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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 x ˙=f(x) are those to the differential inclusion x ˙(t)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(f)=f, where 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:
34A34Nonlinear ODE and systems, general