Schauder's fixed-point theorem in nonlinear controllability problems

By Jerzy Klamka. 2000

127 citations recorded by the source corpus.

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Citations in the corpus

Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces (2003, background): “Controllability of the deterministic systems in finite dimensional spaces has been extensively studied (see [3], [21], and references therein).”
Controllability of semilinear stochastic systems in Hilbert spaces (2003, background): “The controllability of nonlinear deterministic systems in finite dimensional space been extensively studied by several authors, see [3,10] and references therein.”
Existence and optimal control problem for semilinear fractional order (1,2] control system (2020, unknown): “In previous studies, 10-12 Klamka discussed the different kind of fixed point theorem approaches for controllability of nonlinear control systems.”
Approximate controllability of semilinear functional equations in Hilbert spaces (2002, background): “This is consistent with classical finite-dimensional theory (see [17,18] and references therein).”
Controllability of dynamical systems. A survey (2013, background): “Many authors have studied the controllability of nonlinear systems with and without impulses, see for instance [7, 12, 14, 16, 37–38, 40, 43].”
Stochastic controllability of systems with variable delay in control (2008, background): “The extensive list of these publications can be found for example in the monograph [1] or in the survey papers [2, 6, 10].”
Controllability of non-linear stochastic systems (2003, methodology): “…examined by several authors (see Mirza and Womack 1971, Yamamoto 1977, Balachandran and Dauer 1987, Do 1990, Chukwu and Lenhart 1991, Zabczyk 1992, Klamka 2000) using one of the following methods: methods based on stability theory of Lyapunov, methods for systems defined on a manifold,…”
Stochastic controllability of linear systems with delay in control (2016, background): “In the literature there are many different definitions of controllability, both for linear [12], [13] and nonlinear dynamical systems [14]–[17], which strongly depend on the class of dynamical control systems and the set of admissible controls [1], [18].”