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.     

一种基于H∞理论的鲁棒预测控制方法

融合H∞控制的鲁棒概念和预测控制的滚动优化原理,提出了一种全新的约束动态对策预测控制方法.对有状态和控制约束的不确定线性系统,证明了闭环系统的鲁棒稳定性并给出了鲁棒性条件.该方法同时具有H∞控制和预测控制的优点:鲁棒性和显式处理约束的能力.     

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

State-feedback model predictive control (MPC) of discrete-time linear periodic systems with time-dependent state and input dimensions is considered. The states and inputs are subject to periodically time-dependent, hard, convex, polyhedral constraints. First, periodic controlled and positively invariant sets are characterized, and a method to determine the maximum periodic controlled and positively invariant sets is derived. The proposed periodic controlled invariant sets are then employed in the design of least-restrictive strongly feasible reference-tracking MPC problems. The proposed periodic positively invariant sets are employed in combination with well-known results on optimal unconstrained periodic linear-quadratic regulation (LQR) to yield constrained periodic LQR control laws that are stabilizing and optimal. One motivation for systems with time-dependent dimensions is efficient control law synthesis for discrete-time systems with asynchronous inputs, for which a novel modeling framework resulting in low dimensional models is proposed. The presented methods are applied to a multirate nano-positioning system.     

Decomposition principle in model predictive control for linear systems with bounded disturbances

Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach which aims at enlarging the domain of attraction by combining a set-based MPC approach with a decomposition principle. The idea of the paper is to extend the “pre-stabilizing” MPC, where the MPC control sequence is parameterized as perturbations to a given pre-stabilizing feedback gain, to the case where the pre-stabilizing feedback law is given as the linear combination of a set of feedback gains. This procedure leads to a relatively large terminal set and consequently a large domain of attraction even when using short prediction horizons. As time evolves, by minimizing the nominal performance index, the resulting controller reaches the desired optimal controller with a good asymptotic performance. Compared to the standard “pre-stabilizing” MPC, it combines the advantages of having a flexible choice of feedback gains, a large domain of attraction and a good asymptotic behavior.     

Computational complexity analysis of set membership identification of Hammerstein and Wiener systems

This paper analyzes the computational complexity of set membership identification of Hammerstein and Wiener systems. Its main results show that, even in cases where a portion of the plant is known, the problems are generically NP-hard both in the number of experimental data points and in the number of inputs (Wiener) or outputs (Hammerstein) of the nonlinearity. These results provide new insight into the reasons underlying the high computational complexity of several recently proposed algorithms and point out the need for developing computationally tractable relaxations.     

模型预测控制——现状与挑战

30多年来, 模型预测控制(Model predictive control, MPC)的理论和技术得到了长足的发展, 但面对经济社会迅速发展对约束优化控制提出的不断增长的要求, 现有的模型预测控制理论和技术仍面临着巨大挑战. 本文简要回顾了预测控制理论和工业应用的发展, 分析了现有理论和技术所存在的局限性, 提出需要加强预测控制的科学性、有效性、易用性和非线性研究. 文中简要综述了近年来预测控制研究和应用领域发展的新动向, 并指出了研究大系统、快速系统、低成本系统和非线性系统的预测控制对进一步发展预测控制理论和拓宽其应用范围的意义.     

Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

基於稳态映照记忆模型的自学习控制

本文介绍了基於系统集的通用智能控制器的设计思想。作为示例，我们对一类具有相同特征与约束的系统集给出了基於稳态映照记忆模型的自学习算法，证明了它的可学习性与收敛性，在不同的对象上验证了它的通用性。     

通讯信息约束下具有全局稳定性的分布式系统预测控制（英文）

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.     

Identification and adaptive control: Towards a complexity-based general theory

Two recent developments will be surveyed here which are pointing the way towards an input–output theory of H^∞-l¹ adaptive feedback: The solution of problems involving; (1) feedback performance (exact) optimization under large plant uncertainty on the one hand (the two-disc problem of H^∞); and (2) optimally fast identification in H^∞ on the other. Taken together, these are yielding adaptive algorithms for slowly varying data in H^∞-l¹. At a conceptual level, these results motivate a general input-output theory linking identification, adaptation, and control learning. In such a theory, the definition of adaptation is based on system performance under uncertainty, and is independent of internal structure, presence or absence of variable parameters, or even feedback.     

Approximation of the Feasible Parameter Set in worst-case identification of Hammerstein models

The estimation of the Feasible Parameter Set (FPS) for Hammerstein models in a worst-case setting is considered. A bounding procedure is determined both for polytopic and ellipsoidic uncertainties. It consists in the projection of the FPS of the extended parameter vector onto suitable subspaces and in the solution of convex optimization problems which provide Uncertainties Intervals of the model parameters. The bounds obtained are tighter than in the previous approaches.     

Identification and adaptive control: Towards a complexity-based general theory

Two recent developments will be surveyed here which are pointing the way towards an input–output theory of - adaptive feedback: The solution of problems involving; (1) feedback performance (exact) optimization under large plant uncertainty on the one hand (the two-disc problem of ); and (2) optimally fast identification in on the other. Taken together, these are yielding adaptive algorithms for slowly varying data in - . At a conceptual level, these results motivate a general input-output theory linking identification, adaptation, and control learning. In such a theory, the definition of adaptation is based on system performance under uncertainty, and is independent of internal structure, presence or absence of variable parameters, or even feedback.