Robust control of linear discrete-time systems

Given a linear discrete-time system with additive disturbances, a general methodology for designing a stable control algorithm is shown. The approach is Lyapunov-based with certain liberty of tailoring the candidate function for a given problem. Comparison to the existing solutions based on a variable structure approach is given.     

Robust output-feedback control of linear discrete-time systems

The problem of designing H_∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H_∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.     

Robust stabilisation control for discrete-time networked control systems

We consider the analysis and synthesis of discrete-time networked control systems (NCSs), where the plant has additive uncertainty and the controller is updated with the sensor information at stochastic time intervals. It is shown that the problem is linked to H_∞-control of linear discrete-time stochastic systems and a new small gain theorem is established. Based on this result, sufficient conditions are given for ensuring mean square stability of the NCS, and the genetic algorithm is utilised to design the controller of the NCS based on a linear matrix inequality technique. An illustrative example is given to demonstrate the effectiveness of our proposed method.     

Robust adaptive control of uncertain discrete-time state-delay systems

This paper focuses on the controller resilience and performance deterioration issues due to inaccuracies in controller implementation. It addresses the problem of resilient adaptive control problem for a class of discrete-time state-delay systems and norm-bounded uncertainties against controller gain variations. Adaptive control schemes are constructed for the case of known gain perturbation bounds and then extended to accommodate unknown norm-bounded perturbations. Necessary and sufficient conditions for delay-independent asymptotic stability are established. An expanded state-space system called the “Compact Form” is established to derive delay-dependent criteria for stability and adaptive stabilization schemes. All the developed results are conveniently expressed in linear matrix inequalities format. A detailed simulation result is presented to demonstrate the developed theory.     

集值离散动力系统的扩张性*

设(X,d)为紧致度量空间,f∶X→X连续,(k(X),dH)是X所有非空紧致子集构成的紧致度量空间,f∶k(X)→k(X),f(A)={f(a)|a∈A}。运用分析的方法初步给出了集值离散动力系统中的扩张性理论。提出集值映射的全扩张、强全扩张的概念,并研究了f的扩张性与f的扩张性之间的关系。所得结果扩展了集值离散动力系统的研究范围,并提出了该领域未来可研究的方向。     

Robust adaptive control of discrete-time systems using persistent excitation

An important result in the robust adaptive control of continuous-time systems, using the persistent excitation of the reference input, was recently given by Narendra and Annaswamy (1986, IEEE Trans. Aut. Control, AC-31, 306–315). According to this result, the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance. The main theorem in Narendra and Annaswamy (1986) is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real, a condition which involves constraints on the relative degree of the plant. This paper presents a generalization of the above result to plants of arbitrary relative degree. Together with the work reported in the earlier paper, it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input.     

离散广义系统的鲁棒严格正实控制

研究确定的以及具有范数有界不确定性的离散广义系统的严格正实分析和控制问题,首先给出了确定离散广义系统状态反馈扩展严格正实控制器的存在条件和设计方法;然后利用线性矩阵不等式分析了不确定离散广义系统广义二次稳定且扩展严格正实的条件,讨论了状态反馈使闭环系统广义二次稳定且扩展严格正实问题,给出了状态反馈鲁棒扩展严格正实控制器的综合方法;最后通过数值算例说明了所提出方法的有效性．     

Robust discrete-time set-based adaptive predictive control for nonlinear systems

The problem of robust adaptive predictive control for a class of discrete-time nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min–max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min–max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min–max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios.     

Robust control synthesis for discrete-time uncertain semi-Markov jump systems

This paper studies the control synthesis for uncertain semi-Markov jump systems in a discrete-time domain subjected to external disturbance. The switching between modes is determined by a function of the transition probability and the sojourn-time distribution between two neighbouring modes. Based on the σ-error mean square stability criterion, time-varying controllers are designed to stabilise the system. By constructing a holding time dependent Lyapunov function, time-varying state-feedback controllers are obtained that meet a set of sufficient conditions in the form of linear matrix inequalities. Two examples, including a DC motor system, are presented to show the validity of the proposed control scheme.     

Robust observer-based control for uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present a novel robust observer-based controller design method for discrete-time piecewise affine systems with norm-bounded uncertainties.The key ideas are to ...     

二次型耗散线性离散系统的鲁棒性分析与控制

考虑一类不确定离散多变量系统的鲁棒二次型耗散性分析和控制,其中各不确定参数矩阵具有线性分式形式.首先对确定系统建立二次型耗散性与正实性之间的等价关系,由此导出线性系统二次型耗散的充分必要条件;然后证明不确定系统的鲁棒耗散性分析和控制可转化为确定系统的耗散性分析和设计,给出了这类不确定系统鲁棒耗散的充分必要条件以及鲁棒耗散控制问题的线性矩阵不等式解法.所得结果可将H∞控制与正实控制统一起来,提供一种较为灵活、保守性较小的系统设计方法.仿真例子说明了所提方法的有效性.     

Robust stability of discrete-time systems

A new approach is proposed for determining the robust stability of discrete-time systems where each coefficient of the characteristic polynomial can take any value between specified lower and upper bounds. It is based on the use of Rouche's theorem in the theory of complex variables.     

Robust decentralized model reference adaptive control of discrete-time interconnected systems

A robust decentralized model reference adaptive controller is proposed for a class of large-scale systems composed of several interconnected subsystems and described by state space equations. We have formulated a local adaptive controller for each subsystem using only local information such that the state of this subsystem tracks the corresponding state of a reference model. The content of the paper is limited to interconnected subsystems which are described by linear, deterministic, single-input single-output and discrete-time models with unknown and/or slowly time-varying parameters. Sufficient conditions, formulated by utilizing Lyapunov theory, are given for the overall system to be stabilizable by decentralized state feedback adaptive control laws. The results are illustrated by a numerical example.     

基于开环2闭环控制的离散动力系统同步研究

基于开环-闭环控制,提出了一种离散动力系统同步方法.系统地论述了该方法的基本原理,指出了该方法在实际应用中应注意的一系列问题.在此基础上,推导出为实现系统同步应采取控制策略的具体形式,并从理论上对其鲁棒性进行了论证.数字模拟结果表明,该方法不仅具有较高的同步效率,而且具有很强的适用性,能够在不同条件下实现两个同类或异类离散动力系统的同步.     

区间时滞相关离散非线性系统的鲁棒模型预测控制

针对一类带有扰动、输入约束和凸多面体不确定性的区间时滞离散非线性系统, 提出一种鲁棒模型预测控制方法. 一方面, 利用min-max 模型预测控制求解鲁棒模型预测控制器, 以研究鲁棒预测控制在范数有界意义下的扰动抑制问题; 另一方面, 充分利用时滞的上下界信息构造Lyapunov 函数以得到控制器存在的充分条件. 最后给出了闭环系统鲁棒稳定性证明.     

不确定离散半马尔可夫跳变系统的有限时间鲁棒$H_infty$控制

研究一类不确定离散时间半马尔可夫跳变系统的有限时间鲁棒H_∞控制问题.首先,应用半马尔可夫核方法建模离散时间系统的半马尔可夫跳变过程,其中驻留时间的概率密度函数依赖系统当前模态和下一模态,使得所提出理论可考虑不同的驻留时间概率分布类型,针对随机跳变系统有限时间分析中的跳变次数问题,提出估计跳变次数最大值的方法;然后,考虑系统模态驻留时间的上下界,提出新的有限时间有界概念,并保证基于半马尔可夫核方法给出的不确定离散时间半马尔可夫随机跳变系统有限时间有界判据数值可解;接着,在此基础上,分析系统的H_∞性能指标,设计模态依赖的状态反馈控制律保证闭环系统的有限时间鲁棒H_∞性能;最后,通过2个算例仿真验证所提出理论的可行性和有效性.     

Robust control of uncertain discrete-time Markovian jump systems with actuator saturation

In this paper, the robust stochastic stabilization problem for the class of discrete-time uncertain Markovian jump linear systems (MJLS) with actuator saturation is considered. The definition of domain of attraction in mean square sense (DoA-MSS) is introduced to analyze the stochastic stability of the closed-loop system. By using a class of stochastic Lyapunov function which is dependent on the jump mode and saturation function, design procedures for both the mode-dependent and mode-independent state feedback controllers are developed based on the Linear Matrix Inequality (LMI) approach. Finally, a numerical example is provided to show the usefulness of the proposed techniques.     

Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems

This paper proposes a receding horizon control scheme for a set of uncertain discrete-time linear systems with randomly jumping parameters described by a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets. The control scheme for the underlying systems is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix at each time instant. This robust receding horizon control scheme has a more general structure than the existing robust receding horizon control for the underlying systems under the same design parameters. The proposed controller is obtained using semidefinite programming.     

Robust limit cycle control in a class of nonlinear discrete-time systems

This paper studies generation of robust periodic solutions in a class of nonlinear discrete-time system. The sustained oscillations, with the desired frequency and amplitude, are achieved through the creation of the appropriate elliptic limit cycle in the phase plane of the uncertain closed-loop discrete-time system. In the first step, the nominal control law is designed to enforce the trajectories of the nominal closed-loop system to converge to the desired limit cycle. Next, considering uncertain terms, an additional robustifying term is designed. This term is added to the nominal controller to sustain the desirable stable oscillations in the presence of uncertain terms. The resulted robust controller brings the trajectories of the uncertain closed-loop discrete-time system to a boundary layer (with adjustable width) around the desired limit cycle. Moreover, the domain of attraction of the limit cycle and also the ultimate boundary layer around it are calculated via the Lyapunov analysis. Additionally, in order to verify the applicability of the proposed method, it is implemented on the discretised model of a spring–damper system. Computer simulations confirm the theoretical results in generating robust stable oscillations.