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

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.