Abstract: In this paper, non-smooth optimality conditions for a class of event-driven dynamic systems with variable structure are investigated. By introducing a new time variable, the dynamical optimal problems with variable structure are transformed into classical optimal problems. Based on the knowledge of generalized differential and classical optimal theory, necessary optimality conditions of Frechet superdifferential form for this dynamic system are obtained, which generalize some existing relevant results. It is shown that, in the continuous process of the system, the control variable, the adjoint variable and the state variable satisfy the  adjoint equations and the minimum principles. At the changing instants of the system model, the adjoint variables make certain jump and the Hamiltonian is continuous. At last, one example is given to illustrate the efficiency of the main results.

Key words: optimality condition, variable structural dynamical systems, nonsmooth analysis