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Graph completions for impulsive feedback controls

Abstract : The paper considers impulsive control systems, where the evolution equation depends linearly on the time derivatives of the control function. The basic theory of "graph completions" is here extended to control functions in feedback form. In the case where the control u=u(t,x) is piecewise smooth, with a jump along a hypersurface Σ in the t-x space, results are proved on the existence and uniqueness of solutions, and on their approximation by means of smooth feedbacks. The paper is concluded with a couple of examples, concerning the feedback control of mechanical systems by means of active constraints.
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https://hal.inria.fr/hal-01067326
Contributor : Estelle Bouzat <>
Submitted on : Tuesday, September 23, 2014 - 1:35:43 PM
Last modification on : Wednesday, December 9, 2020 - 3:11:09 PM

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Alberto Bressan, Marco Mazzola. Graph completions for impulsive feedback controls. Journal of Mathematical Analysis and Applications, Elsevier, 2014, 412 (2), pp.976-988. ⟨10.1016/j.jmaa.2013.11.015⟩. ⟨hal-01067326⟩

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