Discrete-time H∞ control of linear parameter-varying systems

We introduce new conditions for the H_∞ synthesis of discrete-time linear parameter-varying systems in the form of linear matrix inequalities. A distinctive feature of the proposed conditions is the ability to handle variation in both the dynamics and the input matrices without resorting to dynamic augmentation or iterative procedures. We show that this new condition contains the existing poly-quadratic H_∞ synthesis result as a particular case. We also derive a corollary which shows improvement even in the stronger case of quadratic H_∞ synthesis. Additionally, we show that, surprisingly, a dynamic gain-scheduled quadratic H_∞ controller can result in inferior performance compared to a static robust controller. Numerical examples illustrate our results.     

Fault detection for discrete-time LPV systems using interval observers

This paper is concerned with the fault detection (FD) problem for discrete-time linear parameter-varying systems subject to bounded disturbances. A parameter-dependent FD interval observer is designed based on parameter-dependent Lyapunov and slack matrices. The design method is presented by translating the parameter-dependent linear matrix inequalities (LMIs) into finite ones. In contrast to the existing results based on parameter-independent and diagonal Lyapunov matrices, the derived disturbance attenuation, fault sensitivity and nonnegative conditions lead to less conservative LMI characterisations. Furthermore, without the need to design the residual evaluation functions and thresholds, the residual intervals generated by the interval observers are used directly for FD decision. Finally, simulation results are presented for showing the effectiveness and superiority of the proposed method.     

Stability of a Hysteretic System with Random Signal Inputs†

The stability of a feedback system with a hysteretie relay controller, when forced by a Gaussian signal, is analysed by applying the quasi-linearization approach.A method for computing the sinusoidal and random signal gains of a non-linear element, based on the evaluation of the input—output cross power of the clement, is first explained. Knowledge of these two gains for an ideal relay is then used to find the corresponding gains for a hysteretic relay. These gains are finally used for analysing the effects of both high-frequency and low-frequency random signals on the auto-oscillations of a second-order system with the hysteretic relay. Results of simulator studies are also presented.     

μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time

In this article, the model reduction problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The stability criterion for general discrete-time switched systems is first explored, and a μ-dependent approach is then introduced for the considered systems to the model reduction solution. A reduced-order model is constructed and its corresponding existence conditions are derived via LMI formulation. The admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential H _∞ performance. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results.     

线性切换容错控制系统稳定性的新判据*

研究了线性切换容错控制系统的稳定性问题。利用分段李雅普诺夫函数方法,结合梅茨勒矩阵的性质和矩阵不等式的分析技巧,得到了基于李雅普诺夫—梅兹勒线性矩阵不等式判定系统稳定的新结果。设计依赖于状态的切换规则便于计算、易于检验。最后利用MATLAB工具箱得到的仿真实例验证了本结果的可行性。     

Application of mathematical programming in the design of optimal control systems†

The problem of applying the various computational methods of mathematical programming in the design of an optimal control system is discussed. A general case of non-linear, non-autonomous, state equations, subject to inequality constraints on both state and control variables, is considered. Both continuous and discrete time systems are investigated. In case of discrete time systems, the sampling intervals are assumed generally unequal and aperiodic, with inequality constraints imposed upon them.

Systems like these impose considerable computational difficulties when treated by the maximum principle or dynamie programming. Using mathematical programming, one may simplify a wide class of those computational problems.

Several examples of applying mathematical programming to particular control problems are presented.     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

舰载机着舰侧回路时变风险权值矩阵线性变参数预测控制

针对舰载机钩索阻拦阶段,提出阻拦风险函数的概念和计算方法,通过离线计算获得时变状态权值矩阵和时变控制输入权值矩阵.采用时变状态权值矩阵可以实时调整各状态之间的变化关系,而时变的控制输入权值矩阵能够调整副翼和方向舵的输入峰值,避免出现输入饱和情况,提高横侧向自动着舰的效率和安全性.建立了时变的系统输出约束函数,增加了舰载机进舰阶段控制器的可解性.建立了基于状态偏差的舰载机横侧向着舰模型,针对舰载机上很多状态不能直接测量的特点,采用离线设计状态观测器的方法来估计舰载机的真实状态值,利用线性矩阵不等式求解系统最优解,通过舰载机自动着舰三维仿真模拟平台验证了算法的可行性.     

Computational complexity of randomized algorithms for solving parameter-dependent linear matrix inequalities

Randomized algorithms are proposed for solving parameter-dependent linear matrix inequalities and their computational complexity is analyzed. The first proposed algorithm is an adaptation of the algorithms of Polyak and Tempo [(Syst. Control Lett. 43(5) (2001) 343)] and Calafiore and Polyak [(IEEE Trans. Autom. Control 46 (11) (2001) 1755)] for the present problem. It is possible however to show that the expected number of iterations necessary to have a deterministic solution is infinite. In order to make this number finite, the improved algorithm is proposed. The number of iterations necessary to have a probabilistic solution is also considered and is shown to be independent of the parameter dimension. A numerical example is provided.     

时滞LPV重复过程的H∞控制

将时滞线性参数变化(LPV)思想应用于重复过程,研究其H∞控制问题.基于参数依赖Lyapunov函数方法,给出了该重复过程的稳定性和控制器设计的充分条件;同时通过投影定理引入两个附加矩阵,解除了重复过程矩阵和依赖于参数的Lyapunov函数矩阵之间的耦合,使得到的条件便于求解.仿真实例表明了该设计方法的有效性.