Efficient model predictive control for nonlinear systems modelled by deep neural networks

TL;DR

This paper develops efficient model predictive control strategies for nonlinear systems modeled by deep neural networks, balancing solution accuracy and computational efficiency through exact and relaxed optimization methods.

Contribution

It introduces two novel methods—mixed integer programming and linear relaxation—for solving nonlinear MPC problems with neural network models.

Findings

MIP provides exact solutions but is computationally intensive.

LR methods offer faster, suboptimal solutions suitable for real-time control.

Numerical simulations demonstrate the effectiveness of both approaches on inverted pendulum models.

Abstract

This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex nonlinearity of the system state and control input, the MPC problem is nonlinear and challenging to solve for real-time control. This paper proposes two types of methods for solving the MPC problem: the mixed integer programming (MIP) method which produces an exact solution to the nonlinear MPC, and linear relaxation (LR) methods which generally give suboptimal solutions but are much computationally cheaper. Extensive numerical simulation for an inverted pendulum system modelled by ReLU NNs of various sizes is used to demonstrate and compare performance of the MIP and LR methods.