年龄相关的非线性时变种群扩散系统最优分布控制的存在性

讨论了一类非线性时变种群扩散系统的最优分布控制问题,利用LionsJL的偏微控制理论和先验估计,证明了系统最优分布控制的存在性.所得结果可为非线性种群扩散系统中的最优控制问题的实际研究提供必要的理论基础.     

年龄相关的种群扩散系统的最优分布控制

本文讨论年龄相关的种群扩散系统的最优分布控制 ,证明了最优分布控制的存在性 ,得到了分布控制为最优的充分必要条件及确定最优控制的最优性组 .     

一类具有年龄结构的非线性种群扩散系统的最优收获控制

讨论了一类与年龄相关的非线性种群扩散系统的最优收获控制问题,证明了最优收获控制的存在性,并且给出了控制为最优的必要条件及其由偏微分方程组和变分不等式组成的最优性组.这些结果可为种群扩散系统最优控制问题的实际研究提供理论基础.     

具空间扩散和年龄结构的时变种群系统的最优收获控制

本文讨论了一类具空间扩散和年龄结构的时变种群系统的最优收获控制问题,利用Banach空间的SaksMasur引理,证明了系统最优收获控制的存在性,并利用切向锥、法向锥概念,建立了收获控制为最优的必要条件.     

一类半线性时变种群系统的最优捕获控制

讨论了年龄相关的半线性时变种群系统的最优捕获控制问题.根据微积分方程及泛函分析的知识证明了最优捕获控制的存在性,得到了捕获控制为最优的必要条件.     

时变种群扩散系统最优生育率控制的非线性问题

本文讨论了一类时变种群扩散系统最优生育率控制的非线性问题，证明了最优生育率控制的存在性，给出了控制为最优的必要条件及其最优性组，本结果可为种群扩散系统最优控制问题的实际研究提供物理理论基础。     

具最终状态观测的种群扩散系统最优生育率控制的非线性问题

讨论了一类与年龄相关的时变种群扩散系统最优生育率控制的非线性问题,证明了最优生育率控制的存在性,并给出了控制为最优的必要条件及其由偏微分方程组和变分不等式组成的最优性组.这些结果可为时变种群扩散系统最优控制问题的实际研究提供理论基础.     

一般目标信号和干扰信号下多采样率系统的最优预见控制器设计

针对目标信号和干扰信号为多项式的情形,研究了多采样率离散时间控制系统的最优预见控制问题.首先利用离散时间系统提升技术,把所研究的系统转化成单采样率的扩大系统.然后构造扩大误差系统,把问题转化为包含预见信号的最优调节问题.最后利用最优预见控制理论的结果得到系统的最优预见控制输入,其中包含积分器和预见前馈补偿.本文还对扩大误差系统的能控性和能观测性和相应的代数Riccati方程的可解性进行了讨论.     

具有年龄和加权的非线性随机种群系统的最优边界控制

讨论了与年龄相关的非线性随机种群系统的最优边界控制问题,在外界环境对种群系统产生影响的条件下,考虑了种群的加权系数,应用积分-偏微分方程和变分不等式导出控制为最优的必要条件,得到最优性组.     

具扩散与年龄结构的三种群捕食与被捕食系统的最优收获

研究了一类具有空间扩散和年龄结构的三种群捕食与被捕食系统的最优收获问题,运用Banach不动点原理讨论了系统解的存在唯一性,证明了最优收获控制的存在性,给出了最大值原理.结果可为多种群扩散系统最优控制问题的实际研究提供理论基础.     

Dynamics for Controlled 2D Generalized MHD Systems with Distributed Controls

We study the dynamics of a piecewise (in time) distributed optimal control problem for Generalized MHD equations which model velocity tracking coupled to magnetic field over time. The long-time behavior of solutions for an optimal distributed control problem associated with the Generalized MHD equations is studied. First, a quasi-optimal solution for the Generalized MHD equations is constructed; this quasi-optimal solution possesses the decay (in time) properties. Then, some preliminary estimates for the long-time behavior of all solutions of Generalized MHD equations are derived. Next, the existence of a solution of optimal control problemis proved also optimality system is derived. Finally, the long-time decay properties for the optimal solutions is established.     

Error Estimates for the Approximation of a Class of Optimal Control Systems Governed by Linear PDEs

This paper deals with a class of optimal control problems in which the system is governed by a linear partial differential equation and the control is distributed and with constraints. The problem is posed in the framework of the theory of optimal control of systems. A numerical method is proposed to approximate the optimal control. In this method, the state space as well as the convex set of admissible controls are discretized. An abstract error estimate for the optimal control problem is obtained that depends on both the approximation of the state equation and the space of controls. This theoretical result is illustrated by some numerical examples from the literature.     

Coupled Galerkin and parameterization methods for optimal control of discretely connected parallel beams

Galerkin and wavelet methods for optimal boundary control of a couple of discretely connected parallel beams are proposed. First, the problem with boundary controls is converted into a problem with distributed controls. The problem is, then, reduced by a Galerkin-based approach into determining the optimal control of a linear time-invariant lumped parameter system, which will be solved by a wavelet-based method using Legendre wavelets. The integration-operational matrix and Kronecker product are utilized to significantly simplify the optimization problem into a system of linear equations. A numerical example is presented to demonstrate the applicability and the efficiency of the proposed method.     

Optimal control of the viscous weakly dispersive Degasperis-Procesi equation

In this paper, we study the optimal control problem for the viscous weakly dispersive Degasperis-Procesi equation. We deduce the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Then, according to optimal control theories and distributed parameter system control theories, the optimal control of the viscous weakly dispersive Degasperis-Procesi equation under boundary conditions is given and the existence of an optimal solution to the viscous weakly dispersive Degasperis-Procesi equation is proved.     

分布参数最优控制的边界元共轭梯度算法

研究了一类线性椭圆型分布参数最优控制问题的数值解算法.得到最优控制对应的最优性方程组,在凸性条件下,证明了最优控制的唯一存在性问题.将最优控制问题化为以控制函数和状态函数为局中人的递阶式(Stackelberg)非合作对策问题,其平衡点是最优控制的解.进一步得到求平衡点的边界元共轭梯度算法.最后,研究算法中边界元离散的误差估计,以算例验证该算法.     

Existence of solutions and optimal control for a model of tissue invasion by solid tumours

In this paper we study the distributed optimal control problem for the two-dimensional mathematical model of cancer invasion. Existence of optimal state-control and stability is proved and an optimality system is derived.     

由常规故障和临界人为错误引起系统故障的可修复系统动态解的最优控制

研究了由两个运行部件和一个储备部件并且具有常规故障和临界人为错误的随机模型,故障系统的修复时间是任意分布的.先把系统方程的解转化为Volterra 积分方程的形式,证明了系统方程中正解的存在唯一性,再以泛数指标泛函作为衡量系统可控性的标准,研究该系统的最优控制问题.     

两不同部件并联可修系统稳态解的最优控制

针对修复时间服从任意分布的两不同部件并联可修系统的模型,以泛数指标泛函作为衡量系统可控性的标准,利用Banach空间理论讨论了系统稳态解达到预期概率分布的最优控制问题,给出了其最优解的存在唯一性.     

Optimal control problem of a generalized Ginzburg–Landau model equation in population problems

In this paper, we consider the problem for distributed optimal control of the generalized Ginzburg–Landu model equation in population. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved, and the optimality system is established. Copyright © 2013 John Wiley & Sons, Ltd.