基于观测器的一类连续非线性系统的采样控制

首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器. 接下来, 利用零阶保持法对连续时间状态反馈控制器进行离散化, 获得了状态反馈采样控制器; 利用零阶保持法对基于连续时间观测器 的连续时间控制器离散化, 获得了基于连续时间观测器的采样控制器; 利用Euler法对连续时间观测器离散化, 同时利用零阶保持法对控制器离散化, 从而获得了采样观测器和基于采样观测器的采样控制器. 本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定, 而基于采样观测器的采样控制器可以保证被控对象的状态是有界的, 其最终边界依赖于设计参数与采样周期. 最后, 通过选择适当的采样周期, 完成了闭环采样控制系统的设计. 一个船舶航向控制的例子表明应用本文 所提方法设计出的三种采样控制器具有良好的控制效果.     

Tube-based robust sampled-data MPC for linear continuous-time systems

This note extends to the continuous-time case the “tube-based” approach for the design of discrete-time robust model predictive control (MPC) algorithms developed in Mayne, Seron, and Rakovi? (2005). This extension is of interest in view of the simplicity and popularity of the method as well as of the industrial relevance of continuous-time implementations of MPC. The proposed robust control law is composed of two terms: (1) a sampled-data MPC control law and (2) a continuous-time state feedback term.     

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.     

Preservation of input-to-state stability under sampling and emulation: multi-rate case

The stabilization problem of sampled-data non-linear systems is considered under the low measurement rate constraint. A multi-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state. We show that if we design a continuous-time controller for a continuous-time plant so that the closed-loop continuous-time system is input-to-state stable and then discretize the controller and implement it using sample and zero order hold devices, then input-to-state stability property will be preserved for the sampled-data multi-rate closed loop system in a practical sense.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

多变量分数阶滞后系统预测控制参数解析调优

提出了一种针对各子系统由一阶加分数阶滞后模型描述的多变量系统模型预测控制参数解析调优方法.首先推导了多变量分数阶滞后系统的状态空间模型;其次,基于该模型构建模型预测控制优化问题,并获得了控制信号的解析表达式;再次,对闭环控制系统进行解耦分析,揭示了模型预测控制器参数与系统闭环性能间的定量关系,通过将参数调优问题转化为极点配置问题,得到能够保证闭环系统性能的模型预测控制器参数取值的解析表达式;最后通过仿真实验验证了本文所设计的参数解析调优算法的有效性.     

Discrete-time control of continuous systems with approximate decentralized fixed modes

In this paper, the discrete-time control of decentralized continuous-time systems, which have approximate decentralized fixed modes, is studied. It is shown that under certain conditions, discrete-time controllers can improve the overall performance of the decentralized control system, when a linear time-invariant continuous-time controller is ineffective. In order to obtain these conditions, a quantitative measure for different types of approximate fixed modes in a decentralized system is given. In this case, it is shown that discrete-time zero-order hold (ZOH) controllers, and in particular, that generalized sampled-data hold functions (GSHF), can significantly improve the overall performance of the resultant closed-loop system. The proposed sampled-data controller is, in fact, a linear time-varying controller for the continuous-time system.     

Predictive metamorphic control

In spite of its easy implementation, ability to handle constraints and nonlinearities, etc., model predictive control (MPC) does have drawbacks including tuning difficulties. In this paper, we propose a refinement to the basic MPC strategy by incorporating a tuning parameter such that one can move smoothly from an existing controller to a new MPC strategy. Each change of this tuning parameter leads to a new stabilising control law, therefore, allowing one to gradually move from an existing control law to a new and better one. For the infinite horizon case without constraints and for the general case with state and input constraints, stability results are established. We also examine the practical applicability of the proposed approach by employing it in the nominal prediction model of the tube-based output feedback robust MPC method. The merits of the proposed method are illustrated by examples.     

Improving performance in model predictive control: Switching cost functionals under average dwell-time

In this paper, we propose a novel switched model predictive control (MPC) algorithm for nonlinear continuous-time systems, where we switch between different cost functionals in order to enhance performance. Thus, different performance criteria can be taken into account. In order to ensure stability of the resulting closed-loop system, we consider switching signals which exhibit a certain average dwell-time. When considering switching signals of this type, certain assumptions are common in the switched systems literature in order to ensure stability, like a matching condition for the different Lyapunov functions and the possibility to find Lyapunov functions with an exponential decay rate. In this paper, we show how these assumptions can be satisfied in the MPC context and thus stability of the proposed switched MPC algorithm can be established.     

Model predictive tracking control for a linear system under time‐varying input constraints

In this paper, we propose a tracking control law for a linear dynamical system under time‐varying input constraints. The proposed control law consists of a dual‐mode model predictive control (MPC) law and a target recalculation mechanism. As the terminal controller of the dual‐mode MPC, we propose a saturation‐level‐dependent gain‐scheduled feedback control law that ensures closed‐loop stability against arbitrary change of the position limit of the actuators. We also present conditions that guarantee feasibility and stability of the control algorithm under time‐varying input constraints. The control algorithm is reduced to an online optimization problem under linear matrix inequality constraints. Copyright © 2012 John Wiley & Sons, Ltd.