Ellipsoidal techniques for dynamic systems: The problem of control synthesis

Kurzhanski AB & Valyi I (1991). Ellipsoidal techniques for dynamic systems: The problem of control synthesis. Dynamics and Control 1 (4): 357-378. DOI:10.1007/BF02169766.

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Abstract

This article gives an early account of the application of ellipsoidal techniques to various problems in modeling dynamical systems. The problem of control synthesis for a linear system under bounded controls was selected as the first simple application of these techniques. In forthcoming papers, these results will be extended to the case where unknown but bounded disturbances are present. Guaranteed state estimation—also to be interpreted as a tracking problem—again under unknown but bounded disturbances will also be discussed.

Although the problem is treated here for linear systems only, the synthesized system is driven by a nonlinear control strategy and is therefore generically nonlinear. Taking a scheme based on the notion of extremal aiming strategies of N. N. Krasovski, the present article concentrates on constructive solutions generated through ellipsoidal-valued calculus and related approximation techniques for set-valued maps. The primary problem, which originally required an application of set-valued analysis, is substituted for here by one based on ellipsoidal-valued functions. This yields constructive schemes applicable to algorithmic procedures and simulation with computer graphics.

Item Type: Article
Research Programs: Methodology of Decision Analysis (MDA)
Depositing User: Romeo Molina
Date Deposited: 21 Apr 2016 14:19
Last Modified: 25 Aug 2016 15:01
URI: http://pure.iiasa.ac.at/12877

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