Open-loop control of a plant described by a system with nonsmooth right-hand side

Open-loop control of a plant governed by a system of differential equations in normal form is studied. The right-hand side of this system includes nonsmooth terms. The original problem is reduced to the unconstrained minimization of a nonsmooth functional. Necessary and sufficient minimum conditions in terms of subdifferential are found. Based on these conditions, the subdifferential descent method is used to solve the problem. The proposed approach is illustrated by numerical examples.