Discovering interpretable piecewise nonlinear model predictive control laws via symbolic decision trees

In this paper, we propose symbolic decision trees as surrogate models for approximating model predictive control laws. The proposed approach learns simultaneously the partition of the input domain (splitting logic) as well as local nonlinear expressions for predicting the control action leading to interpretable piecewise nonlinear control laws. The local nonlinear expressions are determined by the learning problem and are modeled using a set of basis functions. The learning task is posed as a mixed integer optimization, which is solved to global optimality with state-of-the-art global optimization solvers. We apply the proposed approach to a case study regarding the control of an isothermal reactor. The results show that the proposed approach can learn the control law accurately, leading to closed-loop performance comparable to that of a standard model predictive controller. Finally, comparison with existing interpretable models shows that the symbolic trees achieve both lower prediction error and superior closed-loop performance.