Neural Co-state Regulator: A Data-Driven Paradigm for Real-time Optimal Control with Input Constraints

TL;DR

This paper introduces a neural co-state regulator (NCR), a data-driven, real-time optimal control framework that predicts co-state trajectories using neural networks and enforces input constraints via quadratic programming, outperforming traditional MPC in speed and accuracy.

Contribution

The paper presents a novel neural network-based co-state prediction method combined with quadratic programming for input constraints, enabling faster and more accurate real-time control of nonlinear systems.

Findings

NCR outperforms nonlinear MPC in convergence error and input smoothness.

NCR achieves two orders of magnitude faster computation than nonlinear MPC.

NCR generalizes well outside its training domain.

Abstract

We propose a novel unsupervised learning framework for solving nonlinear optimal control problems (OCPs) with input constraints in real-time. In this framework, a neural network (NN) learns to predict the optimal co-state trajectory that minimizes the control Hamiltonian for a given system, at any system's state, based on the Pontryagin's Minimum Principle (PMP). Specifically, the NN is trained to find the norm-optimal co-state solution that simultaneously satisfies the nonlinear system dynamics and minimizes a quadratic regulation cost. The control input is then extracted from the predicted optimal co-state trajectory by solving a quadratic program (QP) to satisfy input constraints and optimality conditions. We coin the term neural co-state regulator (NCR) to describe the combination of the co-state NN and control input QP solver. To demonstrate the effectiveness of the NCR, we compare its feedback control performance with that of an expert nonlinear model predictive control (MPC) solver on a unicycle model. Because the NCR's training does not rely on expert nonlinear control solvers which are often suboptimal, the NCR is able to produce solutions that outperform the nonlinear MPC solver in terms of convergence error and input trajectory smoothness even for system conditions that are outside its original training domain. At the same time, the NCR offers two orders of magnitude less computational time than the nonlinear MPC.