Attractive Ellipsoids in Robust Control by Alexander Poznyak, Andrey Polyakov, Vadim Azhmyakov

By Alexander Poznyak, Andrey Polyakov, Vadim Azhmyakov

This monograph introduces a newly built robust-control layout process for a large classification of continuous-time dynamical platforms referred to as the “attractive ellipsoid method.” in addition to a coherent creation to the proposed regulate layout and similar issues, the monograph reports nonlinear affine keep watch over structures within the presence of uncertainty and provides a optimistic and simply implementable keep an eye on procedure that promises definite balance homes. The authors talk about linear-style suggestions keep an eye on synthesis within the context of the above-mentioned structures. the advance and actual implementation of high-performance robust-feedback controllers that paintings within the absence of entire details is addressed, with a variety of examples to demonstrate find out how to follow the sexy ellipsoid way to mechanical and electromechanical structures. whereas theorems are proved systematically, the emphasis is on knowing and using the idea to real-world events. beautiful Ellipsoids in strong regulate will entice undergraduate and graduate scholars with a history in glossy structures concept in addition to researchers within the fields of regulate engineering and utilized mathematics.

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1994). Robust industrial control. Hemel Hempstead, UK: Prentice Hall International. (Grimble 1994). , & Glover, K. (1996). Robust and optimal control. Upper Saddle River, NJ: Prentice Hall. (Zhou et al. 1996). , & Valyi, I. (1997). Ellipsoidal calculus for estimation and control. Boston, MA: Birkhauser. (Kurzhanski & Valyi 1997). – Mahmoud, M. S. (2000). Robust control and filtering for time-delay systems. New York: Marcel Dekker. (Mahmoud 2000). – Blanchini, F. & Miani, S. (2008). Set theoretic methods in control.

Assume that there exists yN 2 Rn such that yN T AyN > 0: Then the inequality y T By 0 y T Ay 0 is a consequence of if and only if there exists a (Lagrange-type) multiplier B 0 such that A: Note that the proof of this fact is based on a specific fact from abstract convex analysis, namely on the Dines’s lemma (published in 1941). This fundamental fact and related results can be found in Poznyak (2008). Recently, the classical Dines’s lemma was generalized by Polyak (2001). , Ben-Tal & Nemirovski 2001; Polik & Terlaky 2007 for details).

If there exists a proper function V W Rn ! x/. Proof. 3) has solutions for every set of initial conditions. t/ be an arbitrary solution. t// hold for almost all t. t// > 1. So the set is invariant and asymptotically attractive. 3), but also for the class (family) of corresponding dynamic processes that possess quasi-Lipschitz right-hand sides. The result presented provides a basic theoretical tool for a possible numerical (algorithmic) scheme for robust control design and analysis of the quasi-Lipschitz systems introduced here.

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