DIRECT ADAPTIVE FEEDBACK DESIGN FOR LINEAR DISCRETE‐TIME UNCERTAIN SYSTEMS

In this paper, we develope a direct adaptive control framework for linear discrete‐time uncertain MIMO systems, based on assumptions that the system is controllable and the difference of the unknown system matrix from the stable solution is bounded by a given value. The proposed framework is Lyapunov‐based, and the controller guarantees adaptive stabilization. In addition, the adaptive laws are characterized by means of Kronecker calculus. Furthermore, the results can easily be extended to time‐varying cases, where the deviation from the stable solution is bounded, and the controllability assumption holds. The controller not only tolerates plant deviation, but also guarantees asymptotical stability of the closed‐loop system. Two numerical examples are provided to demonstrate the performance of the controller.     

Input-to-state stability of switched systems and switching adaptive control

In this paper we prove that a switched nonlinear system has several useful input-to-state stable (ISS)-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.     

Converse Lyapunov–Krasovskii theorems for systems described by neutral functional differential equations in Hale's form

In this article, we show that the existence of a Lyapunov–Krasovskii functional is necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability (GES) of time-invariant systems described by neutral functional differential equations in Hale's form. It is assumed that the difference operator is linear and strongly stable, and that the map on the right-hand side of the equation is Lipschitz on bounded sets. A link between GES and input-to-state stability is also provided.     

A bounded real lemma for jump systems

This note presents a bounded real lemma for discrete-time Markovian jump linear systems (MJLSs). We show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems. For the case of one plant mode, this condition reduces to the standard necessary and sufficient condition for discrete-time systems. We envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for MJLSs.     

Constrained Control of Positive Systems with Delays

This technical note addresses controller design for continuous-time delayed linear systems. The control is under positivity constraint, which means that the resulting closed-loop systems are not only stable, but also positive. Bounded control is also considered, further requiring that the trajectory of the closed-loop system is bounded by a prescribed boundary, if the initial condition is bounded by the same boundary. The contribution lies in three aspects. First, some necessary and sufficient conditions are presented for the existence of controllers satisfying the positivity constraint. Second, a necessary and sufficient condition is established, determining whether the trajectory of a positive system can be bounded by a prescribed boundary, provided that the initial condition is bounded by the same boundary. Third, a sufficient condition is presented for bounded control, and it is shown to be also necessary if asymptotic stability is not required.      

Disturbance attenuation for constrained discrete-time systems via receding horizon controls

In this note, we propose new receding horizon H/sub /spl infin// control (RHHC) schemes for linear input-constrained discrete time-invariant systems with disturbances. The proposed control schemes are based on the dynamic game problem of a finite-horizon cost function with a fixed finite terminal weighting matrix and a one-horizon cost function with time-varying finite terminal weighting matrices, respectively. We show that the resulting RHHCs guarantee closed-loop stability in the absence of disturbances and H/sub /spl infin// norm bound for 2-norm bounded disturbances. We also show that the proposed schemes can easily be implemented via linear matrix inequality optimization. We illustrate the effectiveness of the proposed schemes through simulations.     

Stable inversion and parameter variations

As part of the process of automatically guiding an aircraft, we have been successful in using stable inversion to compute a desired bounded state trajectory and corresponding bounded control. In addition to this feedforward control, we must also construct a regulator to address modeling errors and disturbances. With respect to modeling errors we find that the stable inversion procedures used are so accurate that the regulator can assume a simple form, say a linear regulator about the desired trajectory. We show that under the appropriate assumptions, the bounded state trajectory and bounded control computed through stable inversion depend continuously on the parameters of the system. This is a consequence of a mathematical result that we prove about the continuous dependence of the “particular solution” of a time varying nonlinear system driven by a bounded input. This is distinct from the usual continuous dependence of the initial value problem for systems.     

一类不确定模糊动态时滞系统保成本控制

针对一类不确定非线性动态时滞系统，利用模相T—S模型，通过状态反馈对保成本控制问题进行研究。应用线性矩阵不等式给出模糊闭环系统渐近稳定的充分条件，保证了所有允许的不确定闭环系统是稳定的，而且对于一个给定的二次型成本函数，舱保证闭环成本不超过某个界。仿真结果表明所提出的控制方法是有效的。     

The Popov criterion for strongly stable distributed parameter systems

In this article we generalize the Popov criterion to the class of strongly stable infinite-dimensional linear systems; the semigroup is strongly stable and the input to state, state to output and input to output maps are all bounded on the infinite-time interval. One application is to show that integral control can be used to track constant reference signals for positive-real strongly stable systems in the presence of sectorial non-linearities. A second application is to show the robustness of asymptotic stability of positive-real strongly stable systems to a large class of non-linear perturbations. Systems satisfying the assumptions in this paper include dissipative systems with collocated actuators and sensors.     

On Constrained MMVC of Discrete‐Time First‐Order Linear Stochastic Systems with PSI I: The Critically Stable Case

This paper is devoted to the study of the modified minimal variance control (MMVC) of discrete‐time first‐order linear critically stable stochastic systems with prospective strong intervention (PSI) and control input constraints. Due to different evolutionary characteristics of systems with PSI, that is, the two modes of tending to infinity and having bounded oscillations, the discrete‐time first‐order linear critically stable systems can be partitioned into two types regarding the signs of a key system parameter a. A necessary and sufficient condition for the state mean convergence of a system with a = 1 is derived and the corresponding design of MMVC is formulated. For the critical stable system with a =? 1, its oscillation amplitudes of state means can be effectively suppressed or the means can converge under control. Finally, the effectiveness and advantages of the proposed control strategies comparing with MVC are confirmed by numerical simulations.     

A general formulation and solvability of the global robust output regulation problem

While the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals, the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neutrally stable equilibrium. In particular, when it comes to the robust output regulation problem, the only admissible exogenous signal is a finite combination of step and sinusoidal functions. In this paper, we give a general formulation of the robust output regulation problem that admits unbounded exogenous signals, and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded. Then, we give conditions under which the problem can be solved by solving a robust stabilization problem of an augmented system. Finally, we apply our general result to obtain the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems.     

一类多输入多输出网络控制系统的稳定性分析

研究了具有分布时延、有界输入的多输入多输出网络控制系统的建模和稳定性问题.基于线性时不变对象,建立了系统的数学模型.利用李雅普诺夫第2方法和线性矩阵不等式描述,分析了系统的渐近稳定性,导出了与时延相关的系统渐近稳定判据,同时得到了系统稳定运行的最大允许时延.系统渐近稳定的最大允许时延可用MatlabLMI工具箱从稳定判据获得.仿真算例表明稳定判据是可行的.     

Sufficient conditions for the stability of linear Takagi-Sugeno free fuzzy systems

In this paper, we will study the stability issues of the linear Takagi-Sugeno (T-S) free fuzzy systems. Based on matrix norm, we propose a new sufficient condition for the linear T-S free fuzzy system to be globally asymptotically stable. We then study the stability analysis in the case of systems with consequent parameter uncertainty. Based on Mayer's convergent theorem, we propose a sufficient condition, which is easily implemented, for the systems with consequent parameter uncertainty to be globally asymptotically stable.     

On diffeomorphisms between classes of linear systems

In this paper, we show that the following classes of linear dynamical systems are diffeomorphic to each other: fixed order, asymptotically stable, strictly bounded real, strictly positive real, stable and minimum phase, and invertible. These results are then used to prove the diffeomorphisms between the state bundles associated with these classes of systems, and between their associated principal fibre bundles. We shall conclude this paper by discussing how these results can be used to deduce geometric properties of other classes of linear systems, and to construct overlapping parametrizations.     

Intelligent Packet Dropping for Optimal Energy-Delay Tradeoffs in Wireless Downlinks

We explore the advantages of intelligently dropping a small fraction of packets that arrive for transmission over a time varying wireless downlink. Without packet dropping, the optimal energy-delay tradeoff conforms to a square root tradeoff law, as shown by Berry and Gallager (2002). We show that intelligently dropping any non-zero fraction of the input rate dramatically changes this relation from a square root tradeoff law to a logarithmic tradeoff law. Further, we demonstrate an innovative algorithm for achieving this logarithmic tradeoff without requiring a-priori knowledge of arrival rates or channel probabilities. The algorithm can be implemented in real time and easily extends to yield similar performance for multi-user systems.      

Linear adaptive control of a class of SISO nonaffine nonlinear systems

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.     

基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

应用线性矩阵不等式（LMI）方法研究不确定性关联大系统的分散便棒镇定问题。系统中不稳定项具有数值界,可不满足匹配条件。基于不确定项的表达形式,给出了其可分散状态反馈镇定的充分条件,即一组LMIs有解。在此基础上,通过求第一凸优化问题,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。     

广义时滞系统的时滞相关型H∞控制

研究了广义时滞系统的时滞相关型H_∞控制问题.首先通过引入一个新的Lyapunov-Krasovskii泛函,以严格线性矩阵不等式的形式,得到了广义时滞系统的一个新的有界实引理.在此基础上,设计了使得闭环系统正则、无脉冲和稳定,且满足H_∞性能界的时滞相关型H_∞控制器,并给出了控制器增益的显式表示.最后的算例表明了本文方法具有更小的保守性.     

广义离散系统的状态反馈鲁棒H∞控制及仿真

针对一类范数有界参数不确定性的广义离散线性系统,研究了该系统的状态反馈鲁棒H∞控制问题.利用线性矩阵不等式(LMI)的方法,得到了问题可解的条件,并给出了相应的状态反馈控制律.在一定条件下,所得的状态反馈鲁棒H∞控制律使广义离散线性系统对所有容许的不确定性参数,能够保证闭环系统正则、具有因果关系并且渐进稳定,同时其传递函数矩阵能够满足给定的H∞性能指标.正常离散线性系统的相对应结果可作为论文结果的特殊形式.仿真例子验证了该方法的正确性.     

具有状态和控制约束的受扰离散线性切换系统的反馈控制

本文的主要贡献是针对一类具有重置函数及由外部不能控事件决定动态的离散时间线性切换系统,给出一些稳定性综合结论. 当系统受到外部有界扰动, 及状态和控制量约束时, 在输入到状态稳定性理论框架下, 研究使得系统镇定的线性状态反馈控制器设计方法. 针对这类混杂系统, 本文引入了受控D不变性的概念, 并给出检测某一混杂区域具有受控D不变性的充要条件. 进而, 提出一种能够使得受扰的线性切换系统镇定, 同时保证状态和控制量满足其约束的反馈矩阵的计算方法. 最后, 通过一个由两个子系统构成的数值例子来说明本文技术的应用性.