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Schwartz’ distributions in nonlinear setting: Applications to differential equations, filtering and optimal control. (English) Zbl 1066.93023
This paper is intended to be of tutorial value for Schwartz distributions theory in a nonlinear setting. Mathematical models are presented for nonlinear systems which admit both standard and impulsive inputs. These models are governed by differential equations in distributions whose meaning is generalized to involve nonlinear, non-single-valued objects operating over distributions. The set of generalized solutions to these differential equations is defined via closure, in a certain topology, of the set of the conventional solutions corresponding to standard integrable inputs. The theory is exemplified by mechanical systems with impulsive phenomena, optimal impulsive feedback synthesis, sampled-data filtering of stochastic and deterministic dynamic systems.

93C10 Nonlinear systems in control theory
46F10 Operations with distributions and generalized functions
34A37 Ordinary differential equations with impulses
93C57 Sampled-data control/observation systems
49N20 Periodic optimal control problems
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