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Fixed point methods in nonlinear control. (English) Zbl 0577.93028
Distributed parameter systems, Proc. 2nd Int. Conf., Vorau/Austria 1984, Lect. Notes Control Inf. Sci. 75, 24-51 (1985).

[For the entire collection see Zbl 0572.00027.]

This is an expository article on the application of known fixed point theorems to control problems for semilinear systems defined on abstract spaces. Control problems considered include sufficient conditions for controllability and observability, state and parameter estimation and adaptive regulation. Several examples of applications to distributed systems described by partial differential equations are discussed.

Reviewer: R.Curtain
MSC:
93C10Nonlinear control systems
47H10Fixed point theorems for nonlinear operators on topological linear spaces
93C25Control systems in abstract spaces
93B03Attainable sets
93B05Controllability
93B07Observability