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Control of nonlinear variable structure systems. (English) Zbl 0622.93026
This paper is devoted to the research of different nonlinear control problems with variable structure described by \(\dot x=f(t,x,u)\), \(x(t)\in R^ n\), \(u(t)\subset V\in R^ m\) with sliding manifold \(S(x)=0,S(x)\in R^ m\). Controllability conditions based on Filipov’s definition of the solution of ordinary differential equations with discontinuous right-hand sides are derived. The derived conditions are illustrated via particular control problems with variable structure.
Reviewer: K.Aida-Zade

MSC:
93C10 Nonlinear systems in control theory
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
93B05 Controllability
93B03 Attainable sets, reachability
93C15 Control/observation systems governed by ordinary differential equations
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