A Data-Driven Approach To Stochastic Constrained Control Of Piecewise Affine Systems

This paper addresses the design of the control input to a discrete time piecewise affine system so as to optimize its performance along a finite time horizon. The system is affected by some additive stochastic disturbance and is subject to constraints that need to be appropriately accounted for in the design. By enforcing constraints to be satisfied for almost all disturbance realizations except for a set of probability, e, we can decide to what extent trading robustness for improving performance and also cope with the case of disturbance with unbounded support. Inspired by the existing literature, we propose a method to realize this trade-off, which combines the scenario approach to chance-constrained optimization with robust optimal control of piecewise affine systems. Interestingly, no explicit knowledge of the disturbance distribution is needed but only some disturbance realizations, thus resulting in a data driven design method.