Control Theory and Optimization I - download pdf or read online

By M.I. Zelikin, S.A. Vakhrameev

ISBN-10: 3540667415

ISBN-13: 9783540667414

The single monograph at the subject, this booklet matters geometric tools within the conception of differential equations with quadratic right-hand aspects, heavily on the topic of the calculus of adaptations and optimum keep an eye on concept. in response to the author’s lectures, the publication is addressed to undergraduate and graduate scholars, and clinical researchers.

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Cerned with the Ca rtan system p (x) is not constant. l6). in good form and It wi 11 simp] ify our notation to assume that there are no Cauchy characteristics (the general case is done the same way). 26) the 1-forms give a aoframe on {w;8a;rr~} X. Indeed, these forms are 1 inearly independent and therefore span a subbundle It follows immediately from the definition and K'''cT'''(x). A( I)= (K;,)_L. l3) that K'''=T;'(x). no Cauchy characteristics is equivalent to {3/3w;3/38a;3/3rr~} We denote by Thus our assumption of the dual frame of vector fields.

In fact, the canonical inclusion (cf. Chapter 0, Section b)) gives a global embedding. Again, it is clear that IRm 1-1. may be replaced by any manifold l1oreover, by considering the restriction of the canonical system to submanifolds :/.

Let ~ be a closed Then ~(x) EA 2 T*(;() is an alternating bilinear form in X each tangent space I He define the rank means ~(x)" .. ~(x)). TX(X). 25) ~(x)r Definition (cf. 6). -forms v J 'f where v is a vector field on X. -known theorem of Darboux (cf. 8)), [2], [9]) p. ' p 1 u 1 , .. ,up,v , .. ,v where the functions on X. are part of a coordinate system The Cartan system and Cauchy characteristic system coincide and are given by 1 p span { du 1, .. ,dup,dv , .. ' ) Later on (cf. ') cerned with the Ca rtan system p (x) is not constant.

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Control Theory and Optimization I by M.I. Zelikin, S.A. Vakhrameev

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