A minimum principle of pontryagin in optimal nonlinear discrete-time system with terminal constraints and free terminal time and its applications to reachability problems of discrete event systems

摘要

In this paper, a minimum principle of Pontryagin's type in optimal nonlinear discrete-time system is formulated under the conditions of termina constraints and free terminal time. Applications to the reachablility problems of discrete event systems by using Petri net model are also newly shown. The subject of optimal control theory has a long and deep history, an expanding range of applications, and a large assortment of numerical techniques. Althouth a maximum principle for systems described by nonlinear difference equations has been given under the conditions of fixed time and fixed end-point constraints by Halkin and Holtzman, the above problems discussed in this paper has not been given.