Monotone Lyapunov type functions and global optimality conditions for discrete control problems

S. P. Sorokin

Institute for System Dynamics and Control Theory SB RAS, 134, Lermontova Str., Irkutsk, 664033

Abstract: Sufficient and necessary global optimality conditions for discrete optimal control problems are proposed. These conditions are based on applying of strongly and weakly monotone Lyapunov type functions that do not decrease along any or some trajectories of discrete dynamical systems under consideration. Proposed sufficient conditions are more general than well-known Krotov conditions. There are obtained conditions that converse the discrete maximum principle into sufficient optimality condition.

Keywords: discrete dynamical systems, monotone Lyapunov type functions, inner estimates to reachable sets, sufficient and necessary global optimality conditions, discrete maximum principle.

UDC: 517.977.5