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A piecewise constant Mayer cost function is used to model optimal controlproblems in which the state space is partitioned into several regions, eachhaving its own Mayer cost value. In such a context, the standard numericalmethods used in optimal control theory naturally fail, due to thediscontinuities and the null gradients associated with the Mayer cost function.In this paper an hybrid numerical method, based on both derivative-freeoptimization and smooth optimization techniques, is proposed to solve thisclass of problems. Numerical simulations are performed on some standard controlsystems to show the efficiency of the hybrid method, where NOMAD and IPOPT areused as, respectively, derivative-free optimization and smooth optimizationsolvers.

A derivative-free approach to optimal control problems with piecewise constant Mayer cost function