On Certain Hypotheses in Optimal Control Theory and the Relationship of the Maximum Principle with the Dynamic Programming Method Proposed by L. I. Rozonoer

TL;DR

This paper examines three hypotheses in optimal control theory to establish conditions for the existence of optimal controls and explores the relationship between Pontryagin's maximum principle and dynamic programming.

Contribution

It analyzes Rozonoer's hypotheses to connect the maximum principle with dynamic programming, providing new insights into optimal control conditions.

Findings

Conditions for the existence of optimal controls under all initial states

Relationships established between Pontryagin's maximum principle and dynamic programming

Clarification of Rozonoer's hypotheses in optimal control theory

Abstract

In this paper we will study three hypotheses proposed by L. I. Rozonoer (Automation and Remote Control, 2003, vol.64, no.8, pp.1237--1240) in optimal control theory in order to derive conditions for the existence of an optimal control under all initial conditions, and the relationships between Pontryagin maximum principle and the dynamic programming method.