An approximate maximum principle for finite-difference control systems

Optimal control problems are considered for finite-difference systems with constraints on the control and phase variables. Each problem is regarded as a process with decreasing time quantization period. New necessary conditions are obtained for optimality, in the form of an approximate maximum principle. No assumptions are made about linearity or convexity of the control system. Constructive methods are proved for approximating the phase constraints, so that stability of the Pontryagin maximum principle is ensured in computer calculations of systems with continuous time.