Representation of generalized solutions via differential equations with measures

Boris M. Miller and Evgeny Ya. Rubinovich
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Boris M. Miller: Institute for Information Transmission Problems
Evgeny Ya. Rubinovich: Institute of Control Sciences

Chapter Chapter 4 in Impulsive Control in Continuous and Discrete-Continuous Systems, 2003, pp 137-192 from Springer

Abstract: Abstract In this Chapter we discuss the control of a nonlinear dynamic system with its state governed by the nonlinear differential equation $$\dot X(t) = F(X(t),u(t),w(t),t), $$ where F(x, u, w, t,) is given function, $$ x \in {R^n},t \in [0,T],X(0) = {x_0}$$ is the initial condition, $$u(t),w(t) $$ are measurable controls on $$[0,T]:u(t) \in {R^k}$$ is an ordinary control component, and $$w(t) \in {R^m} $$ is a generalized one.

Keywords: Generalize Solution; Nonlinear Differential Equation; Differential Inclusion; Borel Subset; Auxiliary System (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-0095-7_4

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DOI: 10.1007/978-1-4615-0095-7_4

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