Optimization for discretized switched systems

Switching time optimization is a crucial topic in the optimal control of hybrid systems. Since it is rare that such problems can be solved analytically, the use of numerical discretization schemes for the integration of state and adjoint systems is indispensable. Thus, in this contribution, the switching time optimization problem is studied in a discretized formulation directly from the beginning. An analysis of the discretized problem reveals that smoothness of the original (continuous time) problem is lost, i.e. the problem will in general become nondifferentiable in discrete time. This has to be taken into account when deriving an adjoint-based formula for the optimization of the discretized problem. A hybrid double pendulum example is used for illustration of the results. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)