Explicit stochastic MPC approach to building temperature control

In this paper we show how to synthesize explicit representations of Model Predictive Control (MPC) feedback laws that maintain temperatures in a building within of a comfortable range while taking into account random evolution of external disturbances. The upside of such an explicit MPC solution stems from the fact that optimal control input can be obtained on-line by a mere function evaluation. This task can be accomplished quickly even on cheap hardware. To account for random disturbances, our formulation assumes probabilistic version of thermal comfort constraints. We illustrate how a finite-sampling approach can be used to convert probabilistic bounds into deterministic constraints. To reduce complexity, and to allow for synthesis of explicit feedbacks in reasonable time, we furthermore propose to prune the set of samples depending on activity of constraints. Performance of the stochastic explicit MPC controller is then compared against best-case and worst-case scenarios.