Iterative Learning Stochastic MPC with Adaptive Constraint Tightening for Building HVAC Systems

Most of the existing stochastic model predictive control (SMPC) algorithms for systems subject to random disturbance are designed offline using the distribution information of the uncertainties. In this paper, we propose an iterative learning based MPC for systems subject to time varying stochastic constraints on states. Different from those existing offline design approaches, except for the boundedness, this algorithm does not require to know the distributions or statistics such as the covariances of the uncertainties and the parameters of the controllers are adjusted online using the observations of past state trajectories. By making use of the iterative nature of the process, pointwise in time stochastic constraints are enforced so that it can handle time-varying constraints. Under some proper assumptions, this iterative procedure is shown to be equivalent to a root-searching problem and stochastic approximation theory is applied to show that the empirical average converges to the prescribed expectation in probability. The proposed algorithm is applied to an HVAC control problem to show its effectiveness.