Brief paper: Solutions of nonlinear control and estimation problems in reproducing kernel Hilbert spaces: Existence and numerical determination

Authors:
Gianluigi Pillonetto
Affiliations:
Control and System Theory Group, Department of Information Engineering, University of Padova, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

Many nonlinear optimal control and estimation problems can be formulated as Tikhonov variational problems in an infinite dimensional reproducing kernel Hilbert space. This paper shows that any closed ball contained in such spaces is compact in the sup-norm topology. This result is exploited to obtain conditions which guarantee existence of solutions for the aforementioned problems as well as numerical algorithms whose convergence is guaranteed in the space of continuous functions.