By Alexander Poznyak, Andrey Polyakov, Vadim Azhmyakov
This monograph introduces a newly built robust-control layout method for a large category of continuous-time dynamical platforms referred to as the “attractive ellipsoid method.” in addition to a coherent creation to the proposed keep watch over layout and comparable subject matters, the monograph reports nonlinear affine regulate platforms within the presence of uncertainty and provides a positive and simply implementable keep an eye on process that promises sure balance homes. The authors speak about linear-style suggestions regulate synthesis within the context of the above-mentioned platforms. the improvement and actual implementation of high-performance robust-feedback controllers that paintings within the absence of entire details is addressed, with a number of examples to demonstrate the way to observe the horny ellipsoid way to mechanical and electromechanical platforms. whereas theorems are proved systematically, the emphasis is on figuring out and employing the idea to real-world events. beautiful Ellipsoids in strong regulate will entice undergraduate and graduate scholars with a history in sleek structures conception in addition to researchers within the fields of keep an eye on engineering and utilized mathematics.
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This monograph introduces a newly built robust-control layout procedure for a large category of continuous-time dynamical platforms referred to as the “attractive ellipsoid procedure. ” in addition to a coherent advent to the proposed regulate layout and similar subject matters, the monograph reports nonlinear affine regulate platforms within the presence of uncertainty and provides a positive and simply implementable keep an eye on technique that promises sure balance houses.
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Extra resources for Attractive Ellipsoids in Robust Control
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. Systems and control: Foundations and applications. Boston, MA: Birkhäuser. (Blanchini & Miami 2008). , & Chellaboina, V. (2008). Nonlinear dynamical systems and control. Princeton: Princeton University Press. (Haddad & Chellaboina 2008). 10 1 Introduction Of course, the authors hope that this book may serve as a complement to the excellent books mentioned above and provide a constructive instrument for feedback designing in practical situations.
We focus our attention primarily on motivations of the proposed “attractive ellipsoid” method and illustrate it in some simple situations. 1 Quasi-Lipschitz Dynamical Systems The basic inspiration for classic control theory is the state equation parameterized by an “input parameter” © Springer International Publishing Switzerland 2014 A. 0/ D x0 2 Rn where g W Rn Rm ! t/ is chosen from a control set U Â Rm . 1) have been objects of the theory of ODEs for a long time. 1) by an appropriate feedback control u W Rn !
X/ O < 0: To do this, let us first recall that affine sets M can be written as M D fxj x D x0 C m; m 2 M0 g with x0 2 Rn and M0 a linear subspace of Rn . M0 /, and let e1 ; : : : ; enO 2 Rn be a basis of M0 . 1. x1 ; : : : ; xnO / are the coefficients of x x0 in the basis of M0 . x/ O < 0. Note that the dimension nO of xO is equal to at most the dimension n of x. We now consider some illustrative examples of LMIs in use. 6. 21) where A 2 Rn n . 21). 7. 3 Elements of LMIs 31 Let us assume that the system is asymptotically stable.