This article is cited in 6 scientific papers (total in 6 papers)
Properties of the set of admissible “state-control” pairs for first-order evolution control systems
A. A. Tolstonogov
Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
We consider a control system described by a non-linear first-order evolution equation on an evolution triple of Banach spaces (a “Gelfand triple”) with a mixed multivalued control constraint whose values are non-convex closed sets in the control space. Besides the original system, we consider systems with the following control constraints: the constraint whose values are the closed convex hulls of the values of the original constraint, and the constraint
whose values are the extreme points of the convexified constraint that belong to the original one. We study topological properties of the sets of admissible “state-control” pairs for the same system with various constraints and consider the relations between them. An example of a non-linear parabolic control system is worked out in detail.
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Izvestiya: Mathematics, 2001, 65:3, 617–640
MSC: 34A60, 49J30, 93C25
A. A. Tolstonogov, “Properties of the set of admissible “state-control” pairs for first-order evolution control systems”, Izv. RAN. Ser. Mat., 65:3 (2001), 201–224; Izv. Math., 65:3 (2001), 617–640
Citation in format AMSBIB
\paper Properties of the set of admissible ``state-control'' pairs for first-order evolution control systems
\jour Izv. RAN. Ser. Mat.
\jour Izv. Math.
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This publication is cited in the following articles:
A. A. Tolstonogov, “On solutions of an evolution control system depending on parameters”, Sb. Math., 194:9 (2003), 1383–1409
A. A. Tolstonogov, “Properties of attainable sets of evolution inclusions and control systems of subdifferential type”, Siberian Math. J., 45:4 (2004), 763–784
A. A. Tolstonogov, “Relaxation in control systems of subdifferential type”, Izv. Math., 70:1 (2006), 121–152
A. A. Tolstonogov, “Control systems of subdifferential type depending on a parameter”, Izv. Math., 72:5 (2008), 985–1022
S.A. Timoshin, A.A. Tolstonogov, “Existence and properties of solutions of a control system with hysteresis effect”, Nonlinear Analysis: Theory, Methods & Applications, 2011
A. A. Tolstonogov, “Properties of Solutions of a Control System with Hysteresis”, J Math Sci, 2014
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