15th EUROPT Workshop on Advances in Continuous Optimization
Montréal, Canada, 12 — 14 July 2017
15th EUROPT Workshop on Advances in Continuous Optimization
Montréal, Canada, 12 — 14 July 2017
Dynamic Control and Optimization with Applications V
Jul 14, 2017 10:30 AM – 11:45 AM
Location: Saine Marketing
Chaired by Saroj Biswas
3 Presentations

10:30 AM  10:55 AM
Time optimal control on microwave heating
In this paper, we consider the time optimal control problem of microwave heating. At first, we analyze the controllability of time optimal control of microwave heating through nullcontrollability, which is obtained by observation estimates over a subset of space and time domain. The second, we show the existence of time optimal control of microwave heating with the minimum sequences through the bounded norms. At last, the bangbang property of the time optimal control problem is presented.

10:55 AM  11:20 AM
TimeScaling Technique for TimeDelay Optimal Control Problems
This talk is concerned with the optimization of nonlinear timedelay optimal control problems with canonical equality and inequality constraints. Since it is well known that standard gradientbased optimization algorithms struggle to optimize variable switching times, we develop a novel transformation procedure that converts a given timedelay system into an equivalent systemdefined on a new time horizonin which the switching times are fixed, but the mode dynamics contain a variable timedelay that depends on the mode durations in the original system. Despite the challenge posed by the variable timedelay, we show that an optimal control policy for the equivalent system can be obtained efficiently using gradientbased optimization techniques. This optimal control policy can then be used to determine the optimal switching times and optimal system parameters for the original system. We conclude the paper by considering examples problems in economics and chemical engineering.

11:20 AM  11:45 AM
Optimal Control for Polynomial Matrix Systems
This study considers optimal control problems of polynomial matrix systems. The optimal control framework for a class of polynomial matrix systems is established. First, for descriptor secondorder systems, a state feedback stabilizing controller is derived for minimizing the quadratic performance index functional by solving generalized algebraic Riccati equation or LMI feasibility problem. Then we also analyze the existence of the optimal controller under different performance indexes and the admissibility of the closedloop systems. Furthermore, the results of optimal control for the secondorder systems are extended to highorder systems (i.e., general polynomial matrix systems), and numerical examples are provided to illustrate the results.