Building Temperature Control by Simple MPC-like Feedback Laws Learned from Closed-Loop Data

We show how to synthesize simple, yet well-performing feedback strategies that mimic the behavior of optimization-based controllers, such as those based on model predictive control (MPC). The approach is based on employing regression trees to derive dependence of real-valued control inputs on measurements. Quality of classical regression policies is improved by finding, simultaneously, optimal affine splits and optimal local affine regressors. We furthermore illustrate how to refine the local regressors such that the overal feedback strategy guarantees satisfaction of input constraints. The main advantage of the proposed regression-based control strategy stems from its fast implementation even on very simple hardware. The approach is demonstrated on a case study that assumes control of temperature in a one-zone building. Here, the data used in the learning process are generated by MPC. We show that the simple feedback law attains almost the same level of performance as the complex MPC controller.