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Zbl 0632.34005
Paden, Brad E.; Sastry, Shankar S.
A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators. (English)
[J] IEEE Trans. Circuits Syst. 34, 73-82 (1987). ISSN 0098-4094

A link is established between the definition of Filippov's solution concept for ordinary differential equations with a discontinuous right- hand side [{\it A. F. Filippov}, Mat. Sb., N. Ser. 51(93), 99-128 (1960; Zbl 0138.322)] and Clarke's generalized gradient [{\it 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.
[T.Zolezzi]

MSC 2000:: *34A34 Nonlinear ODE and systems, general

Keywords: discontinuous right-hand side; Clarke's generalized gradient; differential inclusion

Citations: Zbl 0138.322; Zbl 0582.49001

Cited in: Zbl 1133.93311

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