定的滤波方案相比，该滤波器设计方法具有较小的保守性．     

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.     

Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities

An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated.     

Optimal-observer design for linear dynamical systems with uncertain parameters

This paper presents a design technique for the synthesis of robust observers for linear dynamical systems with uncertain parameters. The perturbations under consideration are modelled as unknown but bounded disturbances and an ellipsoidal set-theoretic approach is used to formulate the optimal-observer design problem. The optimal criterion introduced here is the minimization of the ‘size’ of the bounding ellipsoid of the estimation error. A necessary and sufficient condition for this optimal design problem is presented. The results are stated in terms of a reduced-order observer with constant gain matrix, which is then determined by solving a matrix Riccati-type equation. Furthermore, a gradient-search algorithm is presented to find the optimal solution when the free parameter that enters in the construction of the bounding ellipsoids of the estimation error is considered as a design parameter. The effectiveness of the proposed approach is illustrated through a numerical example.