广义系统的H2次优控制问题的一个LMIs条件

研究具有动态输出反馈的连续广义系统的H2次优控制问题.在H2范数的时域计算 方法的基础上,关于连续广义系统进行了H2次优性能分析,得到了满足H2次优性能的线性矩 阵不等式组的充要条件.其次,利用线性矩阵不等式(LMI)方法设计了H2次优动态输出反馈 控制器.最后,通过数值例子进一步说明了该文的设计方法.     

终端约束滚动时域控制的次优性分析

讨论了有终端约束的滚动时域控制相对于传统最优控制的次优性问题．首先考虑一 般形式的非线性系统,通过分析有限时域滚动优化的特点,得到了滚动时域控制次优性的上 界;然后将结果进一步应用于线性系统,得到一个量化的评价指标．     

一种跟踪问题中的次优非线性预测控制算法

针对跟踪问题中无状态和输入约束的非线性预测控制最优解的求取问题,引入参考输入轨迹的概念,利用Ｓｔｉｒｌｉｎｇ插值公式,将非线性系统模型沿参考输入输出轨迹展开,取其一阶近似,处理成参数已知的线性模型．在此基础上,利用线性系统预测控制理论求解得到原系统的次优控制律．该方法不要求系统模型连续可导,且无需对线性化后的模型参数进行在线辨识,计算量小,易于实现．     

非线性系统滚动时域控制的性质研究*

针对非线性系统,对滚动时域控制的一些性质进行了研究.首先提出使系统稳定的充分条件;该条件覆盖了当前保证稳定的若干滚动时域控制策略.在此稳定性框架下,对控制系统的次优性、鲁棒性进行了扩展研究,得到系统次优性的一个上届,以及在外界衰减扰动下的鲁棒稳定性     

广义预测控制的鲁棒化改进

利用内模控制结构分析了广义预测控制在未建模动态鲁棒性方面的缺陷,提出采用失配滤波器以增强系统的鲁棒性。针对广义预测控制的特点,提出了次优失配滤波器的简单设计方法。     

时变系统的模型匹配与跟踪问题

仿照时不变系统的次优模型匹配解的存在性证明方法,可以得到J–谱分解条件下时变系统的Nehari型模型匹配问题的次优解存在性.如何针对双边模型匹配的次优问题证明解的存在性还没有有效的方法.本文在套代数框架下研究了时变线性系统的次优模型匹配和跟踪问题.首先,应用Douglas值域定理证明了耦合J–谱分解条件下次优模型匹配解的存在性,然后指出应用双参数控制器同时镇定n个系统,并且要求跟踪指标小于r的次优跟踪问题等价于同时强r镇定n-1个相关四块问题,最后给出了次优解的参数化.     

高速列车精确停车的鲁棒自触发预测控制

列车精确停车作为列车自动运行(Automatic train operation, ATO)系统的一项核心功能, 对高速列车的安全和高效运行至关重要. 本文针对高速列车停车过程的特点, 考虑在避免控制输出频繁切换的前提下实现高精度的停车曲线跟踪, 提出了基于模型预测控制(Model predictive control, MPC)的精确停车算法. 针对列车停车过程中外部不确定性阻力干扰, 采用鲁棒模型预测控制方法, 提高对外部干扰的鲁棒性. 引入自触发控制策略, 以进一步减少控制输出的频繁切换, 提高停车过程的舒适度. 该方法不需要每个采样时间都求解线性约束二次规划问题, 降低了对系统采样和通信能力的要求, 提高了算法的实用性. 分析结果表明, 高速列车精确停车控制方法的稳定性和性能指标的次优性可以得到保证. 基于高速列车实际运行数据的仿真结果验证了算法的有效性.     

一种跟踪问题中的次优非线性预测控制算法

针对跟踪问题中无状态和输入约束的非线性预测控制最优解的求取问题,引入参考输入轨迹的概念,利用Ｓｔｉｒｌｉｎｇ插值公式,将非线性系统模型沿参考输入输出轨迹展开,取其一阶近似,处理成参数已知的线性模型．在此基础上,利用线性系统预测控制理论求解得到原系统的次优控制律．该方法不要求系统模型连续可导,且无需对线性化后的模型参数进行在线辨识,计算量小,易于实现．

     

时滞系统的降维状态预测观测器及预测控制器设计

研究控制项含有时滞的线性系统的预测控制问题.利用被控对象的预测输出向量和系统的控制向量,设计了一种降维状态预测观测器,并将该状态观测器用于时滞控制系统的最优状态反馈控制中.利用该状态预测观测器可将闭环系统的时滞项移至系统闭环结构之外,从而最优控制规律完全可以按无时滞系统进行设计.由性能指标计算公式表明,该预测控制器关于二次型性能指标是次优的.     

奇异摄动时滞系统次优控制的Chebyshev多项式级数方法

研究奇异摄动时滞系统次优控制的近似设计问题.基于奇异摄动的快慢分解理论,将系统的最优控制问题转化为无时滞快子问题和线性时滞慢子问题;利用Chebyshev多项式级数方法将时滞慢子问题的近似求解问题转化为线性代数方程组的求解问题,进而得到原系统的次优控制律,该控制律由Chebyshev多项式级数的基向量表示.仿真算例表明了该方法的有效性.     

Suboptimality of decentralized stochastic control and estimation

A stochastic version of suboptimal decentralized control is formulated to study the effects of interactions on performance of systems which are composed of locally optimal subsystems. Turning this approach the other way, we also investigate suboptimality of the decentralized control which arises from the globally optimal control of the overall interconnected system due to the loss of feedback control connections among the subsystems. Various characterizations of suboptimality are given in terms of interconnection and feedback gain matrices. By duality, we derive the suboptimality conditions for decentralized estimation. The separate solutions of control and estimation problems are used to provide a suboptimal decentralized design for incomplete state information. Additional conditions are obtained for robustness and reliability of the interconnected systems synthesized by a suboptimal decentralized control.     

Resource-aware MPC for constrained linear systems: Two rollout approaches

In systems with resource constraints, such as actuation limitations in sparse control applications or limited bandwidth in networked control systems, it is desirable to use control signals that are either sparse or sporadically changing in time. Motivated by these applications, in this paper we propose two resource-aware MPC schemes for discrete-time linear systems subject to state and input constraints. The two MPC schemes exploit ideas from rollout strategies to determine simultaneously the new (continuous) control inputs and the (discrete) time instants at which the control actions are updated. The first scheme provides performance guarantees by design, in the sense that it allows the user to select a desired suboptimal level of performance, where the degree of suboptimality provides a trade-off between the guaranteed closed-loop control performance on the one hand and the utilization of (communication/actuation) resources on the other hand. The second scheme provides a guaranteed (average) resource utilization, while cleverly allocating these resources in order to maximize the control performance. By means of numerical examples, we demonstrate the effectiveness of the proposed strategies.     

Analysis of the suboptimality of large-scale systems with stochastic perturbations

In this paper the sensitivity of optimal control systems with respect to modelling errors is discussed. In particular, the deterioration of the performance due to deterministic and stochastic perturbations, or to unmodelled interconnections with other systems, is explicitly expressed by a degree of suboptimality.     

Efficient suboptimal parametric solutions to predictive control for PLC applications

The prime aim of this paper is to embed a predictive control (MPC) algorithm with constraint handling capabilities into a programmable logic controller (PLC). In order to achieve it, this paper develops parametric approaches to MPC but differs from more conventional approaches in that it predefines the complexity of the solution rather than the allowable suboptimality. The paper proposes a novel parameterisation of the parametric regions which allows efficiency of definition, effective spanning of the feasible region and also highly efficient search algorithms. Despite the suboptimality, the algorithm retains guaranteed stability, in the nominal case. A laboratory test was carried out to demonstrate the code on real hardware and the effectiveness of the solution.     

Robustness of suboptimal control: Gain and phase margin

The purpose of this paper is to introduce the gain and phase margin as measures of robustness of suboptimal linear-quadratic regulators. It will be shown that the suboptimal control retains the infinite gain margin of the corresponding optimal system, but that the phase margin and gain reduction tolerance depend on the degree of suboptimality of the nominal optimal control law. This establishes the degree of suboptimality as an index of both the system performance regarding the optimality criterion and the robustness to plant parameter uncertainties and distortions of the optimal control law. It will also be shown that the suboptimal closed-loop systems remain stable despite insertion of memoryless nonlinear gains inside individual feedback loops, thus raising further the confidence in suboptimal designs of linear-quadratic regulators.     

Optimal and suboptimal control of bundle of trajectories of deterministic logical-dynamical systems

The optimal control problem for deterministic logical-dynamical systems, with their continuous part described by differential equations and their discrete part described by recurrence equations, which simulate the operation of an automaton with memory, is considered. Algorithms for constructing the suboptimal guaranteeing and suboptimal on average controls under uncertainty are proposed based on sufficient optimality conditions for complete feedback control. It is shown that for linear logical-dynamical systems with the quadratic control criterion, the optimal open-loop control of the bundle coincides with the optimal control of its trajectory, i.e., the suboptimal control is optimal. Examples are given to illustrate the way to apply optimality and suboptimality conditions.     

Control Optimization by the Quantile Criterion

For the continuous-time and discrete-time stochastic controllable systems with the quantile performance index, the sufficient conditions for optimality and suboptimality of the feedback control were obtained by generalizing the conditions for equivalence of the probabilistic optimization problems and the dynamic programming method. The results are illustrated by orbit correction of the geostationary satellite.     

Optimal and suboptimal control for sets of trajectories of deterministic continuous-discrete systems

The optimal control problem for deterministic continuous-discrete systems whose continuous part is described by differential equations and the discrete part, by recurrence equations simulating the control device operation, is considered. Based on sufficient optimality conditions for complete feedback control, algorithms for construction of optimal control with limited set of exact measurements and suboptimal guaranteeing and suboptimal on average controls under uncertainty conditions are proposed. It is shown that for linear continuous-discrete systems with quadratic cost function the optimal open-loop control for the set coincides with the optimal control for one set trajectory, i.e., the suboptimal control is optimal. The application of optimality and suboptimality conditions is demonstrated using examples.     

Hierarchically accelerated dynamic programming for finite-statemachines

A procedure called hierarchically accelerated dynamic programming (HADP) is presented which, at the cost of a degree of suboptimality, can significantly accelerate dynamic programming algorithms for discrete event systems modeled by finite-state machines (FSMs). The methodology is based. upon the (possibly iterated) dynamical abstraction of a given FSM by state aggregation in order to generate a so-called partition machine hierarchy. Necessary and sufficient conditions for the HADP procedure to generate globally optimal solutions are given as well as bounds on the degree of suboptimality of the method. A group of examples called the Broken Manhattan Grid problems is used to illustrate an implementation of HADP with two and three level hierarchies. A set of open problems is described concerning the construction and selection of the partition machine abstractions and the improvement of the estimation of HADP suboptimality