Abstract
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.
Highlights
The expansion and contraction of a material exposed to temperature changes are of great importance in many applications such as stabilization of satellite antennas, which is commonly with large temperature variations and characterized by the thermoelastic coupling [1]
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
We have proposed a numerical approximation method for the time optimal control problem of the thermoelastic system
Summary
The expansion and contraction of a material exposed to temperature changes are of great importance in many applications such as stabilization of satellite antennas, which is commonly with large temperature variations and characterized by the thermoelastic coupling [1]. Control parametrization method, which involves approximating the control function by a piecewise-constant function with possible discontinuities at a set of preassigned switching points [26, 27], will be carried out and the original problem can be reduced to an optimal parameter selection problem. In principle, this problem can be solved as a nonlinear optimization problem by standard mathematical programming algorithms such as SQP.
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