TY - JOUR
T1 - Graph completions for impulsive feedback controls
AU - Bressan, Alberto
AU - Mazzola, Marco
N1 - Funding Information:
This research was partially supported by NSF , with grant DMS-1108702 : “Problems of Nonlinear Control”.
PY - 2014/4/15
Y1 - 2014/4/15
N2 - 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.
AB - 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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U2 - 10.1016/j.jmaa.2013.11.015
DO - 10.1016/j.jmaa.2013.11.015
M3 - Article
AN - SCOPUS:84891560667
SN - 0022-247X
VL - 412
SP - 976
EP - 988
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -