Robust stochastic control based on imprecise probabilities ⋆

This paper deals with the optimal quadratic control problem for non Gaussian discrete-time linear stochastic systems from the perspective of imprecise probabilities. The adopted philosophy is to use a convex set of probability distributions to characterize the imprecision in the knowledge about the probabilistic relationships present in the system to be controlled. In particular, an uncertain system model, named Linear Gaussian Vacuous Mixture (LGVM ), in which disturbances and initial state uncertainty are described as convex combinations (mixtures) of nominal Gaussian distributions and unknown vacuous distributions, is adopted. A novel control approach is then derived, according to a worst-case paradigm, by minimizing the upper expectation of a finite-horizon quadratic cost functional with respect to all admissible probability distributions and exploiting a receding horizon strategy. Simulation experiments demonstrate its robustness in presence of large unexpected impulsive disturbances.