## 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

### Citations:

Zbl 0138.322; Zbl 0582.49001
Full Text: