基于多面体不变集的离线鲁棒预测控制器综合

提出一种基于多面体不变集的离线鲁棒预测控制器综合算法.该算法离线确定一组反馈控制律及其对应的不变集,在线控制时根据当前状态所处的位置选择相应的控制律,不仅扩大了初始可行域,还能在一定程度上改善控制性能.仿真结果表明了采用多面体不变集的优越性.     

离线鲁棒预测控制器综合方法的改进方案

对离线鲁棒预测控制器综合方法进行改进.离线鲁棒预测控制算法离线确定一个控制律序列,对应一组吸引域;在线根据当前状态位于哪个吸引域内部(或哪两个吸引域之间)选择相应的一个控制律(或相邻的两个控制律的线性插值).引入参数Lyapunov函数得到多包椭圆型吸引域和多包二次稳定的离线控制律,改进了控制器的可行性和最优性.改进的控制器保持了稳定性以及控制律关于系统状态的连续性.     

有界扰动系统高效鲁棒预测控制器设计

具有有界扰动的有约束线性系统是一类常见的不确定系统. 针对此类系统, 本文借鉴扰动不变集方法, 通过离线设计两个椭圆不变集以降低以往设计的保守性, 进而提出一种有界扰动系统的高效鲁棒预测控制器(SD–ERPC)的设计方法. 该方法能够较好地处理扰动对系统的影响, 在减小控制器在线计算量的同时, 扩大原ERPC设计的初始可行域, 且具有较好的控制性能. 文中给出了SD–ERPC控制器可行性和鲁棒稳定性的理论证明,并通过仿真算例验证了该控制器的有效性.     

基于多LPV 模型的调度离线鲁棒预测控制

针对一类具有大工作区域和快时变特性的约束非线性系统, 采用多个线性参数时变(LPV) 模型近似描述原非线性系统. 对于各LPV 模型, 设计基于参数独立Lyapunov 函数的局部离线预测控制器. 构造各局部控制器间的切换策略, 在保证切换稳定性的同时, 使相互重叠的稳定域覆盖期望的工作区域. 仿真结果表明, 相比于已有的调度预测控制方法, 所提出的方法不仅能够保证控制输入在给定的约束范围内, 而且在局部控制器切换次数少的情况下, 获得良好的控制性能.

     

一种基于衰减集结的鲁棒预测控制器

高效鲁棒预测控制 (ERPC) 是一种在线计算量较小, 且控制性能较好的鲁棒预测控制算法. 但采用单一椭圆不变集的设计方法存在保守性. 本文采用衰减集结策略, 通过离线设计在系统状态空间中投影彼此正交的两个椭圆不变集, 在线进行凸组合的方法设计 ERPC 控制器, 使系统初始可行域进一步扩大, 并在一定程度上改善了控制性能.     

衰减扰动下非线性预测控制系统的鲁棒稳定性

考虑一般形式的非线性预测控制系统,研究带终端约束的稳定预测控制策略在衰减扰动下的鲁棒稳定性问题,首先引入离散非线性系统的输入状态稳定性,然后针对上述预测控制策略得出了系统的稳定性结论。     

基于多步控制集的鲁棒预测控制器设计

针对有约束多胞不确定系统, 本文提出多步控制集的概念, 并将其作为终端集进而设计鲁棒预测控制器. 由于设计了一系列可变的反馈律, 鲁棒预测控制器可以得到更好的控制性能和更大的初始可行域. 另外, 利用多步控制集的特性, 本文提出了一种将预测控制器的在线计算量转移到离线完成的算法. 通过该算法, 可以有效地平衡鲁棒预测控制器的控制性能、在线计算量和初始可行域. 仿真算例验证了这些算法的有效性.     

高超声速飞行器的调度离线预测控制

本文将调度预测控制的思想应用于离线鲁棒预测控制,设计了高超声速飞行器计算有效的调度离线预测控制器.首先在不同的平衡点离线设计一系列控制规则,实际实施时只需要在不同的控制器之间进行切换,避免进行在线优化,大幅度减少了在线计算时间.通过估计局部控制器的稳定域,保证了切换控制器的稳定性.另外在确保良好控制品质的同时,还能够保证所有输入和状态均在给定约束范围.仿真试验表明,提出的方法能实现速度和高度较大范围的指令跟踪,所有输入和状态均在给定约束范围内;相比于在线鲁棒预测控制方法,仿真运行时间减少,可以实现高超声速飞行器的实时控制.     

NMPS基于DCS的预测PID控制器鲁棒稳定性分析

针对基于DCS的预测PID的控制系统,利用Kharitonov定理和边缘理论分析其在参数不确定情况下输入输出鲁棒稳定性。具体对NMPS（非最小相位系统）给出了系统保持稳定的最大过程参数区间。理论和分析仿真结果表明,当过程参数偏离标称值时,该算法能使系统保持很好的鲁棒稳定性。     

A tool to analyze robust stability for constrained nonlinear MPC

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.     

MPC for stable linear systems with model uncertainty

In this paper, we developed a model predictive controller, which is robust to model uncertainty. Systems with stable dynamics are treated. The paper is mainly focused on the output-tracking problem of a system with unknown steady state. The controller is based on a state-space model in which the output is represented as a continuous function of time. Taking advantage of this particular model form, the cost functions is defined in terms of the integral of the output error along an infinite prediction horizon. The model states are assumed perfectly known at each sampling instant (state feedback). The controller is robust for two classes of model uncertainty: the multi-model plant and polytopic input matrix. Simulations examples demonstrate that the approach can be useful for practical application.     

Tube-based robust economic model predictive control

In this paper, we develop a tube-based economic MPC framework for nonlinear systems subject to unknown but bounded disturbances. Instead of simply transferring the design procedure of tube-based stabilizing MPC to an economic MPC framework, we rather propose to consider the influence of the disturbance explicitly within the design of the MPC controller, which can lead to an improved closed-loop average performance. This will be done by using a specifically defined integral stage cost, which is the key feature of our proposed robust economic MPC algorithm. Furthermore, we show that the algorithm enjoys similar properties as a nominal economic MPC algorithm (i.e., without disturbances), in particular with respect to bounds on the asymptotic average performance of the resulting closed-loop system, as well as stability and optimal steady-state operation.     

Robust stability of economically oriented infinite horizon NMPC that include cyclic processes

Nonlinear model predictive control (NMPC) with economic objective attracts growing interest. In our previous work [1], nominal stability of economically oriented NMPC for cyclic processes was proved by introducing a transformed system, and an infinite horizon NMPC formulation with discount factors was proposed. Moreover, the nominal stability property for economically oriented NMPC was analyzed in [2] for a class of systems satisfying strong duality. In this study, we extend the previous stability analysis in [1] to a general infinite horizon NMPC formulation with economic objectives. Instead of the strong duality assumption, we require the stage cost to be strongly convex, which is easier to check for a general nonlinear system. In addition, robust stability of this NMPC controller is also analyzed based on the Input-to-State Stability (ISS) framework. A simulated nonlinear double tank system subject to periodic change in electricity price is presented to illustrate the stability property. Finally, an industrial size air separation unit case study with periodic electricity cost is presented.     

Robust output feedback model predictive control of constrained linear systems

This paper provides a solution to the problem of robust output feedback model predictive control of constrained, linear, discrete-time systems in the presence of bounded state and output disturbances. The proposed output feedback controller consists of a simple, stable Luenberger state estimator and a recently developed, robustly stabilizing, tube-based, model predictive controller. The state estimation error is bounded by an invariant set. The tube-based controller ensures that all possible realizations of the state trajectory lie in a simple uncertainty tube the ‘center’ of which is the solution of a nominal (disturbance-free) system and the ‘cross-section’ of which is also invariant. Satisfaction of the state and input constraints for the original system is guaranteed by employing tighter constraint sets for the nominal system. The complexity of the resultant controller is similar to that required for nominal model predictive control.