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13 Mar 2016

Numerical Methods for Constrained Optimal Control Problems

Hartono, July 2012
The University of Western Australia

In this thesis we consider numerical methods for solving state-constrained optimal control problems. There are two main focii in the research, i.e. state-constrained optimal open-loop and feedback control problems. For all cases, we reformulate the constrained optimal control problem to the unconstrained problem through a penalty method. The state-constraints which we discuss here are only in the form of inequalities but for both purely state-constraint and control-state constraint types.

For solving state-constrained optimal open-loop control problems, we establish a power penalty method and analyze its convergence. This method is then implemented in MISER 3.3 to do some numerical tests. The results con rm that the method work very well. Furthermore, we use the power penalty method to discuss a sensitivity analysis.

On the other hand, for solving state-constrained optimal feedback control problems we construct a new numerical algorithm. The algorithm based on upwind nite di erence scheme is iterated in order to increase the accuracy and speed of computation. In particular, to address the curse of dimensionality, a special method for generating grid points in the domain is developed. Numerical experiment shows that the computational speed increases significantly with this modi ed method. Moreover, for further improvement in the accuracy the algorithm can be combined with Richardson extrapolation method.

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