Relaxation of optimal control problems and linear-quadratic systems

Kryazhimskiy, A.V. (2012). Relaxation of optimal control problems and linear-quadratic systems. Dynamics of Continuous, Discrete and Impulsive Systems, Series B (DCDIS-B) 19 (1) 17-42.

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Abstract

The paper suggests an approach to characterizing global solutions for optimal control problems with integral objective functions. The approach is based on relaxation of the system's states to probability measures on the system's state space. The associated relaxed control problem falls, typically, to the scope of convex optimization problems with linear equality constraints. Under additional conditions assuming, in particular, that the objective function and state equation are linear-quadratic in the state variable, the equivalency of the original and relaxed problems is proved and a successive solution approximation method is constructed.

Item Type:	Article
Uncontrolled Keywords:	Global optimization; Non-convex optimization; Optimal control; Relaxation of optimization problems; Successive optimization methods
Research Programs:	Advanced Systems Analysis (ASA)
Bibliographic Reference:	Dynamics of Continuous, Discrete and Impulsive Systems, Series B (DCDIS-B); 19(1-2):17-42
Depositing User:	IIASA Import
Date Deposited:	15 Jan 2016 08:46
Last Modified:	27 Aug 2021 17:39
URI:	https://pure.iiasa.ac.at/10017

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