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Schauder’s fixed-point theorem in nonlinear controllability problems. (English) Zbl 1011.93001
The paper presents a review of results existing in the literature which show how Schauder’s fixed-point theorem can be practically used to solve several controllability problems for different types of nonlinear control systems in both finite- and infinite-dimensional spaces. The following nonlinear control systems are considered: finite-dimensional systems, systems with delays in control or in the state variables, and infinite-dimensional systems.

MSC:
93-02Research monographs (systems and control)
93B05Controllability
47J05Equations involving nonlinear operators (general)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
93C10Nonlinear control systems
93C23Systems governed by functional-differential equations
93C25Control systems in abstract spaces