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

TL;DR

This letter explores the efficacy of rectified linear unit artificial neural networks in addressing the intricate challenges of convoluted constraints arising from feedback linearization mapping and transforms these constraints into an equivalent representation of mixed-integer linear constraints, seamlessly integrating them into other stabilizing control architectures.

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.

Figures (2)

• Figure \ref{fig:simMSD}: Stabilization with ANN-based constraint characterization.
• Figure \ref{fig:Quad1D_state}: Trajectory tracking with the MPC \ref{['eq:MPC_form_miqp']} for \ref{['eq:quad1D_nonlinear']}.