Minimum entropy open loop control for linear dynamical systems with uncertain parameters

This paper presents a minimum entropy approach for the design of an optimal bang-bang control for linear dynamical systems with parametric uncertainty. The curse of dimensionality is of major concern when the dimension of the uncertain parameter space increases while designing robust controllers. In this paper an alternative probabilistic approach is developed to account for parameter uncertainty when designing a rest to rest maneuver. Specifically the entropy of the final time energy is minimized with respect to an assumed control profile. Efficient quadrature/cubature points such as the recently developed Conjugate Unscented Transform points are shown to be highly advantageous for estimating entropy via the principle of maximum entropy. Finally numerical examples are shown to validate the proposed approach.