Maximum principle, dynamic programming and their connection in deterministic control
type: Item
instance of: scholarly article
title: Maximum principle, dynamic programming and their connection in deterministic control
zbMATH Open document ID: 0676.49024
DOI: 10.1007/BF01102352
author: S. H. Smith
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: Two major tools for studying optimally controlled systems are Pontryagin's maximum principle and Bellman's dynamic programming, involving the adjoint function, the Hamiltonian function, and the value function. The relationships among these functions are investigated in this work, in the case of deterministic, finite-dimensional systems, by employing the notion of superdifferential and subdifferential introduced by \textit{M. G. Crandall} and \textit{P.-L. Lions} [Trans. Am. Math. Soc. 277, 1-42 (1983; Zbl 0599.35024)]. Our results are essentially nonsmooth versions of the classical ones. The connection between the maximum principle and the Hamilton-Jacobi-Bellman equation (in the viscosity sense) is thereby explained by virtue of the above relationship.
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 4107551
zbMATH Keywords: Pontryagin's maximum principle
zbMATH Keywords: Bellman's dynamic programming
zbMATH Keywords: superdifferential
zbMATH Keywords: subdifferential
zbMATH Keywords: Hamilton-Jacobi-Bellman
zbMATH Keywords: viscosity
MaRDI profile type: Publication
cites work: Q3241581
cites work: Q4086303
cites work: Viscosity Solutions of Hamilton-Jacobi Equations
cites work: Q3961832
cites work: The Relationship between the Maximum Principle and Dynamic Programming
cites work: The Pontryagin Maximum Principle From Dynamic Programming and Viscosity Solutions to First-Order Partial Differential Equations
cites work: Optimization and nonsmooth analysis
cites work: The Maximum Principle under Minimal Hypotheses
cites work: Local Optimality Conditions and Lipschitzian Solutions to the Hamilton–Jacobi Equation
full work available at URL: https://doi.org/10.1007/bf01102352
OpenAlex ID: W2082734851
description: scientific article; zbMATH DE number 4107551