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Exponentially convergent control laws for nonholonomic systems in power form. (English) Zbl 0909.93029

Summary: This paper introduces a method for constructing exponentially convergent control laws for n-dimensional nonholonomic systems in power form. The methodology is based on the construction of a series of nested invariant manifolds associated to the closed-loop system under a linear control law. A recursive algorithm is presented; it uses these manifolds to construct a three-dimensional system in power form. It is shown that the feedback controller for the original system is the one for this three-dimensional system with proper choice of the gains.

MSC:

93C10 Nonlinear systems in control theory
70F25 Nonholonomic systems related to the dynamics of a system of particles
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