具有执行器饱和特性的不确定系统预测控制器设计

针对具有执行器饱和特征的不确定系统,提出了一种带有状态观测器的新型预测控制器设计方法.该方法在滚动优化的每一步,采用带有饱和特性的反馈控制结构得到一个最优控制律.使无穷时域性能指标最小.考虑在状态不完全已知的情况下,设计了带有状态观测器的预测控制器,并通过观测器参数调整使闭环系统渐近稳定.通过仿真实验验证了所设计控制器的有效性.     

Output-feedback control for switched linear systems subject to actuator saturation

This article is devoted to the output-feedback ?_∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous- and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ?₂ (?₂)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach.     

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.     

Set invariance analysis and gain-scheduling control for LPV systems subject to actuator saturation

In this paper, a set invariance analysis and gain scheduling control design approach is proposed for the polytopic linear parameter-varying systems subject to actuator saturation. A set invariance condition is first established. By utilizing this set invariance condition, the design of a time-invariant state feedback law is formulated and solved as an optimization problem with LMI constraints. A gain-scheduling controller is then designed to further improve the closed-loop performance. Numerical examples are presented to demonstrate the effectiveness of the proposed analysis and design method.     

A robust distributed model predictive control algorithm

Although distributed model predictive control (DMPC) has received significant attention in the literature, the robustness of DMPC with respect to model errors has not been explicitly addressed. In this paper, a novel online algorithm that deals explicitly with model errors for DMPC is proposed. The algorithm requires decomposing the entire system into N subsystems and solving N convex optimization problems to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Simulations examples were considered to illustrate the application of the proposed method.     

Preview control of polytopic time-varying systems subject to actuator saturation

In this study, a novel method is proposed to track a previewable reference signal in the polytopic time-varying system with input saturation. Firstly, an augmented model containing future information is constructed using a new formal variable. This leads to the tracking control problem of polytopic time-varying system with input saturation is transformed into a stability problem of augmented error system. Next, the state and static output feedback preview controls are introduced, and the corresponding controller gains are produced by the proposed conditions. Two examples are presented to validate the effectiveness of the proposed preview controller.     

不确定广义系统的输出反馈鲁棒预测控制

针对一类具有范数有界不确定性的广义系统,当系统状态不可测时,提出了一种基于输出反馈的鲁棒预测控制器综合算法．采用ＬＭＩ方法以及变量变换思想,将无限时域“最小最大”优化问题转化为线性规划问题．确定出一组分段连续的输出反馈控制序列,给出了输出反馈控制律存在的充分条件,证明了优化问题在初始时刻的可行解可以保证广义闭环系统是渐近稳定且正则无脉冲的．仿真实例验证了所提出方法的有效性．     

Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.     

互联电力系统鲁棒分布式模型预测负荷频率控制

负荷频率控制是现代互联电力系统运行的重要保障.本文针对含有不确定因素和负荷扰动的多区域互联电力系统提出了一种基于线性矩阵不等式参数可调节的鲁棒分布式预测控制算法.设计各个区域控制器目标函数引入相邻区域的状态变量和输入变量,同时考虑发电机变化速率约束和阀门位置约束,将求解一组凸优化问题转化成线性矩阵不等式求解,得到各个区域的控制律,在线性矩阵不等式中引入一组可调参数,将优化一个上限值转化成优化吸引区,降低算法的保守性.仿真结果验证了该算法在负荷扰动、系统参数不确定和结构不确定性情况下具有鲁棒性.     

Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

This paper is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems with state saturation nonlinearities under the Round‐Robin (RR) protocol. With respect to the practical application, one of the most commonly encountered obstacles that stem from the physical limitation of system components, ie, state saturation, is adequately taken into consideration. In order to reduce the network transmission burden and improve the utilization of the network from the controller nodes to the actuator node, a so‐called RR protocol is employed to orchestrate the data transmission order. At each transmission instant, only one controller node that obtains the priority is accessible to the shared communication network. Our aim of the underlying problem is to design a set of controllers in the framework of RMPC such that the closed‐loop system is asymptotically stable. By taking the influence of the RR protocol and the state saturation precisely into account, some sufficient criteria are established in terms of the token‐dependent Lyapunov‐like approach. Then, an online optimization problem subjected to some matrix inequality constraints is provided, and the desired controllers can be obtained by solving the certain upper bound of the objective addressed. Finally, a distillation process example is provided to illustrate the effectiveness of the proposed RMPC approach.     

Distributed model predictive control of nonlinear systems subject to asynchronous and delayed measurements

In this work, we design distributed Lyapunov-based model predictive controllers for nonlinear systems that coordinate their actions and take asynchronous measurements and delays explicitly into account. Sufficient conditions under which the proposed distributed control designs guarantee that the state of the closed-loop system is ultimately bounded in a region that contains the origin are provided. The theoretical results are demonstrated through a chemical process example.     

Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation

The design of robust H-infinity controller for uncertain discrete-time Markovian jump systems with actuator saturation is addressed in this paper. The parameter uncertainties are assumed to be norm-bounded. Linear matrix inequality (LMI) conditions are proposed to design a set of controllers in order to satisfy the closed-loop local stability and closed-loop H-infinity performance. Using an LMI approach, a set of state feedback gains is constructed such that the set of admissible initial conditions is enlarged and formulated through solving an optimization problem. A numerical example is given to illustrate the effectiveness of the proposed methods.     

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.     

A robust model predictive control algorithm for incrementally conic uncertain/nonlinear systems

This paper presents a robustly stabilizing model predictive control algorithm for systems with incrementally conic uncertain/nonlinear terms and bounded disturbances. The resulting control input consists of feedforward and feedback components. The feedforward control generates a nominal trajectory from online solution of a finite‐horizon constrained optimal control problem for a nominal system model. The feedback control policy is designed off‐line by utilizing a model of the uncertainty/nonlinearity and establishes invariant ‘state tubes’ around the nominal system trajectories. The entire controller is shown to be robustly stabilizing with a region of attraction composed of the initial states for which the finite‐horizon constrained optimal control problem is feasible for the nominal system. Synthesis of the feedback control policy involves solution of linear matrix inequalities. An illustrative numerical example is provided to demonstrate the control design and the resulting closed‐loop system performance. Copyright © 2010 John Wiley & Sons, Ltd.