An exact penalty function algorithm for constrained optimal control problems

Abstract

The presence of control constraints, because they are non-differentiable in the space of control functions, makes it difficult to cope with terminal equality constraints. For this reason some existing algorithms employ exact penalty functions to handle the cost and terminal constraints and use the control constraints to define the space of permissible search directions; with this approach a convex optimal control problem is (approximately) solved to obtain a search direction and the step length is determined by (approximately) minimising the exact penalty along the direction. It is the purpose of this paper to show (with numerical results) that existing algorithms of this type do not have good performance because the search direction is not automatically scaled. A new algorithm, with automatic scaling, is presented and its convergence is established. Numerical results indicate a considerable improvement in performance.