Optimal Multiprocesses

Abstract

A theory of necessary conditions for optimal multiprocesses is presented. Optimal multiprocesses are solutions to dynamic optimization problems described by families of control systems coupled through the boundary conditions and cost functions. The theory treats in a unified fashion a wide range of nonstandard dynamic optimization problems, and in many cases provides new optimality conditions. These include problems arising in impulse control, robotics, and optimal investment. Even when specialized to the (single process) free time optimal control problem, the theory improves on known necessary conditions. Detailed analysis of a number of applications and special cases appears in a companion paper.