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Differential geometric methods in variable-structure control. (English) Zbl 0658.93022

The theory of variable structure control of nonlinear systems is presented in a differential geometric framework. In particular, conditions for the existence of sliding regimes and the associated ideal sliding dynamics are given. The author studies also regular canonical forms and disturbance invariant properties of sliding regimes. Both single-input and multi-input cases are considered, and several examples are worked out.
Reviewer: A.Bacciotti

MSC:

93B27 Geometric methods
93C10 Nonlinear systems in control theory
57R27 Controllability of vector fields on \(C^\infty\) and real-analytic manifolds
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
93C15 Control/observation systems governed by ordinary differential equations
93B10 Canonical structure
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