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A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulators. (English) Zbl 0632.34005

A link is established between the definition of Filippov’s solution concept for ordinary differential equations with a discontinuous right- hand side [A. F. Filippov, Mat. Sb., N. Ser. 51(93), 99-128 (1960; Zbl 0138.322)] and Clarke’s generalized gradient [F. H. Clarke, Optimization and nonsmooth analysis (1983; Zbl 0582.49001)]. According to Filippov’s definition, solutions to \(\dot x=f(x)\) are those to the differential inclusion \(\dot x(t)\in K(f)(x(t))\), where K(f) is a suitably defined multifunction depending on f. The authors remark that if f is locally Lipschitz, then \(K(\nabla f)=\partial f\), where \(\partial f\) denotes Clarke’s generalized gradient. This relation is useful for computing K in various situations. Such a calculus is applied to the variable structure control of a robot manipulator.
Reviewer: T.Zolezzi

MSC:

34A34 Nonlinear ordinary differential equations and systems
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