项目名称: 基于凸松弛-滤子算法的切换系统全局最优控制及应用
项目编号: No.11501574
项目类型: 青年科学基金项目
立项/批准年度: 2016
项目学科: 数理科学和化学
项目作者: 王娟
作者单位: 中国石油大学(华东)
项目金额: 18万元
中文摘要: 在自然和人工智能系统中,广泛存在着逻辑切换、控制输入和连续动态相互作用、共同演化的现象。应用切换系统研究这类动态过程的优化控制是国际控制界热点课题之一。本项目拟从以下三方面研究一类非线性切换系统的全局最优控制问题:第一,基于McCormick技术和αBB技术构造最优控制问题的凸松弛方法,并证明其收敛性;第二,考虑约束条件的松紧性差异,并基于滤子算法和微分代数方程积分技术构造一种有效的约束异化处理方法;第三,利用控制参数化、时间尺度转化、光滑技术、一致逼近理论、灵敏度函数和分支定界法等数学工具,研究一类非线性混合切换系统的确定性全局最优控制算法及其收敛性,并应用于一类生化反应过程的优化与控制。本项研究涉及生物、数学、工程学、运筹学与控制论、计算机科学,不仅可以丰富不可微优化、非光滑分析、全局优化、最优控制、生物化工等学科理论与应用研究,还可以为生化反应实验设计提供参考。
中文关键词: 不可微优化;非光滑非凸规划;全局优化;混杂控制;凸松弛
英文摘要: Interaction and evolution of the logic-based switchings, the controlled input and continuous dynamics exist extensively in the natural and artificial intelligent systems. Exploring the theory of switching systems to the study of this dynamical process is a hot topic in the international control field. In this project, we will study the global optimal control of a class of nonlinear switching systems in the following three aspects. Firstly, we will construct the convex relaxations for the optimal control problem, and verify the convergence of the relaxations. Secondly, in consideration of the coexistence of tighten constraints and loose ones, we will develop an efficient numerical framework to treat them based on the filter method and integration techniques for differential algebraic equations. Thirdly, based on control parameterization enhancing transform, smoothing technique, uniform approximation theory, sensitivity function and branch-and-bound approach, we will present a deterministic global optimization algorithm for the optimal control problem of a class of nonlinear hybrid switching systems, discuss its global convergence, and apply it to optimize and control a class of biochemical reaction process. The study of this project concerns biology, mathematics, engineering, operations research and control theory, computer science, and the results of this project can enrich the study of non-differentiable optimization, nonsmooth analysis, global optimization, optimal control, biological chemical, etc. It can also provide a reference for designing experiment scheme of biochemical reaction.
英文关键词: nondifferentiable optimization;nonsmooth nonconvex programming;global optimization;hybrid control;convex relaxation