报告题目：On a Class of Stochastic Impulsive Optimal Parameter Selection Problems

主 讲 人：Kok Lay Teo 教授

报告时间：3月21日（周四）下午14:30--15:30

报告地点：数理楼221

报告摘要：

In this talk, we consider a class of stochastic optimal parameter selection problems, where its dynamics are described by a system of linear Ito stochastic differential equations with state jumps. The times at which the jumps occurred as well as their heights are decision variables. This stochastic impulsive optimal parameter selection problem is subject to probabilistic constraints on the state. We show that this constrained stochastic impulsive optimal parameter selection problem is equivalent to a deterministic impulsive optimal parameter selection problem with its dynamics described by deterministic impulsive differential equations subject to continuous state inequality constraints, where the times at which the jumps occurred as well as their heights remain as decision variables. Then, by introducing a time scaling transform, we show that this constrained deterministic impulsive optimal parameter selection problem is transformed into an equivalent constrained deterministic impulsive optimal parameter selection problem with the jump times being fixed. A constraint tranion technique is then used to approximate the continuous state inequality constraints by a sequence of canonical inequality constraints. This leads to a sequence of approximate deterministic impulsive optimal parameter selection problems subject to canonical inequality constraints. For each of these approximate problems, we derive the gradient formulas of the cost function and the constraint functions. On this basis, an efficient computational method is developed.