Bilinear optimal control of a Kirchhoff plate

We consider the problem of optimal control of a Kirchhoff plate. A bilinear control is used as a force to make the plate close to a desired profile taking into the account, a quadratic cost of control. We prove the existence of an optimal control and characterize it uniquely through the solution of an optimality system.     

Optimal control of batch reactors by iterative dynamic programming

Four batch reactor systems are chosen to examine the viability of using iterative dynamic programming (IDP) for highly nonlinear systems encountered by chemical engineers. The first system is mildly nonlinear and rapid convergence resulted with the use of only a single state grid point. The use of piecewise linear continuous control with 40 stages yielded better results that the use of 80 stages with piecewise constant control. The need for more than a single grid point for the other three systems led to a systematic study of the effects of the number of grid points, of the number of allowable values for control and of the region contraction factor on the convergence of IDP. In every case the global optimum could be obtained with reasonable computational effort, and no difficulties were encountered even with systems exhibiting several local optima. The use of stages of different length allowed a refined solution to be obtained with a reasonably small number of stages in the last example.     

Optimal control of stochastic dynamic systems with past history and poison switchings

An optimal control problem for systems of stochastic differential-functional linear equations with past history and Poisson switchings is formulated. The Bellman equation is solved for this problem.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 112–118, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

Optimal control of polymer flooding based on mixed-integer iterative dynamic programming

Polymer flooding is one of the most important technologies for enhanced oil recovery. In this article, a mixed-integer optimal control model of distributed parameter systems (DPS) for the injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding and some inequalities constraints, such as polymer concentration and injection amount limitation. The control variables are the volume size, the injection concentration of each slug and the terminal flooding time. For the constant injection rate, the slug size is determined by the integer time stage length, and thus the integer variables are introduced in the DPS. To cope with the optimal control problem (OCP) of this DPS, a mixed-integer iterative dynamic programming incorporating a special truncation procedure to handle integer restrictions on stage lengths is proposed. First, the OCP with variable time stage lengths is transformed into a fixed time stage problem by introducing a normalised time variable. Then, the optimisation procedure is carried out at each stage and preceded backwards in a systematic way. Finally, the numerical results of an example illustrate the effectiveness of the proposed method.     

Optimal decentralized control of dynamic systems

In this paper, several aspects of decentralized control theory applied to dynamic systems are studied. First of all, some classical definitions about matricial functions and new results on gradient calculations are presented. In the following we generalize to matricial problems the method of gradient projection of Rosen. Finally, some aspects of stability, initialization and initial condition independence are studied in detail, and two numerical examples are considered in order to emphasize the advantages of the given procedure: the decentralized Kalman filter and the optimal power-frequency control.     

Optimal Control of a System Described by a Two-Dimensional Quartic Equation with Conjugation Conditions

New problems of optimal control of distributed systems described by partial differential two-dimensional quartic equations with conjugation conditions and quadratic cost functions are considered in the paper. The theorems of existence of unique optimal solutions are proved for every considered case.     

一类离散线性切换系统的最优控制

研究了一类离散线性切换系统在切换时间、切换次数固定的情况下的二次最优控制问题.利用离散动态规划的方法,将多级决策过程分解成一系列易于求解的单级决策过程,求出最优控制序列和最优切换序列,并给出算法.最后通过一个数值例子来说明所提出的方法的有效性.     

基于Lanchester方程的作战混合动态系统最优变招控制

根据作战混合动态过程特性,提出了一种基于Lanchcstcr方程的作战混合动态系统模型.该模型可较好的描述离散事件驱动的对阵招法和连续作战实力变化之间的相互作用.在合理战术假设的基础上,讨论了作战混合动态系统最优变招控制问题.首先,利用微分对策理论得到了作战招法存在的必要条件.进而对作战变招过程进行分析,并提出了一种最优变招控制策略的求解方法.最后,应用算例验证了所构建作战混合系统模型和所设计最优变招策略的可行性.     

Optimal control of an elliptic system with a nonsymmetric state operator

New optimal control problems for elliptic systems with contact conditions and nonsymmetric state operators are considered. Existence theorems for optimal solutions are proved. High-accuracy schemes for approximating optimal controls are proposed for the case where the set of admissible controls coincides with a complete Hilbert space. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 67–85, November–December 2005.     

参数激励和外激励联合作用下薄板的非线性动力学

研究了在参数激励和外激励联合作用下四边简支矩形薄板的非线性动力学.基于von Karman理论,推导出了在参数激励和外激励联合作用下四边简支矩形薄板的动力学方程.利用Galerkin法对偏微分方程进行三阶离散,得到一个三自由度的常微分方程.考虑1:2:4内共振-主参数共振-1/2亚谐共振的情况,利用多尺度法得到了薄板系统的六维的平均方程.最后,采用数值方法研究了薄板的周期和混沌运动.结果发现外激励对薄板的混沌运动是敏感的.     

Optimal guaranteed cost control of discrete-time uncertain linear systems

This paper considers the problem of constructing a controller which quadratically stabilizes an uncertain system and minimizes a guaranteed cost bound on a quadratic cost function. The solution is obtained via a parameter-dependent linear matrix inequality problem. © 1998 John Wiley & Sons, Ltd.     

复合材料层合板的双Hopf分叉分析

利用高维非线性系统的Hopf分叉定理,研究复合材料层合板的双Hopf分叉.研究了一类受面内激励和横向外激励联合作用下的复合材料层合板在主参数共振—1∶1内共振情况下的双Hopf分叉.首先利用多尺度法得到系统的平均方程,经过简化得到了系统的分叉响应方程.根据对分叉响应方程的分析,得到了系统平衡解的稳定性临界曲线,并给出了系统产生双Hopf分叉的条件.利用数值方法得到系统在参数平面上的分叉集,通过对不同分叉区域的分析,我们发现随着参数的变化复合材料层合板存在不同的周期运动现象.     

人口发展系统最优控制β(t)的存在唯一性

本文证明了当人口系统的控制函数β(t)为有界可测函数时,人口系统的最优控制是存在唯一的。     

Optimal control for linear systems with state equality constraints

This paper deals with the optimal control problem for linear systems with linear state equality constraints. For deterministic linear systems, first we find various existence conditions for constraining state feedback control and determine all constraining feedback gains, from which the optimal feedback gain is derived by reducing the dimension of the control input space. For systems with stochastic noises, it is shown that the same gain used for constraining the deterministic system also optimally constrains the expectation of states inside the constraint subspace and minimizes the expectation of the squared constraint error. We compare and discuss performance differences between unconstrained (using penalty method), projected, and constrained controllers for both deterministic and stochastic systems. Finally, numerical examples are used to demonstrate the performance difference of the three controllers.     

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。     

Optimal dynamic pricing for deteriorating items with reference-price effects

In this paper, a dynamic pricing problem for deteriorating items with the consumers’ reference-price effect is studied. An optimal control model is established to maximise the total profit, where the demand not only depends on the current price, but also is sensitive to the historical price. The continuous-time dynamic optimal pricing strategy with reference-price effect is obtained through solving the optimal control model on the basis of Pontryagin's maximum principle. In addition, numerical simulations and sensitivity analysis are carried out. Finally, some managerial suggestions that firm may adopt to formulate its pricing policy are proposed.     

板类结构动力检测与控制中的一种新方法

曲率模态在结构动力检测中具有对动力结构损伤部位非常敏感的特性，传统方法主要是运用中心差分法求解曲率模态，由于中心差分法的计算精度依赖于测点分布的紧密程度，这样就使动力检测结果具有很大的误差，本文利用函数的契贝雪夫多项式的展开式具有很高的逼近特性，提出了板类结构动力检测的曲率模态算法——契贝雪夫多项式算法，构造出了板类结构振型的契贝雪夫多项式函数，对该函数进行求二阶偏导得到x和y方向的曲率模态，进而求出结构损伤前后的曲率模态差，该方法可为结构损伤检测提供可靠的数据，从而达到良好的检测控制效果。     

状态和输入受限的切换奇异布尔控制网络的最优控制

本文研究了状态和输入均受限的切换奇异布尔控制网络的最优控制问题.利用矩阵半张量积方法获得受限切换奇异布尔控制网络的等价代数形式.然后通过类似针变化得到了存在最优控制的必要条件,并且提出了一个算法设计切换序列和控制策略使收益函数最大化.最后给出例子验证所得结果的有效性.     

Convergence rate analysis of the state increment dynamic programming method

It is shown that if the discretization of the state space is sufficiently fine and if the limiting trajectory is an interior point of the admissible policies then the state increment dynamic programming technique (SIDP) has linear convergence, and the coefficient of convergence can be explicitly related to the control problem components. In the course of this analysis, it is seen that the SIDP method is, in essence, a nonlinear generalization of the block Gauss-Seidel algorithm for solving linear equations. Some consequences of this insight are suggested, and a computational example comparing SIDP with differential dynamic programming is offered.     

Optimal control problem for stochastic evolution equations in Hilbert spaces

In this article, we consider an optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in Hilbert spaces and the cost functional has a quadratic growth. The existence and uniqueness of the optimal control are obtained by the means of an associated backward stochastic differential equations with a quadratic growth and an unbounded terminal value. As an application, an optimal control of stochastic partial differential equations with dynamical boundary conditions is also given to illustrate our results.