Abstract
Optimal control problems are found in state and parameter estimation, experimental design, and model-based control for complex dynamical systems. Parsimonious input parameterization is an approach for obtaining solutions to these problems, which comprises two tasks: the first corresponds to the generation of arc sequences and the second consists in the computation of optimal values of a small number of decision variables for each sequence. This paper proposes an adaptive method for global solutions to single-input optimal control problems that accounts for the mismatch between the true system and its model by using Gaussian processes to represent the mismatch in the cost and constraints for an arc sequence. This adaptive approach converges to the global solution for the true system and ensures constraint satisfaction with a prespecified probability. The proposed approach is illustrated by a simulation example of a reaction system.
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