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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:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B05 Controllability
47J05 Equations involving nonlinear operators (general)
47H10 Fixed-point theorems
93C10 Nonlinear systems in control theory
93C23 Control/observation systems governed by functional-differential equations
93C25 Control/observation systems in abstract spaces
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