基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列与状态之间的显式函数关系, 减少多参数规划问题求解的工作量; 另一方面能够同时求解得到状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.     

混杂系统优化控制的动态规划方法研究

研究了末态自由、时间一定的混杂系统的最优控制问题.提出了基于可达网络的混杂系统优化控制的动态规划方法.这种方法能够给出问题的全局最优解,并有效地降低系统的计算量.     

混杂系统优化控制的动态规划方法研究

研究了末态自由、时间一定的混杂系统的最优控制问题. 提出了基于可达网络的混杂系统优化控制的动态规划方法. 这种方法能够给出问题的全局最优解, 并有效地降低系统的计算量.     

基于控制参数化的切换系统最优控制方法研究

针对一类特殊的混杂系统——切换系统的最优控制问题,利用控制函数参数化方法和时间尺度转化法,将切换系统最优控制问题转化为最优参数选择问题,可利用Miser 3.2来求解该问题,这样能有效地简化求解切换系统最优控制的难度,而且算法易于理解,编程易于实现。     

一类混杂系统建模和优化控制的研究

为解决混杂系统优化控制的计算复杂性问题,针对结合逻辑规则的工业过程混杂模型,采用结合约束程序的混合整数非线性规划算法,求解这种混杂模型的优化控制。计算实例表明,通过混杂建模方法,可以充分利用工业对象的机理模型以及操作工经验或专家经验,建立系统的更精确模型;结合约束程序混合整数非线性规划算法可以较迅速地求解混杂模型优化控制问题,从而使该方法可以用于工业过程实时控制中。     

基于控制参数化的切换系统最优控制方法研究

针对一类特殊的混杂系统——切换系统的最优控制问题．利用控制函数参数化方法和时间尺度转化法,将切换系统最优控制问题转化为最优参数选择问题,可利用Miser3．2来求解该问题,这样能有效地简化求解切换系统最优控制的难度,而且算法易于理解,编程易于实现。     

含扩散项不可靠生产系统最优生产控制的数值求解

针对含扩散项不可靠随机生产系统最优生产控制的优化命题, 采用数值解方法来求解该优化命题最优控制所满足的模态耦合的非线性偏微分HJB方程. 首先构造Markov链来近似生产系统状态演化, 并基于局部一致性原理, 把求解连续时间随机控制问题转化为求解离散时间的Markov决策过程问题, 然后采用数值迭代和策略迭代算法来实现最优控制数值求解过程. 文末仿真结果验证了该方法的正确性和有效性.     

自由时间最优控制问题的一种控制向量参数化方法

针对自由时间最优控制问题,提出一种控制向量参数化（CVP）方法.通过引入时间尺度因子,将自由时间最优控制问题转化为固定时间问题,并将终端时刻作为优化参数.基于CVP方法,最优控制问题被转化为一个非线性规划（NLP）问题.建立目标和约束函数的Hamiltonian函数,通过求解伴随方程获得目标和约束函数的梯度,采用序列二次规划（SQP）方法获得问题的数值解.对于控制有切换结构的优化问题,给出了一种网格精细化策略,以提高控制质量.补料分批反应器最优控制问题的仿真实验验证了所提出方法的有效性.     

输入饱和的双积分系统的复合时间最优控制

针对典型的有输入饱和的双积分环节或系统的时间最优控制问题,建立了双积分环节的传递函数和状态空间方程两种数学模型,设计双积分环节的闭环时间最优控制律;对时间最优控制在系统存在干扰和不确定性存在条件下出现的振颤现象进行分析;基于对振颤问题的分析,提出一种对时间最优控制的改进,即一种复合控制方法,当输入作用时,系统先由时间最优控制律控制,当误差达到预定值限,控制律由时间最优控制律切换到另一种线性控制律。采用了比例微分控制律,来解决时间最优控制的振颤问题,响应时间达到最优,并解决振颤问题。     

多元时间序列的子空间回声状态网络预测模型

针对采用回声状态网络预测多元混沌时间序列时储备池学习算法可能存在的病态解问题,该文提出了一种基于快速子空间分解方法的回声状态网络预测模型.所提模型利用Krylov子空间分解方法提取储备池状态矩阵的子空间,子空间代替原状态矩阵进行输出权值求解,可以消除储备池状态矩阵的冗余信息,有效地解决伪逆算法存在的病态解问题,并且降低计算复杂度,提高泛化性能和预测精度.基于两组多元混沌时间序列的仿真结果验证了该文所提模型的有效性和实用性.     

Near optimal control for a class of stochastic hybrid systems

To address a computationally intractable optimal control problem for a class of stochastic hybrid systems, this paper proposes a near optimal state feedback control scheme, which is constructed by using a statistical prediction method based on approximate numerical solution that samples over the entire state space. A numerical example illustrates the potential of the approach.     

Globally robust explicit model predictive control of constrained systems exploiting SVM‐based approximation

This paper presents a systematic method to address the reduction of online computational complexity and infeasibility problem of explicit model predictive control for constrained systems under external disturbance. In feasible state space, in order to avoid the expensive database searching procedure, support vector machine‐based approximation is proposed to yield a novel unified explicit optimal control law rather than a piecewise affine one developed by explicit model predictive control. In infeasible state space, through constructing finite maximum control invariant sets around fictitious equilibrium points, a reachable controller is devised to steer the infeasible state asymptotically to the feasible state space without violating the hard constraint. Consequently, global robustness is guaranteed by introducing a minimum robust positively invariant set by means of the tube‐based technique, despite the coexistence of external disturbance and training error. Finally, the performance of the presently proposed control law is evaluated through three groups of numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal control computation for nonlinear systems with state-dependent stopping criteria

In this paper, we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion. This stopping criterion is defined by a smooth surface in the state space; when the state trajectory hits this surface, the governing dynamic system stops. By restricting the controls to piecewise constant functions, we derive a finite-dimensional approximation of the optimal control problem. We then develop an efficient computational method, based on nonlinear programming, for solving the approximate problem. We conclude the paper with four numerical examples.     

Using hash tables to manage the time-storage complexity in a point location problem: Application to explicit model predictive control

The online computational burden of linear model predictive control (MPC) can be moved offline by using multi-parametric programming, so-called explicit MPC. The solution to the explicit MPC problem is a piecewise affine (PWA) state feedback function defined over a polyhedral subdivision of the set of feasible states. The online evaluation of such a control law needs to determine the polyhedral region in which the current state lies. This procedure is called point location; its computational complexity is challenging, and determines the minimum possible sampling time of the system. A new flexible algorithm is proposed which enables the designer to trade off between time and storage complexities. Utilizing the concept of hash tables and the associated hash functions, the proposed method solves an aggregated point location problem that overcomes prohibitive complexity growth with the number of polyhedral regions, while the storage–processing trade-off can be optimized via scaling parameters. The flexibility and power of this approach is supported by several numerical examples.     

连续状态自适应离散化基于K-均值聚类的强化学习方法

使用聚类算法对连续状态空间进行自适应离散化．得到了基于K-均值聚类的强化学习方法．该方法的学习过程分为两部分：对连续状态空间进行自适应离散化的状态空间学习,使用K-均值聚类算法;寻找最优策略的策略学习．使用替代合适迹Sarsa学习算法．对连续状态的强化学习基准问题进行仿真实验,结果表明该方法能实现对连续状态空间的自适应离散化,并最终学习到最优策略．与基于CMAC网络的强化学习方法进行比较．结果表明该方法具有节省存储空间和缩短计算时间的优点．     

基于状态聚类的多站点CSPS系统的协同控制方法

单站点传送带给料加工站（Conveyor-serviced production station,CSPS）系统中,可运用强化学习对状态——行动空间进行有效探索,以搜索近似最优的前视距离控制策略.但是多站点CSPS系统的协同控制问题中,系统状态空间的大小会随着站点个数的增加和缓存库容量的增加而成指数形式（或几何级数）增长,从而导致维数灾,影响学习算法的收敛速度和优化效果.为此,本文在站点局域信息交互机制的基础上引入状态聚类的方法,以减小每个站点学习空间的大小和复杂性.首先,将多个站点看作相对独立的学习主体,且各自仅考虑邻近下游站点的缓存库的状态并纳入其性能值学习过程;其次,将原状态空间划分成多个不相交的子集,每个子集用一个抽象状态表示,然后,建立基于状态聚类的多站点反馈式Q学习算法.通过该方法,可在抽象状态空间上对各站点的前视距离策略进行优化学习,以寻求整个系统的生产率最大.仿真实验结果说明,与一般的多站点反馈式Q学习方法相比,基于状态聚类的多站点反馈式Q学习方法不仅具有收敛速度快的优点,而且还在一定程度上提高了系统生产率.     

Optimally maintaining a multi-state system with limited imperfect preventive repairs

In this paper, the optimal maintenance policy for a multi-state system with no observation is considered. Different from most existing works, only a limited number of imperfect preventive maintenance actions can be performed between two successive replacements. Assume that the system's deterioration state cannot be observed during its operation expected after each replacement, and it evolves as a discrete-time Markov chain with a finite state space. After choosing the information state as state variable, the problem is then formulated as a Markov decision process over the infinite time horizon. In order to increase the computational efficiency, several key structural properties are developed by minimising the total expected cost per unit time. The existence of the optimal threshold-type maintenance policy is proved and the monotonicity of the threshold is obtained. Finally, a numerical example is given to illustrate the optimal policy.     

基于相容粗糙集技术的连续值属性决策树归纳

决策树是常用的数据挖掘方法,扩展属性的选择是决策树归纳的核心问题。基于离散化方法的连续值决策 树归纳在选择扩展属性时,需要度量每一个条件属性的每一个割点的分类不确定性,并通过这些割点的不确定性选择 扩展属性,其计算时间复杂度高。针对这一问题,提出了一种基于相容粗糙集技术的连续值属性决策树归纳方法。该 方法首先利用相容粗糙集技术选择扩展属性,然后找出该属性的最优割点,分割样例集并递归地构建决策树。从理论 上分析了该算法的计算时间复杂度,并在多个数据集上进行了实验。实验结果及对实验结果的统计分析均表明,提出 的方法在计算复杂度和分类精度方面均优于其他相关方法。     

低计算复杂度的永磁同步电机多步预测电流控制

传统的永磁同步电机模型预测电流控制策略仅在一个采样周期内寻优,难以避免陷入局部最优问题,而多步预测会增加预测次数,计算复杂度成倍增长.为此,提出一种低复杂度的永磁同步电机三步电流预测控制策略.首先,在延时补偿的基础上,两步预测结合三矢量电压控制和最优占空比电压控制,三步预测保持与两步预测相同的电压矢量,然后由代价函数选出控制电压矢量;最后,设计电感dq轴分量双闭环的鲁棒控制.仿真结果表明,相比其他控制策略,所提策略具有良好的动静态性能,寻优代码执行时间降低了约51%;在不影响输出电能质量的前提下,开关频率降低了约17%;并对电感失配造成的性能恶化具有抑制性.     

Dynamic selling of quality-graded products under demand uncertainties

This paper examines dynamic selling (DS) problems under demand uncertainties. Quality-graded products with fully downward substitutable demands are considered. Downward demand substitution indicates that demands for lower quality grade products can be fulfilled by either designated or higher quality grade products. In this dynamic selling problem, decision makers need to choose an optimal selling policy in each decision epoch. The objective is to identify an optimal policy for the dynamic selling of quality-graded inventory.DS problems are formulated as a discrete-time Markov decision process (MDP) model. In the MDP model, demand type and inventory levels are state variables. The objective is to maximize expected profits. In such a multi-dimensional dynamic decision problem, computational complexity is a chief concern. This study proves the structure of optimal policies that significantly reduce computational complexity. Performance of optimal dynamic selling policies is evaluated in detailed numerical studies.