Controlled Systems

Werner Krabs and Stefan Pickl ()
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Werner Krabs: Technical University of Darmstadt, Department of Mathematics
Stefan Pickl: Universität der Bundeswehr München, Department of Computer Science

Chapter 2 in Dynamical Systems, 2010, pp 77-147 from Springer

Abstract: Abstract We start with a system of differential equations of the form 2.1 $$ \dot{x}_i = f_i (x,u), \qquad i = 1,\ldots,n $$ where $$ x \in {\mathbb R}^n, \,\, u \in {\mathbb R}^m, $$ $$ f_i : {\mathbb R}^n \times {\mathbb R}^m \to {\mathbb R} $$ with $$ f_i \in C \left( {{\mathbb R}^{n + m}, {\mathbb R}} \right) $$ and $$ f_i \left( {\cdot, u} \right) \in C^1 \left( {\mathbb{R}^n, \mathbb{R}} \right) $$ for every $$ u\, \in \,\mathbb{R}^m $$ and for i = 1, …, n.

Keywords: Interior Point; Control Function; Inverse Function Theorem; Rest Point; Normality Condition (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-13722-8_2

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