Tailored neural networks for learning optimal value functions in MPC

TL;DR

This paper demonstrates how tailored neural networks can exactly represent the optimal value and Q-functions in linear MPC, leveraging their piecewise quadratic structure for improved learning efficiency.

Contribution

It extends the use of tailored neural networks from control policies to value and Q-functions in linear MPC, providing a theoretical foundation for their exact representation.

Findings

Tailored neural networks can exactly represent the optimal value function in linear MPC.

The approach leverages the piecewise quadratic nature of the value and Q-functions.

This method enhances the understanding of neural network approximation in control systems.

Abstract

Learning-based predictive control is a promising alternative to optimization-based MPC. However, efficiently learning the optimal control policy, the optimal value function, or the Q-function requires suitable function approximators. Often, artificial neural networks (ANN) are considered but choosing a suitable topology is also non-trivial. Against this background, it has recently been shown that tailored ANN allow, in principle, to exactly describe the optimal control policy in linear MPC by exploiting its piecewise affine structure. In this paper, we provide a similar result for representing the optimal value function and the Q-function that are both known to be piecewise quadratic for linear MPC.