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.     

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.     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

Exponential stabilization of discrete-time switched linear systems

This article studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic Lyapunov functions for convenience or heuristic reasons. In addition, it is also proved that if a switched linear system is exponentially stabilizable, then it must be stabilizable by a stationary suboptimal policy of a related switched linear-quadratic regulator (LQR) problem. Motivated by some recent results of the switched LQR problem, an efficient algorithm is proposed, which is guaranteed to yield a control-Lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable.     

Global stabilization of discrete-time homogeneous systems

The feedback stabilization of continuous time Δ^r-homogeneous systems has been studied by several authors, see for instance (Dayawansa and Martin, Proceedings of the 28th C.D.C., Tampa, Florida, December, 1989, Hermes, J. Differential Equations 92 (1991) 76–89, Hermes, Systems Control Lett. 24 (1995) 7–11, Kawski, Proceedings of the 27th C.D.C., Texas, 1988, Texas, Kawski, Control Theory and Advanced Technology, vol. 6, MITA Press, Tokyo, 1996, pp. 497–516, Sepulchre and Aeyels, Math. Control Signal Systems 9 (1996) 34–58). In (Kawski, Analysis of Controlled Dynamical Systems, Birkhauser, Basel, 1991, Kawski, Proceedings of IFAC NOLCOS, 1995), Kawski gave an intrinsic concept of homogeneity with respect to general smooth dilations. In this note, we define the homogeneity of transition maps w.r.t. continuous dilations and we show how one can construct a global stabilizing feedback control for discrete-time homogeneous systems which are locally asymptotically stabilizable.     

Constrained optimal control: an application to semiactive suspension systems

This article applies three different control techniques to the design of a quarter-car semiactive suspension system. The three techniques, originally developed to solve a constrained optimal control problem, are optimal gain switching, discontinuous variable structure control and explicit model predictive control. All of them divide the state space into convex regions and assign a linear or affine state feedback controller to each region. The partition of the state space is computed off-line. During the on-line phase, the controller switches between the subcontrollers according to the current state. All the above techniques gave satisfactory results when applied to the design of semiactive suspension systems. A detailed comparison in terms of computational complexity, performance and simplicity of the design is proposed in the article.     

Feedback stabilization of discrete-time homogeneous semi-linear systems

For discrete-time semi-linear systems satisfying an accessibility condition asymptotic null controllability is equivalent to exponential feedback stabilizability using a piecewise constant feedback. A constructive procedure that yields such a feedback is presented.     

约束非线性系统的滑模预测控制方法

将预测控制和滑模控制结构起来,提出一种新的非线性模型预测控制方法,通过对系统状态预测得到切换函数预测值,求解约束开环优化求得预测控制律,并将当前时刻的控制作用于对象,下一时刻重复此过程,该方法具有预测控制在线处理约束及滑模控制滑动模态对干扰的不变性的优点,分析了零终端滑模约束模型预测控制的稳定性。     

Non-smooth finite-time stabilization for a class of nonlinear systems

Finite-time convergent control design via continuous time-invariant feedback laws has become the focal point of several recent studies. Based on the analysis of differential equations and homogeneity, continuous (and non-smooth) finite-time controllers vi…     

约束不确定非线性系统的鲁棒优化镇定

针对状态和输入约束不确定非线性仿射系统,提出一种鲁棒镇定的优化控制器设计方法.基于弱鲁棒控制Lyapunov函数概念,构造一个参数可调控制器.再利用LaSalle定理和逆优化理论,验证该控制器的鲁棒镇定性和逆最优性.进一步,采用滚动优化原理在线计算控制器的可调参数,实现闭环系统的鲁棒优化镇定.最后对一个开环不稳定振荡器系统进行鲁棒优化镇定,其结果验证了文中方法的有效性.     

Global stabilization of linear discrete-time systems with bounded feedback

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections (“single hidden layer neural networks”) of simple saturation functions.     

Reachability and stabilization of discrete-time affine systems with disturbances

This paper studies the fundamental problems: whether an affine system affected by additive disturbances is robustly transferable from a source set (simplex) to a target set (polytope) and whether it is robustly stabilizable with its state constrained in a simplex. First, a necessary and sufficient condition is derived for the existence of affine feedback control that solves the robust reachability problem. Further investigation is provided for two situations relying on whether the union of the source set and the target set is convex or non-convex. For the former one, a necessary and sufficient condition is obtained in the form of linear inequalities, while for the latter, several computationally feasible sufficient conditions are found. Second, we show that robust stabilization subject to a state constraint is equivalent to find a feasible solution to a linear equation. Once it is known that either of the problems has a solution by checking the derived conditions, design of control laws is then straightforward.     

Robust stabilization of switched discrete-time systems with actuator saturation

This paper studies the robust stabilization problem of switched discrete-time linear systems subject to actuator saturation. New switched saturation-dependent Lyapunov functions are exploited to design a robust stabilizing state feedback controller that maximizes an estimation of the domain of attraction. The design problem of controller （coefficient matrices） is then reduced to an optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to show the effectiveness of the proposed method.     

通讯信息约束下具有全局稳定性的分布式系统预测控制

本文针对一类由状态相互耦合的子系统组成的分布式系统, 提出了一种可以处理输入约束的保证稳定性的非 迭代协调分布式预测控制方法(distributed model predictive control, DMPC). 该方法中, 每个控制器在求解控制率时只与 其它控制器通信一次来满足系统对通信负荷限制; 同时, 通过优化全局性能指标来提高优化性能. 另外, 该方法在优化 问题中加入了一致性约束来限制关联子系统的估计状态与当前时刻更新的状态之间的偏差, 进而保证各子系统优化问 题初始可行时, 后续时刻相继可行. 在此基础上, 通过加入终端约束来保证闭环系统渐进稳定. 该方法能够在使用较少 的通信和计算负荷情况下, 提高系统优化性能. 即使对于强耦合系统同样能够保证优化问题的递推可行性和闭环系统的 渐进稳定性. 仿真结果验证了本文所提出方法的有效性.     

加性噪声下网络化多输入离散系统均方可镇定

本文研究了静态信噪比约束下多输入离散系统均方可镇定问题,其中信道资源固定且不可任意分配,信道被建模为加性高斯白噪声.主要目的是借用优化序理论讨论系统可镇定时各子信道的信道容量与系统拓扑熵的关系.本文基本思想是从供需平衡角度讨论可镇定性.具体地,对于通信资源,每个系统输入被视为需求方,而信道被视为供应方.信道的供应资源由其各自的均方容量刻画,网络化系统均方可镇定要求通信资源供求平衡.因信道资源不可配置,人们可以通过调节需求方(一定的传输机制)来满足供给方要求.给出了网络化系统均方可镇定时的一个充分条件和一个必要条件.最后数值算例验证所得结论.     

Constrained stabilization of continuous-time linear systems

In this paper we consider the stabilization problem for linear continuous-time systems, under state and control constraints. We show that the largest domain of attraction to the origin can be arbitrarily closely approximated by a polyhedral domain of attraction associated to a certain (continuous) feedback stabilizing control and we show how to use existing numeric procedures for discrete-time systems to solve the continuous-time problem. We propose a new discontinuous stabilizing control law for scalar-input systems which has the advantage of being successfully applicable to systems with quantized control.     

输入受限广义预测控制算法的可行性

在系统输入受限的情况下,采用一般的广义预测控制或受限时域预测控制有可能会造成控制算法不可行,从而使系统的性能变坏或不稳定,针对这个问题,本文提出一种保证可行性的控制算法,并证明该虎法能够使系统渐近稳定且最终使条件设定值跟踪系统的实际设定值。     

Global robust stabilization of nonlinear systems subject to input constraints

Our main purpose in this paper is to further address the global stabilization problem for affine systems by means of bounded feedback control functions, taking into account a large class of control value sets: p, r ‐weighted balls ??^m _r (p), with 1<p?∞, defined via p, r ‐weighted gauge functions. Observe that p=∞ is allowed, so that m‐dimensional r ‐hyperboxes ??^m _r (∞)?[?r₁^?,r₁⁺]×???×[?r_m^?,r_m⁺], r_j^±>0 are also considered. Working along the line of Artstein–Sontag's approach, we construct an explicit formula for a one‐parameterized family of continuous feedback controls taking values in ?? _r ^m(p) that globally asymptotically stabilize an affine system, provided an appropriate control Lyapunov function is known. The designed family of controls is suboptimal with respect to the robust stability margin for uncertain systems. The problem of achieving disturbance attenuation for persistent disturbances is also considered. Copyright © 2002 John Wiley & Sons, Ltd.     

约束非线性系统的一个准无限时域预测控制方案

提出了一个具有准无限预测时域的模型预测控制方案,该方案可用于输入和状态的非线性系统的控制,用优化柔性状态约束条件代替了硬性状态约束,以避免优化问题的不可解,开环优化问题含有附加的终端代价项和终的约束条件,这样预测时域延伸至准无限,而需在线优化获得的控制函数仅为有限时域,如果在最初时刻优化问题有解,则闭环系统具有保证稳定性。