Discovering interpretable piecewise nonlinear model predictive control laws via symbolic decision trees
Ilias Mitrai
TL;DR
This paper tackles the challenge of deploying interpretable, data-driven control in model predictive control (MPC) by introducing symbolic decision trees that simultaneously learn the input-domain partition and nonlinear leaf expressions. Framed as a mixed-integer optimization, the method yields a globally optimal surrogate map $\pi(\cdot)$ from state $x_0$ to control $u$, where each region uses a nonlinear combination of basis functions. The approach is demonstrated on an isothermal CSTR, showing that the learned symbolic tree achieves close to MPC performance in closed-loop behavior while outperforming baseline interpretable models in predictive accuracy. The findings suggest that symbolic trees offer a practical, interpretable pathway to approximate complex MPC laws with strong performance and efficient computation.
Abstract
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.