讲座一：
讲座题目：Optimal Discrete-Valued Control Computation
讲座时间: 2011年11月25日10:00
讲座地点: 哈工大科学园2F栋，214房间
张国礼教授简介：K.L. Teo，John Curtin Distinguished Professor。Department of Mathematics and Statistics
Curtin University
Abstract:
In this seminar, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control problem into an equivalent problem subject to additional linear and quadratic constraints. The feasible region defined by these additional constraints is disconnected, and thus standard optimization methods struggle to handle these constraints. We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective. This leads to an approximate optimal control problem that can be solved by optimal control theory and optimal control software packages, such as MISER. Convergence results show that any local solution of the approximate problem is also a local solution of the original problem. We conclude the talk by using our method to solve two train control problems.
讲座二：
讲座题目：Optimal Control Computation for Nonlinear Systems with State-dependent Stopping Criteria
讲座时间: 2011年11月29日15:30
讲座地点: 哈工大科学园2F栋，214房间
张国礼教授简介：K.L. Teo，John Curtin Distinguished Professor。Department of Mathematics and Statistics
Curtin University
Abstract:
In this seminar, we consider a challenging optimal control problem in which the terminal time is determined by a stopping criterion. This stopping criterion is defined by a smooth surface in the state space; when the state trajectory hits this surface, the control system stops. By restricting the controls to piecewise constant functions, we derive a finite-dimensional approximation of the optimal control problem. We then develop an efficient computational method, based on nonlinear programming, for solving the approximate problem. Three numerical examples are included for the purpose of illustration.
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