多面体不确定系统时滞依赖鲁棒预测控制

将线性状态变换引入连续时间多面体不确定时滞系统中,利用线性矩阵不等式(LMI)方法,设计时滞相关型鲁棒预测控制器;通过适当选择Lyapunov函数,推导出闭环系统渐近稳定的充分条件,并且该条件是时滞相关的.仿真算例验证了该方法的有效性.     

Model predictive control for constrained uncertain piecewise linear systems

For constrained piecewise linear (PWL) systems, the possible existing model uncertainty will bring the difficulties to the design approaches of model predictive control (MPC) based on mixed integer programming (MIP). This paper combines the robust method and hybrid method to design the MPC for PWL systems with structured uncertainty. For the proposed approach, as the system model is known at current time, a free control move is optimized to be the current control input. Meanwhile, the MPC controller uses a sequence of feedback control laws as the future control actions, where each feedback control law in the sequence corresponds to each partitions and the arbitrary switching technique is adopted to tackle all the possible switching. Furthermore, to reduce the online computational burden of MPC, the segmented design procedure is suggested by utilizing the characteristics of the proposed approach. Then, an offline design algorithm is proposed, and the reserved degree of freedom can be online used to optimize the control input with lower computational burden.     

Non-fragile observer-based output feedback control for polytopic uncertain system under distributed model predictive control approach

In this paper, a non-fragile observer-based output feedback control problem for the polytopic uncertain system under distributed model predictive control (MPC) approach is discussed. By decomposing the global system into some subsystems, the computation complexity is reduced, so it follows that the online designing time can be saved.Moreover, an observer-based output feedback control algorithm is proposed in the framework of distributed MPC to deal with the difficulties in obtaining the states measurements. In this way, the presented observer-based output-feedback MPC strategy is more flexible and applicable in practice than the traditional state-feedback one. What is more, the non-fragility of the controller has been taken into consideration in favour of increasing the robustness of the polytopic uncertain system. After that, a sufficient stability criterion is presented by using Lyapunov-like functional approach, meanwhile, the corresponding control law and the upper bound of the quadratic cost function are derived by solving an optimisation subject to convex constraints. Finally, some simulation examples are employed to show the effectiveness of the method.     

基于Backstepping设计的不确定非线性系统的预测控制

本文的目的是针对一类带有不确定性的单输入单输出的仿射非线性系统,设计一种非线性预测控制器.用反步设计思想获得具有待定参数的控制器表达式,然后用预测控制在线优化获得控制器的参数.用这种方法设计的控制器更易使闭环系统稳定,且闭环系统具有良好的动态特性.连续发酵过程的仿真结果也验证了控制器是有效的.     

Distributed model predictive control for polytopic uncertain systems subject to actuator saturation

In this paper, we present a distributed model predictive control (MPC) algorithm for polytopic uncertain systems subject to actuator saturation. The global system is decomposed into several subsystems. A set invariance condition for polytopic uncertain system with input saturation is identified and a min–max distributed MPC strategy is proposed. The distributed MPC controller is designed by solving a linear matrix inequalities (LMIs) optimization problem. An iterative algorithm is developed for making coordination among subsystems. Case studies are carried out to illustrate the effectiveness of the proposed algorithm.     

不确定跳变系统反馈预测控制

针对一类受限不确定离散Markov跳变系统,提出一种反馈预测控制器设计方法.为便于工程应用,该方法考虑了各模态下的动态系统参数存在多胞不确定性,以及各模态间的跳变转移概率部分未知的情形.通过优化无穷时域的二次型性能指标来确定预测控制器及其对应的椭圆不变集,控制器保证了闭环系统鲁棒均方稳定.同时,用所求得的控制增益在线构造了一组渐近稳定的多面体不变集,在一定程度上扩大了系统状态可行集的范围.数值示例验证了所提方法的可行性和有效性.     

非线性不对称系统的模型预测控制

针对基于正反方向上的两个线性模型分别设计 PID 控制器的缺陷,提出根据正反方向上的线性模型分别设计相应的状态反馈预测控制器.采用输入输出约束策略保证模型准确,并通过可行性分析确定最终的控制作用. pH 值控制的仿真实验表明,其对不对称非线性系统的控制效果明显优于传统的基于单一线性模型的预测控制及正反方向分别采用 PID 控制的控制效果.     

Stochastic model predictive control for probabilistically constrained Markovian jump linear systems with additive disturbance

Model predictive control (MPC) for Markovian jump linear systems with probabilistic constraints has received much attention in recent years. However, in existing results, the disturbance is usually assumed with infinite support, which is not considered reasonable in real applications. Thus, by considering random additive disturbance with finite support, this paper is devoted to a systematic approach to stochastic MPC for Markovian jump linear systems with probabilistic constraints. The adopted MPC law is parameterized by a mode‐dependent feedback control law superimposed with a perturbation generated by a dynamic controller. Probabilistic constraints can be guaranteed by confining the augmented system state to a maximal admissible set. Then, the MPC algorithm is given in the form of linearly constrained quadratic programming problems by optimizing the infinite sum of derivation of the stage cost from its steady‐state value. The proposed algorithm is proved to be recursively feasible and to guarantee constraints satisfaction, and the closed‐loop long‐run average cost is not more than that of the unconstrained closed‐loop system with static feedback. Finally, when adopting the optimal feedback gains in the predictive control law, the resulting MPC algorithm has been proved to converge in the mean square sense to the optimal control. A numerical example is given to verify the efficiency of the proposed results.     

Fast model predictive control for linear periodic systems with state and control constraints

The design of stabilizing model predictive control laws for discrete‐time linear periodic systems with state and control constraints is considered. Two algorithms are presented. The first one is based on interpolation between several unconstrained periodic controllers. Among them, one controller is chosen for the performance while the rest are used to extend the domain of attraction. The second algorithm aims to improve the performance by combining model predictive control and interpolating control. The proposed approaches not only guarantee recursive feasibility and asymptotic stability but also are optimal for states near the origin. Copyright © 2017 John Wiley & Sons, Ltd.     

基于神经网络的非线性系统多步预测控制

针对离散非线性系统,利用非线性激励函数的局部线性表示,提出一种可用于非线性过程的神经网络多步预测控制方法,并给出了控制律的收敛性分析．该方法将非线性系统处理成简单的线性和非线性两部分,对复杂的非线性多步预测方程给出了直观而有效的线性形式,并用线性预测控制方法求得控制律,避免了复杂的非线性优化求解．仿真结果表明了该算法的有效性．     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.     

钢铁炉温不确定时滞系统Smith免疫预测控制

针对钢铁炉温不确定时滞系统,将免疫反馈控制与Smith预估控制结合而提出了一种Smith免疫预测控制方法。利用克隆选择实现滚动优化避免了求Diophantine方程及逆矩阵,不需要复杂的推导,可以在线调整Smith 预估器的时滞时间常数和对扰动进行补偿,消除传统Smith预估对模型的依赖。通过实验仿真表明了该方法的有效性,并对外部干扰及系统建模误差具有很好的适应性,将该方法应用于钢铁高炉炉温控制过程,取得较好的控制效果。     

Observer-based tracking controller design for networked predictive control systems with uncertain Markov delays

This paper is concerned with a tracking controller design problem for discrete-time networked predictive control systems. The control law used here is a combined state-feedback control and integral control. Since not all the states are available in practice, a local Luenberger observer is utilised to estimate the state vector. The measured output and estimated state vector are packed together and transmitted to the tracking controller via a communication channel with a limited capacity. Meanwhile, the control signal is also transmitted through a communication network.Network-induced delays on both links are considered for the signal transmission and modelled by Markov chains. Moreover, it is assumed that the elements in Markov transition matrices are subject to uncertainties. In order to fully compensate for network-induced delays, the controller generates a sequence of control signals which are dependent on each possible delay in the feedforward channel. By taking the augmentation twice, we obtain delay-free stochastic closed-loop systems and the controlled output is chosen as the tracking error. Sufficient conditions are provided for the energy-to-peak performance of the closed-loop systems. The feedback gains of the controller can be derived by solving a minimisation problem. Two examples are illustrated to demonstrate the effectiveness of the proposed design method.     

Model predictive control for perturbed max-plus-linear systems

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Recently, we have extended MPC to a class of discrete event systems that can be described by a model that is “linear” in the (max,+) algebra. In our previous work, we have only considered MPC for the deterministic noise-free case without modeling errors. In this paper, we extend our previous results on MPC for max-plus-linear systems to cases with noise and/or modeling errors. We show that under quite general conditions the resulting optimization problems can be solved very efficiently.     

Output feedback model predictive control of uncertain norm‐bounded linear systems

A constrained output feedback model predictive control (MPC) scheme for uncertain Norm‐Bounded discrete‐time linear systems is presented. This scheme extends recent results achieved by the authors under full‐state availability to the more interesting case of incomplete and noisy state information. The design procedure consists of an off‐line step where a state feedback and an asymptotic observer (dynamic primal controller) are designed via bilinear matrix inequalities and used to robustly stabilize a suitably augmented state plant. The on‐line moving horizon procedure adds N free control moves to the action of the primal controller which are computed by solving a linear matrix inequality optimization problem whose numerical complexity grows up only linearly with the control horizon N. The effectiveness of the proposed MPC strategy is illustrated by a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.