On second order conditions for singular optimal control of port-Hamiltonian systems

Abstract: We study singular optimal control problems of port-Hamiltonian (descriptor) systems. We employ general control-affine cost functionals that include as a special case the energy supplied to the system. We first derive optimality conditions for the case of ordinary differential equations with and without control bounds by applying the general theory to the specially structured port-Hamiltonian case, and show that this leads to nice optimality conditions, in particular in the linear case. We then extend these results to classes of port-Hamiltonian descriptor systems.