Approximate Closed-loop minimax MPC for Climate Control in Buildings in Presence of Additive Bounded Uncertainty

In this work, a minimax control formulation is presented for climate control in buildings. The design of the controller is based upon model predictive control (MPC) framework; it includes time-varying constraints. The objective of the proposed controller is to handle additive external disturbances acting on the system. The presented approach does not explicitly model the disturbance and/or uncertainty. The only information that is provided to the controller is the maximum and minimum bounds on the disturbances. In another scenario, it is considered that the disturbance predictions are available; however, there is a bounded uncertainty involved in the predictions. The problem is formulated as a closed-loop minimax optimization problem to minimize the “worst-case” objective function in the presence of uncertainty. To make the problem tractable control input vector is parametrized in terms of disturbances to get a bilinear mapping from control input to the system states. The simulation results demonstrate the effectiveness of the control formulation and show that the control system is able to meet the objective in the presence of remote disturbances and the uncertainty associated with disturbances predictions.