Robust practical output regulation for a class of uncertain linear minimum‐phase systems by output‐based event‐triggered control

In this paper, we consider the robust practical output regulation problem for a class of SISO uncertain linear minimum‐phase systems subject to external disturbances by an output‐based event‐triggered control law, where the reference inputs and the external disturbances are both generated by a so‐called exosystem with known dynamics. Our approach consists of two steps. First, on the basis of the internal model principle, we convert the problem into the robust practical stabilization problem of a well‐defined augmented system. Second, we design an output‐based event‐triggered mechanism and an output‐based event‐triggered control law to solve the stabilization problem, which in turn leads to the solvability of the original problem. What is more, we show that the event‐triggered mechanism prevents the Zeno behavior from happening. A numerical example is given to illustrate the design. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust control for uncertain linear delay systems via sliding mode control

In this paper, a novel discontinuous control strategy for robust stabilization of a class of uncertain multivariable linear time‐delay systems with delays in both the state and control variables is proposed. Two predictors are first designed to compensate the delay effect in the control input, and then an integral sliding mode control technique is applied to compensate partially the effect of the perturbation term. Finally, a nominal delay‐free component of the full control input is designed to stabilize the sliding mode dynamics. Conditions for the stability of the closed‐loop perturbed system are then derived. The proposed framework is then extended to the class of systems modeled in regular form. Some examples illustrate the feasibility of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust stability and performance analysis for uncertain linear systems—The distance measure approach

This paper presents readily applicable distance measures, robust stability margins and associated robust stability and robust performance theorems for three commonly used uncertainty structures (additive, input/output multiplicative, output/input inverse multiplicative). Besides providing robust stability results for a larger uncertainty class than previously reported (???_∞ instead of ???_∞), this paper also states robust performance theorems for the above uncertainty structures. In contrast to previous methods for robust performance analysis, they only require the computation of two infinity norms for every uncertain plant considered. The theorems in this paper enable practising engineers to choose the most suitable uncertainty structure for a family of uncertain plants, as illustrated through a physically motivated numerical example. Copyright © 2011 John Wiley & Sons, Ltd.     

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 adaptive fault‐tolerant control of uncertain linear systems via sliding‐mode output feedback

This paper is concerned with the robust adaptive fault‐tolerant compensation control problem via sliding‐mode output feedback for uncertain linear systems with actuator faults and exogenous disturbances. Mismatched disturbance attenuation is performed via H_∞ norm minimization. By incorporating the matrix full‐rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under the assumption that redundancy is available in the system. Without the need for a fault detection and isolation mechanism, an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H_∞ performance of closed‐loop systems. The effectiveness of the proposed design method is illustrated via a B747‐100/200 aircraft model. Copyright © 2014 John Wiley & Sons, Ltd.     

Constrained control for uncertain discrete-time linear systems

In this paper the problem of stabilizing uncertain linear discrete-time systems under state and control linear constraints is studied. Many formulations of this problem have been given in the literature. Here we consider the case of finding a linear state feedback control law making a given polytope in the state space positively invariant while the control remains bounded within prefixed values under the effect of all the uncertainty sequences belonging to a given polytope in the perturbations space. A necessary and sufficient condition for the existence of a solution of this problem is first given. This condition leads to a set of linear constraints which can be solved using linear programming tecniques by defining an appropriate objective function. A worked example shows the effectiveness of the proposed algorithm. © 1998 John Wiley & Sons, Ltd.     

An interval observer for uncertain continuous‐time linear systems

To design robust interval observers for uncertain continuous‐time linear systems, a new set‐integration approach is proposed to compute trajectory tubes for the estimation error. Because this approach, the order‐preserving condition on the dynamics of the estimation error is no longer required. Therefore, synthesis methods can be used to compute observer gains that reduce the impact of the system uncertainties on the accuracy of the estimated state enclosures. The performance of the proposed approach is showcased through illustrative numerical examples.     

An LMI approach to output‐feedback‐guaranteed cost control for uncertain time‐delay systems

This paper considers the problem of output‐feedback‐guaranteed cost controller design for uncertain time‐delay systems. The uncertainty in the system is assumed to be norm‐bounded and time‐varying. The time‐delay is allowed to enter the state and the measurement equations. A linear quadratic cost function is considered as a performance measure for the closed‐loop system. Necessary and sufficient conditions are provided for the construction of a guaranteed cost controller. These conditions are given in terms of the feasibility of LMIs which depend on a positive definite matrix and a scaling variable. A numerical algorithm is developed to search for a full order dynamic output‐feedback controller which minimizes the cost bound. Copyright © 2000 John Wiley & Sons, Ltd.     

不确定线性系统新的稳定性准则

研究了带有区间时滞的不确定系统的稳定性问题。通过采用时滞分割法,把时滞区间分割成任意两小段,并构造恰当的Lyapunov函数,利用积分不等式,得到了新的时滞相关的稳定性准则。通过数值例子验证了结果的有效性。     

Finite‐time control of switching linear systems: The uncertain resetting times case

In recent years, a number of papers have treated the problem of the finite‐time stability and stabilization of impulsive (or, more in general, switching) dynamical linear systems. Generally, these works assume that the sequence of switching (in the following resetting) times is a priori known. In this paper, we remove such (strong) assumption, so making the technique more appealing from the practical control engineering point of view. A first result provided in this work is a sufficient condition for finite‐time stability when the resetting times are known with a certain degree of uncertainty. Such condition requires the solution of a suitable feasibility problem based on coupled difference/differential LMIs. We show that as the uncertainty intervals reduce in size, our condition becomes less conservative, becoming necessary and sufficient in the certain case (i.e., the resetting instants are perfectly known). Eventually, we consider the conceptually different situation in which the resetting times are totally unknown, namely, the arbitrary switching case. The analysis results are then used to derive sufficient conditions for the existence of state‐feedback controllers that finite time stabilizes the closed‐loop system in the three cases mentioned earlier. A nontrivial example, considering the finite‐time control of the liquid levels into three interconnected reservoirs, shows the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust H∞ output‐feedback control of retarded state‐multiplicative stochastic systems

Linear, state‐delayed, continuous‐time systems are considered with both stochastic and norm‐bounded deterministic uncertainties in the state–space model. The problem of robust dynamic H_∞ output‐feedback control is solved, for the stationary case, via the input–output approach where the system is replaced by a nonretarded system with additional deterministic norm‐bounded uncertainties. A delay‐dependent result is obtained which involves the solution of a simple linear matrix inequality. In this problem, a cost function is defined which is the expected value of the standard H_∞ performance cost with respect to the stochastic parameters. A practical example taken from the field of guidance control is given that demonstrates the applicability of the theory. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust constrained predictive control of uncertain norm-bounded linear systems

A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to a number of LMI feasibility constraints which grows up only linearly with the control horizon length N. The general case of arbitrary N is considered. Closed-loop stability and feasibility retention over the time are proved and comparisons with robust multi-model (polytopic) MPC algorithms are reported.     

不确定离散线性系统的鲁棒单调反馈–前馈迭代学习控制

针对一类不确定离散线性系统,提出一种沿迭代方向鲁棒单调收敛和沿时间方向有界输入有界输出(bouned-input bounded-output,BIBO)稳定的反馈–前馈迭代学习控制策略.首先,将不确定反馈–前馈迭代学习系统表示为不确定二维Roesser模型系统;然后,把二维系统沿迭代方向的鲁棒单调收敛问题转化成一维系统的H∞干扰抑制控制问题,并给出系统的稳定性证明和用线性矩阵不等式(linear matrix inequality,LMI)表示的沿迭代方向鲁棒单调收敛的充分条件,该LMI充分条件不仅可以用于确定反馈–前馈控制器的增益矩阵,而且还可以保证系统沿时间轴方向是BIBO稳定的;最后,仿真结果证明了该反馈–前馈迭代学习控制策略的有效性.     

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.     

Robust H∞ control of uncertain linear impulsive stochastic systems

This paper develops robust stability theorems and robust H_∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous‐time stochastic dynamics and unstable/unstabilizable discrete‐time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete‐time dynamics, and the systems in which both the continuous‐time stochastic dynamics and the discrete‐time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell‐time condition. Then, a linear matrix inequality‐based approach to the design of a robust H_∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

An LMI approach to guaranteed cost control for uncertain linear neutral delay systems

This paper considers the problem of guaranteed cost control for uncertain neutral delay systems with a quadratic cost function. The system under consideration is subject to norm‐bounded time‐varying parametric uncertainty appearing in all the matrices of the state‐space model. The problem we address is the design of a state feedback controller such that the closed‐loop system is not only stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is given in terms of a linear matrix inequality (LMI). When this condition is feasible, the desired state feedback controller gain matrices can be obtained via convex optimization. An illustrative example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust non‐minimal order filter and smoother design for discrete‐time uncertain systems

This paper is concerned with the design of robust non‐minimal order H_∞ filters for uncertain discrete‐time linear systems. The uncertainty is assumed to be time‐invariant and to belong to a polytope. The novelty is that a convex filtering design procedure with Linear Matrix Inequality constraints is proposed to synthesize guaranteed‐cost filters with order greater than the order of the system. An H_∞‐norm bound for the transfer‐function from the system input to the filtering error is adopted as performance criterion. The non‐minimal order filters proposed generalize other existing filters with augmented structures from the literature and can provide better performance. An extension to the problem of robust smoothing is proposed as well. The procedure is illustrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.     

High‐order sliding‐mode observer for linear time‐varying systems with unknown inputs

In this article, an observer for linear time variant systems affected by unknown inputs is suggested. The proposed observer combines the deterministic least squares filter and the high‐order sliding‐mode differentiator to provide exact state reconstruction in spite of bounded unknown inputs and system instability. The cascade structure of the algorithm provides a correct state reconstruction for the class of linear time variant systems that satisfy the structural property of strong observability. Simulations illustrate the performance of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Reciprocal convex approach to output‐feedback control of uncertain LPV systems with fast‐varying input delay

Robust control of parameter‐dependent input delay linear parameter‐varying (LPV) systems via gain‐scheduled dynamic output‐feedback control is considered in this paper. The controller is designed to provide disturbance rejection in the context of the induced ‐norm or the norm of the closed‐loop system in the presence of uncertainty and disturbances. A reciprocally convex approach is employed to bound the Lyapunov‐Krasovskii functional derivative and extract sufficient conditions for the controller characterization in terms of linear matrix inequalities (LMIs). The approach does not require the rate of the delay to be bounded, hence encompasses a broader family of input‐delay LPV systems with fast‐varying delays. The method is then applied to the air‐fuel ratio (AFR) control in spark ignition (SI) engines where the delay and the plant parameters are functions of the engine speed and mass air flow. The objectives are to track the commanded AFR signal and to optimize the performance of the three‐way catalytic converter (TWC) through the precise AFR control and oxygen level regulation, resulting in improved fuel efficiency and reduced emissions. The designed AFR controller seeks to provide canister purge disturbance rejection over the full operating envelope of the SI engine in the presence of uncertainties. Closed‐loop simulation results are presented to validate the controller performance and robustness while meeting AFR tracking and disturbance rejection requirements.