10h30 - 10h55
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 null-controllability, 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 bang-bang property of the time optimal control problem is presented.
10h55 - 11h20
Time-Scaling Technique for Time-Delay Optimal Control Problems
This talk is concerned with the optimization of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. Since it is well known that standard gradient-based optimization algorithms struggle to optimize variable switching times, we develop a novel transformation procedure that converts a given time-delay system into an equivalent system---defined on a new time horizon---in which the switching times are fixed, but the mode dynamics contain a variable time-delay that depends on the mode durations in the original system. Despite the challenge posed by the variable time-delay, we show that an optimal control policy for the equivalent system can be obtained efficiently using gradient-based 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.
11h20 - 11h45
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 second-order 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 closed-loop systems. Furthermore, the results of optimal control for the second-order systems are extended to high-order systems (i.e., general polynomial matrix systems), and numerical examples are provided to illustrate the results.