Generalization of Pontryagin Maximum Principle with Stochastic Initial Conditions

TL;DR

This paper extends the Pontryagin Maximum Principle to systems with stochastic initial conditions, providing a new theoretical framework and a practical method for solving expectation maximization problems in such systems.

Contribution

The paper introduces a generalized PMP for non-feedback control systems with stochastic initial conditions, bridging the gap to classical PMP when randomness is absent.

Findings

Established a generalized PMP for stochastic initial conditions

Proved the generalized PMP reduces to classical PMP in deterministic cases

Demonstrated the method's feasibility through an example

Abstract

Based on Pontryagin Maximum Principle (PMP), this paper established a generalized PMP aiming at non-feedback control system with stochastic initial conditions. We proved the conclusion and show its coming back to PMP when the randomness collapses. Through the generalized PMP, a general method is introduced to solve expectation maximum problem of these systems and thereafter an example showed its feasibility.