RUS  ENG
Full version
JOURNALS // Avtomatika i Telemekhanika // Archive

Avtomat. i Telemekh., 2014 Issue 5, Pages 31–49 (Mi at9092)

This article is cited in 18 papers

Nonlinear Systems

Weakly monotone solutions of the Hamilton–Jacobi inequality and optimality conditions with positional controls

V. A. Dykhta

Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

Abstract: We obtain necessary global optimality conditions for classical optimal control problems based on positional controls. These controls are constructed with classical dynamical programming but with respect to upper (weakly monotone) solutions of the Hamilton–Jacobi equation instead of a Bellman function. We put special emphasis on the positional minimum condition in Pontryagin formalism that significantly strengthens the Maximum Principle for a wide class of problems and can be naturally combined with first order sufficient optimality conditions with linear Krotov's function. We compare the positional minimum condition with the modified nonsmooth Kaśkosz–Lojasiewicz Maximum Principle. All results are illustrated with specific examples.

Presented by the member of Editorial Board: V. I. Gurman

Received: 23.08.2013


 English version:
Automation and Remote Control, 2014, 75:5, 829–844

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025