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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:
93B27Geometric methods in systems theory
93C10Nonlinear control systems
57R27Controllability of vector fields on C and real-analytic manifolds
49J30Optimal solutions belonging to restricted classes (existence)
93C15Control systems governed by ODE
93B10Canonical structure of systems