Pollution's ambient problems and regularity of optimal cost function

We study pollution's ambient problems by using the optimal control theory applied to partial differential equations. We consider the problem to find the optimal way to eliminate pollution in the time, such that the concentration is close to a standard level which does not affect the ecological equilibrium when the source is pointwise. We consider a quadratic cost functional and we prove the existence and uniqueness of optimal control. We find a characterisation which makes possible the computing of optimal control. Additionally, we consider the problem moving the pointwise source. So, we define a function j(b) that associates to any point b ∈ Ω the optimal cost functional applied to the optimal control. We show that j is differentiable, provided that the controls are taken in a convenient subset of admissible functions satisfying the cone properties. We also find the point in Ω, for which the cost functional is minimum.     

一类混杂系统的最优控制

研究了一类脉冲依赖于状态的混杂系统的最优控制问题.与传统的变分方法不同,通过将跳跃瞬间转化为一个新的待优化参数,得到了该混杂系统的必要最优性条件,从而将最优控制问题转化为一边界值问题,该边界值问题可由数值方法或解析方法解决.此外,利用广义微分的理论,将该必要最优性条件推广到Frechet微分形式.结论表明,在混杂动态系统运行的连续部分,最优解所满足的必要性条件和传统的连续系统相同.在混杂动态系统的脉冲点处,哈密尔顿函数满足连续性条件,协态变量则满足一定的跳跃条件.最后,通过两个实例分析,表明该方法是有效的.     

Optimal control of nonlocal thermistor equations

We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e. in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of an optimal control is proved. The optimality system consisting of the state system coupled with adjoint equations is derived, together with a characterisation of the optimal control. Uniqueness of solution to the optimality system, and therefore, the uniqueness of the optimal control, is established. The last part is devoted to numerical simulations.     

Optimal control for multi-stage and continuous-time linear singular systems

In this paper, optimal control problems for multi-stage and continuous-time linear singular systems are both considered. The singular systems are assumed to be regular and impulse-free. First, a recurrence equation is derived according to Bellman's principle of optimality in dynamic programming. Then, by applying the recurrence equation, bang-bang optimal controls for the control problems with linear objective functions subject to two types of multi-stage singular systems are obtained. Second, employing the principle of optimality, a equation of optimality for settling the optimal control problem subject to a class of continuous-time singular systems is proposed. The optimal control problem may become simpler through solving this equation of optimality. Two numerical examples and a dynamic input–output model are presented to show the effectiveness of the results obtained.     

随机运动目标搜索问题的最优控制模型

提出了Rn空间中做布朗运动的随机运动目标的搜索问题的最优控制模型.采用分析的方法来研究随机运动目标的最优搜索问题,并将原问题转化为由一个二阶偏微分方程(HJB方程)所表示的确定性分布参数系统的等价问题,推导出随机运动目标的最优搜索问题的HJB方程,并证明了该方程的解即是所寻求的最优搜索策略.由此给出了一个计算最优搜索策略的算法和一个实例.     

离散时间非线性时滞系统最优控制的DISOPE算法

对于非线性时滞系统的最优控制,提出一种基于线性时滞模型和二次型性能指标问题的迭代处蒙混过关针时滞系统化为满足可尔可夫性质的增广状态系统,在模型和实际存在差异的情况下,该算法通过迭代求解时滞线性最优控制问题和参数估计问题,获得原问题的最优解,仿真实例表明该算法的有效性和实用性。     

具有模型和实际差异的非线性系统最优控制算法及其收敛性

针对模型和实际之间的差异,提出了一种基于时变线性二次型问题的动态系统优化和参数估计集成的算法该算法能逼近实际问题最优解,给出了该模型收敛的一个充分条件,分析了它的最优性,仿真例子说明了该算法的有效性和实用性。     

线性连续时滞系统最优预见重复控制

针对一类线性连续时滞系统,提出一种最优预见重复控制设计方法.首先,通过一种等价变换,将被控时滞系统转化为无时滞系统.然后,利用L阶差分算子提升技巧,获得包含状态变量导数和跟踪误差的增广连续系统.在此基础上,通过定义一种新的性能指标,将预见重复控制设计问题转化为连续非自治系统的线性二次调节问题.进一步,基于最优控制理论,得到包含状态反馈、误差积分、重复控制、时滞补偿和预见补偿的最优预见重复控制器.该控制器包含了已有文献的多种控制器形式.最后,通过一个数值仿真实例,说明所提方法的有效性.     

Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon

This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.     

Optimal guidance law for cooperative attack of multiple missiles based on optimal control theory

This article considers the problem of optimal guidance laws for cooperative attack of multiple missiles based on the optimal control theory. New guidance laws are presented such that multiple missiles attack a single target simultaneously. Simulation results show the effectiveness of the proposed algorithms.     

Optimal sulfur dioxide gas discharge control for Osaka city,Japan

This paper, using actual data, establishes a dynamical model of sulfur dioxide pollution and gives an optimal discharge control policy for Osaka city in Japan.From a mass balance of the gas, a linear scalar state equation is obtained. In spite of the simplicity of the model, it can represent the effect of wind speed, inversion layer, diffusion, boundary concentration and discharge intensity of the pollutant sources. Six unknown parameters in the model and system noise variance are identified by maximizing likelihood function by Flexible Polyhedron Search. This makes the model reasonably representative.A quadratic loss function for the control problem is the weighted sum of two terms; the loss caused by the discharge control and the loss due to the air pollution. The wind speed varies at random according to a Markov transition matrix, considering actual emergency control situations. The optimal control policy is obtained by Dynamic Programming, resulting in linear feedback control dependent on the wind speed, involving a Riccati equation. A practical method of the determination of the weighting coefficient in the loss function is proposed.Since the model is a scalar state system, the whole calculation can be performed with a relatively small computer. This ease of computation and the Markov property of the wind speed suggest that the proposed method is applicable to the actual emergency discharge control.     

基于粗糙集和分形理论的交通流优化控制设计模型

为解决交通预测的全局优化控制问题,在运用粗糙集理论对路网节点所测得的历史交通流量进行量化分析的基础上,建立了规则简化的数据清洗模型;基于分形理论的相似性原理建立了交通流量的预测模型,并给出了交通流优化控制系统的运行机制和相应的网络拓扑结构。用某交通观测站的实测数据对模型进行仿真,仿真结果表明,文中所设计的模型和算法是有效的。     

一类脉冲切换系统的最优控制

研究一类脉冲依赖于状态的脉冲切换系统的最优控制问题. 考虑了目标函数的两种情况: 当目标函数光滑时, 通过将跳跃瞬间转化为一个新的待优化参数, 得到了该脉冲切换系统的必要最优性条件; 当目标函数不光滑时, 利用非光滑分析的知识, 得到了广义微分形式的必要最优性条件. 算例分析验证了所提出方法的有效性.     

Optimal control during feedback failure

The problem of controlling a perturbed open loop system so as to keep its performance errors within bounds is considered. The objective is to maximise the time during which performance errors remain below a prescribed ceiling, while the controlled system's parameters are within a specified neighbourhood of their nominal values. It is shown that there is an optimal open loop controller that achieves this objective. Conditions under which the optimal controller generates a bang-bang control input signal are characterised. In general, it is shown that the performance of the optimal controller can always be approximated by a bang-bang signal.     

多电机驱动系统的保性能鲁棒Funnel控制

本文针对含参数不确定性的多电机驱动系统,提出一种基于最优保性能鲁棒的Funnel控制方法实现系统的规定跟踪性能.该控制方法通过构造Funnel函数对误差系统进行变换,并设计自适应反步控制器保证变换后系统的稳定性即可使跟踪误差的瞬态和稳态响应均被限制在给定的Funnel边界内.然而由于系统中存在的参数不确定性会影响系统的规定控制性能,本文在Funnel控制基础上又设计了最优保性能鲁棒控制器.它是通过将参数不确定性系统的保性能鲁棒控制问题转化为标称系统的最优控制问题,并求解新的黎卡提方程而得到的.因此所设计的控制器不但消除了参数不确定性对系统的影响并且能够使系统的性能指标达到一确定的上界.最后,对四电机驱动系统进行了仿真和实验验证,说明所提出控制方法的有效性.     

事件驱动的网络化系统最优控制

针对随机事件驱动的网络化控制系统, 研究其中的有限时域和无限时域内最优控制器的设计问题. 首先, 根据执行器介质访问机制将网络化控制系统建模为具有多个状态的马尔科夫跳变系统; 然后, 基于动态规划和马尔科夫跳变线性系统理论设计满足二次型性能指标的最优控制序列, 通过求解耦合黎卡提方程的镇定解, 给出最优控制律的计算方法, 使得网络化控制系统均方指数稳定; 最后, 通过仿真实验表明了所提出方法的有效性.

     

资源约束系统的控制与调度协同优化方法

对于一类通信约束的网络控制系统, 应用通信序列的概念和混合逻辑动态的构架, 将其建模成一类集成控制和调度的资源约束系统模型. 采用线性矩阵不等式来描述离散周期系统的周期通信序列和H_∞ 控制的协同优化问题, 并用一种递增优化序列算法来求解优化的调度策略及其相应的渐近稳定及r指数稳定的H_∞控制器. 该算法结合线性矩阵不等式凸优化问题解决了调度与控制的协同设计问题, 同时也节省了搜索优化解的计算时间.     

水下滑翔机垂直面运动优化控制

水下滑翔机是一种依靠水动力和净浮力驱动的新型水下机器人. 本文分析了滑翔机在垂直面滑翔时, 浮力变化和内置可动质量块位置变化对滑翔机运动状态的影响．针对滑翔机在潜浮切换时, 由于机翼受力不对称产生的无升力现象而导致的切换过程不稳定的问题, 采用两点边值的优化控制方法, 规划了内置质量块的位量, 以消除滑翔机在潜浮切换过程中各个时刻产生的不对称无升力现象．最后给出了滑翔机实际机械系统可接受的最优控制 方案. 仿真表明了这种优化方法的有效性.     

New system theory and its impact on control theory

Real systems can include two types of state variables – dynamic and static. While dynamic state variables are a common part of each system, static variables are not and their presence in a system may cause some problems if standard system theories are used. In this paper, it is shown that, due to a new system theory (NST), it is possible to work correctly with systems and subsystems which include not only dynamic state variables, but also static state variables. If standard system theories are used, static variables in the real system cause not only problems in describing systems but also some challenges in control theory. These challenges involve, for example, some questions of controllability, reachability, or observability of a plant that includes static variables or the optimal control design of a plant that includes statical state variables. Some of the challenges mentioned are addressed in this paper after a brief introduction of the NST.     

不完全柔性制造系统的最优控制

考虑具有随机需求的不完全柔性制造系统的最优控制，系统在各种产品间的切换时间是不可忽略的。运用马尔可夫最优决策过程归纳方法，导出机器服务率的最优控制策略。通过分析最优值函数的性质，证明最优策略具有简单的阈值结构，从而可得到次优生产策略--阈值控制策略。