On the constrained feedback linearization control based on the MILP representation of a ReLU-ANN

TL;DR

This paper presents a method to convert ReLU neural network constraints into MILP form for feedback linearization control, enabling integration with linear control and MPC while ensuring constraint satisfaction.

Contribution

It introduces a comprehensive approach to approximate neural network constraints with MILP, facilitating their use in feedback linearization and model predictive control.

Findings

Effective MILP reformulation of ReLU constraints

Compatibility with linear control and MPC

Validated through simulations

Abstract

In this work, we explore the efficacy of rectified linear unit artificial neural networks in addressing the intricate challenges of convoluted constraints arising from feedback linearization mapping. Our approach involves a comprehensive procedure, encompassing the approximation of constraints through a regression process. Subsequently, we transform these constraints into an equivalent representation of mixed-integer linear constraints, seamlessly integrating them into other stabilizing control architectures. The advantage resides in the compatibility with the linear control design and the constraint satisfaction in the model predictive control setup, even for forecasted trajectories. Simulations are provided to validate the proposed constraint reformulation.