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JOURNALS // Bulletin of Irkutsk State University. Series Mathematics // Archive

Bulletin of Irkutsk State University. Series Mathematics, 2014 Volume 8, Pages 86–103 (Mi iigum189)

This article is cited in 3 papers

Variational Optimality Conditions with Feedback Descent Controls that Strengthen the Maximum Principle

V. A. Dykhta

Institute for System Dynamics and Control Theory SB RAS, 134, Lermontova st., Irkutsk, 664033

Abstract: We derive nonlocal necessary optimality conditions that strengthen both classical and nonsmooth Maximum Principles for nonlinear optimal control problems with free right-hand end of trajectories. The strengthening is due to employment of feedback controls, which are assumed to ensure a descent of a value of the cost functional, and are extremal with respect to certain solutions of a Hamilton–Jacobi inequality for weakly monotone functions. The main results are Feedback Minimum Principles for smooth and nonsmooth problems, that are formulated through accessory dynamic optimization problems. Effectiveness of these necessary optimality conditions are illustrated by examples.

Keywords: Hamilton–Jacobi inequality, feedback control of descent, Maximum Principle, necessary conditions.

UDC: 517.977.5



© Steklov Math. Inst. of RAS, 2025