带有随机跳跃干扰的线性二次随机最优控制问题

给出一类布朗运动和泊松过程混合驱动的正倒向随机微分方程解的存在唯一性结果,应用这一结果研究带有随机跳跃干扰的线性二次随机最优控制问题,并得到最优控制的显式形式,可以证明最优控制是唯一的.然后,引入和研究一类推广的黎卡提方程系统,讨论该方程系统的可解性并由该方程的解得到带有随机跳跃干扰的线性二次随机最优控制问题最优的线性反馈.     

飞行器与机器人的区域目标搜索最优控制

描述了飞行器导航或移动机器人的区域搜索控制问题.为了使该问题得到优化解决,首先建立了基于区域搜索控制问题的模型,将最优控制原理运用于此模型上,得到其伴随方程和控制方程,后基于此分析了该问题,且讨论了此方法的可行性.然后,通过解出问题的规范方程,使飞行器导航或移动机器人的区域搜索控制问题最终得以解决,进而推导得到了飞行器导航或移动机器人的区域目标搜索最优控制以及最优轨线.最后,通过计算仿真结果表明,该方法是有效的,故为飞行器导航与移动机器人的区域目标搜索最优控制提供了依据.     

正倒向随机微分方程与一类线性二次随机最优控制问题

讨论一类正倒向随机微分方程解的存在唯一性及其对应的一类线性二次随机最优控制问题,利用单调性方法证明了一类特殊的正倒向随机微分方程解的存在唯一性定理,利用该结果研究一类耦合了一个倒向随机微分方程的线性随机控制系统广义最优指标随机控制问题,得到由正倒向随机微分方程的解所表示的唯一最优控制的显式表达式,并得到精确的线性反馈及其对应的Riccati方程.     

采用带时滞的输入—输出模型的随机最优控制

由于在系统模型中未引入时滞,以及计算量大等原因,尽管随机最优控制有很多优点,但未能成功地应用于过程控制。本文从新的角度,提出一种离散随机最优控制算法,该法采用带有时滞的输入-输出对象模型,而且无需求解Riccati方程和进行谱因子分解。本算法要求很少的计算量,因而易在微型计算机上实现。文中还对系统闭环特性进行分析。     

卫星搜索移动目标问题中的目标运动预测方法研究

目标运动参数未知给移动目标搜索计划编制引入了不确定性,降低了卫星的侦察效能.为了降低不确定性和优化卫星的搜索方案,在采用贝叶斯规则对目标概率分布更新的基础上,提出一种基于高斯分布的目标转移概率密度函数,并绐出相应的转移计算方法.采用最大发现概率和与最大覆盖作为搜索策略,建立移动目标搜索仿真场景.结果显示,该方法能够减少卫星搜索计划制定过程中的不确定性,降低了搜索的盲目性,提高了卫星的效能.     

不确定拟哈密顿系统的随机最优控制

本文提出了不确定拟哈密顿系统、基于随机平均法、随机极大值原理和随机微分对策理论的一种随机极大极小最优控制策略.首先,运用拟哈密顿系统的随机平均法,将系统状态从速度和位移的快变量形式转化为能量的慢变量形式,得到部分平均的It随机微分方程;其次,给定控制性能指标,对于不确定拟哈密顿系统的随机最优控制,根据随机微分对策理论,将其转化为一个极小极大控制问题;再根据随机极大值原理,建立关于系统与伴随过程的前向-后向随机微分方程,随机最优控制表达为哈密顿控制函数的极大极小条件,由此得到最坏情形下的扰动参数与极大极小最优控制;然后,将最坏扰动参数与最优控制代入部分平均的It随机微分方程并完成平均,求解与完全平均的It随机微分方程相应的Fokker-Planck-Kolmogorov(FPK)方程,可得受控系统的响应量并计算控制效果;最后,将上述不确定拟哈密顿系统的随机最优控制策略应用于一个两自由度非线性系统,通过数值结果说明该随机极大极小控制策略的控制效果.     

MIMO雷达对高速运动目标搜索策略研究

高速运动目标,是现代雷达探测中遇到的一种新情况。针对海军相控阵雷达对海上空中高速运动目标的探测,推导了多元阵列的MIMO雷达探测概率的计算公式,在此基础上,计算了距离单元内目标探测概率,并比较了正交信号模式下与有向波束模式下MIMO雷达对高速运动目标探测概率。研究表明,对于高速运动目标,使用有向波束探测模式,在相同的信噪比下可以达到更高的探测效率。     

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.     

针对运动目标的多无人机协同鸽群优化搜索方法

针对多无人机协同运动目标搜索问题,本文设计了改进鸽群优化算法的协同搜索决策.首先,基于运动目标的独立性,建立了服从正态分布的目标概率信息图模型;为了提高环境中目标存在的确定度,建立了搜索环境的确定度信息图.其次,通过建立的吸引和排斥数字信息素图,引导无人机向未搜索区域飞行,减少重复搜索概率,提高协同目标搜索效率,并基于传统的鸽群算法,通过加入速度更新修正机制和精英代机制对其进行改进.然后,结合环境中目标的存在概率信息以及无人机搜索目标的探测信息,使用改进鸽群优化算法,规划无人机的最优搜索飞行路径.并设计避碰机制,以有效防止无人机搜索过程中的碰撞.最后,通过比较仿真实验验证了改进鸽群优化算法对运动目标协同搜索的有效性.     

Hamilton-Jacobi-Bellman formalism for optimal climate control of greenhouse crop

The paper describes a simplified dynamic model of a greenhouse tomato crop, and the optimal control problem related to the seasonal benefit of the grower. A HJB formalism is used and the explicit form of the Krotov-Bellman function is obtained for different growth stages. Simulation results are shown.     

Hybrid Solution Method for Dynamic Programming Equations for MDOF Stochastic Systems

An optimal control problem is considered for a multi-degree-of-freedom (MDOF) system, excited by a white-noise random force. The problem is to minimize the expected response energy by a given time instantT by applying a vector control force with given bounds on magnitudes of its components. This problem is governed by the Hamilton-Jacobi-Bellman, or HJB, partial differential equation. This equation has been studied previously [1] for the case of a single-degree-of-freedom system by developing a hybrid solution. Specifically, an exact analitycal solution has been obtained within a certain outer domain of the phase plane, which provides necessary boundary conditions for numerical solution within a bounded in velocity inner domain, thereby alleviating problem of numerical analysis for an unbounded domain. This hybrid approach is extended here to MDOF systems using common transformation to modal coordinates. The multidimensional HJB equation is solved explicitly for the corresponding outer domain, thereby reducing the problem to a set of numerical solutions within bounded inner domains. Thus, the problem of bounded optimal control is solved completely as long as the necessary modal control forces can be implemented in the actuators. If, however, the control forces can be applied to the original generalized coordinates only, the resulting optimal control law may become unfeasible. The reason is the nonlinearity in maximization operation for modal control forces, which may lead to violation of some constraints after inverse transformation to original coordinates. A semioptimal control law is illustrated for this case, based on projecting boundary points of the domain of the admissible transformed control forces onto boundaries of the domain of the original control forces. Case of a single control force is considered also, and similar solution to the HJB equation is derived.     

一类部分信息下带有劳动力收入的最优投资消费问题

最优投资消费问题属于一类典型的随机最优控制问题. 劳动力收入可通过影响期望效用从而影响投资消 费策略的制定. 本文首次在股票收益率和劳动力收入均为不可观测过程情形下, 研究了一类部分信息下的最优投资 消费问题. 首先综合运用Kalman滤波和非线性滤波, 得到了Zakai方程的显式解, 将部分信息下的随机最优控制问题 转化为完备信息下的随机最优控制问题. 其次通过求解HJB方程以及证明验证定理, 得到了该类最优投资消费问题 的最优策略以及值函数的显式表达. 最后采用真实市场数据进行仿真, 对比经典完备信息模型与本文部分信息模型 所得最优策略的差异, 验证了本文所得最优策略在有效利用市场信息方面的优越性.     

红外运动小目标检测的小面拟合算法

针对红外图像序列中运动小目标,提出一种基于预测的小面拟合目标检测算法。首先根据图像序列中目标运动的连续性及方向性,采用二阶自回归模型预测目标的搜索窗口。然后根据天空背景红外图像中小目标灰度高于背景的特征,利用小面拟合模型对搜索窗口的局部区域作灰度曲面拟合,提取搜索窗口内灰度极值点作为目标,提出了相应的目标检测算子。对红外图像序列的实验表明,该算法可有效检测天空背景下红外运动小目标,算法的实时性和抗干扰能力优于传统的目标检测方法。     

双目轮式移动机器人的运动目标识别与跟踪

研究在室内相对复杂背景下的运动目标识别与跟踪,采用Hu氏不变矩作为目标特征,通过环形方式搜索种子点进行目标区域生长,在有干扰的情况下检出目标,并估计相对位姿和控制本体机器人快速跟踪目标.用Intel的计算机视觉库OpenCV实现图像预处理、图像分割、孔洞填充、区域生长和特征提取.实验结果表明,系统能对运动目标进行实时稳定快速的跟踪,适用性强.     

Optimal control theory for ambient pollution

We study optimal control of systems of distributed parameters applied to problems of ambient pollution. The model consists of a parabolic partial differential equation that models the transport of a pollutant in an incompressible viscous fluid, with boundary conditions and initial value, that is in our model we consider the velocity that the pollutant propagates in the environment. The developed mathematical modelling allows us to calculate the pollution concentration that is poured in a region of the space in such a way that at time t?=?T, the pollution concentration is as close as possible to the acceptable maximum concentration in the environment. We characterise the optimal control to obtain an optimality system that allows the numerical calculation of the problem and show the convergence of the method. As application, we study the case of the contamination of a river with mercury (Hg) in water without movement and with movement. We present some numerical experiments.     

Optimal control of mobile sources for heat conductivity processes

We consider a problem of optimal control of the mobile sources for heat conductivity processes, described by parabolic equation and systems of ordinary differential equations. Sufficient conditions for Frechet differentiability of the performance criterion and an expression for its gradient were determined. The necessary optimality condition was established in the form of the integral principles of maximum. The theoretical conclusions are illustrated by the solution of a numerical example.     

UNCERTAIN OPTIMAL CONTROL WITH APPLICATION TO A PORTFOLIO SELECTION MODEL

Optimal control is a very important field of study not only in theory but in applications, and stochastic optimal control is also a significant branch of research in theory and applications. Based on the concept of uncertain process, an uncertain optimal control problem is dealt with. Applying Bellman's principle of optimality, the principle of optimality for uncertain optimal control is obtained, and then a fundamental result called the equation of optimality in uncertain optimal control is given. Finally, as an application, the equation of optimality is used to solve a portfolio selection model.