Determining switching strategies of multiprocesses via time partitioning and Pontryagin’s maximum principle

This paper addresses necessary optimality conditions in the form of the Pontryagin Maximum Principle for optimal multiprocesses. By a multiprocess, we understand a finite system of classical control processes, between which switching is freely permitted at any point in time. A particular challenge in studying multiprocesses is determining an optimal switching strategy. To this end, we present a new approach that identifies possible switching strategies with certain partitions of the finite time horizon. This enables us to incorporate the switching strategies as control variables and to interpret the problem of optimal multiprocesses as a classical control problem. The identification of an optimal switching strategy is thus achieved without a priori assumptions. However, the proposed approach imposes limitations in that the state trajectories must be continuous and no switching costs are allowed.