一类受限线性系统的最优控制

研究了一类受限线性系统的最优控制问题.对于输入和状态联合受限线性系统的最优控制,引入多参数二次规划方法进行求解;首先将控制问题转化为标准的多参数二次规划问题,然后应用多参数二次规划方法求得系统的可行状态空间及其子空间,并对每个子空间的求出其时变最优控制率,最后归纳上述过程得到一般性结论.方法不仅能使系统约束的处理更加系统化和透明化,还可以获得系统的显式分段仿射控制率.仿真结果表明了该方法的有效性.     

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。     

带不等式路径约束最优控制问题的惩罚函数法

控制变量参数化（Control variable parameterization,CVP）方法是目前求解流程工业中最优操作问题的主流数值方法,但如果问题中包含路径约束,特别是不等式路径约束时,CVP方法则需要考虑专门的处理手段.为了克服该缺点,本文提出一种基于L1精确惩罚函数的方法,能够有效处理关于控制变量、状态变量、甚至控制变量/状态变量复杂耦合形式下的不等式路径约束.此外,为了能使用基于梯度的成熟优化算法,本文还引进了最新出现的光滑化技巧对非光滑的惩罚项进行磨光.最终得到了能高效处理不等式路径约束的改进型CVP架构,并给出相应数值算法.经典的带不等式路径约束最优控制问题上的测试结果及与国外文献报道的比较研究表明：本文所提出的改进型CVP 架构及相应算法在精度和效率上兼有良好表现.     

二级倒立摆的二次型最优控制研究

倒立摆系统以其自身的不稳定性而难以控制,也因此成为自动控制实验中验证控制策略优劣的极好的实验装置。针对二级倒立摆系统的平衡控制问题,对其进行数学建模,应用二次型最优控制理论设计了控制器。仿真结果表明,二次型最优控制对于典型非线性自不稳定系统有着很好的控制能力。     

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.     

远程高空滑翔UUV的最优控制设计与仿真

针对远程高空滑翔UUV突防段飞行高度稳定控制问题,建立了远程高空滑翔UUV的数学模型,并运用连续系统线性二次型最优控制理论,设计了远程高空滑翔UUV控制系统的线性二次型调节器。最后利用Matlab仿真平台,分别采用线性二次型最优控制理论和传统PID方法对远程高空滑翔UUV的突防段进行仿真,结果表明,采用最优控制的远程高空滑翔UUV控制系统振荡次数明显减少,抗扰动能力强,为以后该理论在高空滑翔UUV上的实际应用,提供了理论依据和参考。     

A Control Parameterization Approach with Variable Time Nodes for Optimal Control Problems

This paper presents a novel computational approach to deal with optimal multivariable control problems using a control vector parameterization approach with multiple time grids, where each of the control variables has its own time grid of parametrization. Both the control parameters and time nodes in the grid partition are treated directly as variables to be optimized. Based on the derived relationship between the gradients of time nodes and the ones of interval lengths, the gradient formulae for parameters are presented. Compared with the existing approaches, for which all the control variables are parameterized on the same time grid, the proposed method is more general and flexible. To illustrate, two numerical cases are tested, and the results demonstrate that fewer parameters are needed to achieve the same level of optimization.     

一种采用方块脉冲函数求解延时最优控制问题的算法

本文采用方块脉冲函数方法,将线性延时系统二次型最优控制问题转化为函数极值问题,得到了最优控制规律的分段恒定解答,导出了一种不同迭代求解的简便算法.所提算法对小延时和大延时系统均有效.     

Optimal Control of an Elliptic-Parabolic System with Conjugation Conditions

New optimal control problems for distributed systems described by initial boundary-value problems are considered in the paper for an elliptic-parabolic equation with conjugation conditions and quadratic cost functions. Theorems of existence of a unique optimal control are proved for all the considered cases.     

Linear Problems of Optimal Control of Multiple-Valued Trajectories

This paper deals with rapidity and rendezvous problems and with problems with multi-valued and vector quality criteria for objects whose behavior is described by linear differential inclusions that contain controls.     

一类不确定系统的最优鲁棒控制

运用最优方法探讨了一类模型不确定系统的鲁棒控制问题。定义了一个实际敏感度和标称敏感度之间的加权敏感度误差,并通过调整标称控制器最小化加权敏感度误差在整个频段上的方差,从而为一类不确定系统提供了一种最优的鲁棒控制器设计方法,可使系统性能对模型误差具有良好的鲁棒性。针对控制工程领域典型的一阶时滞系统进行仿真研究,其结果说明了该方法的有效性。     

Optimal Control of a Conventionally Correct System with Conjugation Conditions

New optimal control problems are constructed and considered for distributed systems whose states are described by Neumann boundary-value problems with conjugation conditions and non-unique solutions. The paper proposes accurate higher-order computation schemes for discretization of optimization problems for the case where a control set coincides with a full Hilbert space.     

解一类最优控制问题的一种自适应拟谱方法

提出一种解常微分方程最优控制问题的自适应拟谱方法.对状态函数和控制函数使用不同次数的多项式逼近.设计了一个自适应算法决定不同的次数,并给出了理论分析.数值算例比较了本文方法与一种常用的拟谱方法.     

Mixed Constrained Infinite Horizon Linear Quadratic Optimal Control

For a given initial state, a constrained infinite horizon linear quadratic optimal control problem can be reduced to a finite dimensional problem [12]. To find a conservative estimate of the size of the reduced problem, the existing algorithms require the on‐line solutions of quadratic programs [10] or a linear program [2]. In this paper, we first show based on the Lyapunov theorem that the closed‐loop system with a mixed constrained infinite horizon linear quadratic optimal control is exponentially stable on proper sets. Then the exponentially converging envelop of the closed‐loop trajectory that can be computed off‐line is employed to obtain a finite dimensional quadratic program equivalent to the mixed constrained infinite horizon linear quadratic optimal control problem without any on‐line optimization. The example considered in [2] showed that the proposed algorithm identifies less conservative size estimate of the reduced problem with much less computation.     

Numerical Solution of Optimal Control Problems with Constant Control Delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a state-of-the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.      

求解最优控制问题的Chebyshev-Gauss伪谱法

提出了一种求解最优控制问题的Chebyshev-Gauss伪谱法, 配点选择为Chebyshev-Gauss点. 通过比较非线性规划问题的Kaursh-Kuhn-Tucker条件和伪谱离散化的最优性条件, 导出了协态和Lagrange乘子的估计公式. 在状态逼近中, 采用了重心Lagrange插值公式, 并提出了一种简单有效的计算状态伪谱微分矩阵的方法. 该法的独特优势是具有良好的数值稳定性和计算效率. 仿真结果表明, 该法能够高精度地求解带有约束的复杂最优控制问题.     

宏观经济管理中一类系统的最优控制问题研究

把宏观经济系统抽象成由状态方程相同但各自状态不同的系统构成的组合系统，运用分布参数系统的建模方法建立了数学模型，并研究了系统的最优控制问题。最后给出了这种建模与优化方法在最优广告策略中的一个应用例子。     

Optimal Control of a System Described by Hyperbolic Equation with Conjugation Conditions

New problems of optimal control of distributed systems described by a hyperbolic equation with conjugation conditions and a quadratic cost function are considered in the paper. Unique optimal control existence theorems are proved for all the analyzed cases.     

基于Hopfield神经网络的双线性离散系统最优控制

将基于二次型性能指标的离散双线性系统最优控制问题转化为动态规划问题，并用Hopfield神经网络（HNN）求解．该方法具有结构简单、易于硬件实现、求解速度快且能求得精确最优解等特点．在复杂系统的实时优化与控制等方面具有广阔的应用前景．     

模糊神经网络补偿的伺服系统二次型最优控制

针对伺服系统二次型最优控制存在的问题,提出了基于模糊神经网络补偿的二次型最优控制方法,该控制方法利用模糊神经网络的实时学习能力,能够及时补偿被控对象建模不准确、参数摄动和外界干扰等非线性因素对控制系统性能的影响,增强控制系统的自适应能力,有效提高控制系统的跟踪性能和抗干扰鲁棒性能.仿真试验结果验证了该控制方法的有效性.