Time Optimal Control of a Thermoelastic System

This paper considers the numerical approximation for the time optimal control problem of a thermoelastic system with some control and state constraints. By the Galerkin finite element method (FEM), the original problem is projected into a semidiscrete optimal control problem governed by a system of ordinary differential equations. Then the optimal time and control parameterization method is applied to reduce the original system to an optimal parameter selection problem, in which both the optimal time and control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a hybrid algorithm consisting of chaotic particle swarm optimization (CPSO) and sequential quadratic programming (SQP) algorithm. The numerical simulations demonstrate the effectiveness of the proposed numerical approximation method.