Abstract
Existing algorithms for the indirect solution of hybrid optimal control problems suffer from several deficiencies: Min-$H$ algorithms are not applicable to hybrid systems and are not globally convergent. Indirect multiple shooting and indirect collocation are difficult to initialize and have a small domain of convergence. Contrary to these existing algorithms, a novel min-$H$ algorithm is introduced here, which is initialized intuitively and converges globally to a locally optimal solution. The algorithm solves hybrid optimal control problems with autonomous switching, a fixed sequence of discrete states, and unspecified switching times. Furthermore, the convergence of the proposed algorithm is at least quadratic near the optimum, and solutions are found with high accuracy. A numerical example shows the efficiency of the novel min-$H$ algorithm.
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