Amortized Nonlinear Model Predictive Control

2026-06-04

AI Summary

This work addresses the high computational burden of nonlinear model predictive control (NMPC), which requires solving a constrained nonlinear program online and is thus challenging to deploy on resource-constrained or high-sample-rate systems. Focusing on input-affine nonlinear systems, the authors propose an efficient approximation scheme that models the optimal control law as a state-dependent quadratic program (QP) and introduces a single-network residual correction architecture to learn the discrepancy between the QP solution and the true nonlinear programming (NLP) solution. A differentiable interior-point optimization layer is embedded to guarantee constraint satisfaction for the first control step, and the network is trained jointly using a hybrid loss combining supervised imitation learning and KKT residual minimization. Evaluated on a three-link robotic arm trajectory tracking task, the method achieves an order-of-magnitude speedup over the original NLP solver while maintaining comparable tracking accuracy.

Abstract

Nonlinear Model Predictive Control requires solving a constrained nonlinear program (NLP) in real-time at every sampling instant, a computational bottleneck that limits deployment on resource-constrained hardware or at high sampling rates. We address this challenge for the broad class of input-affine nonlinear systems to show that the optimal control move can be approximated by a state-dependent quadratic program (QP) whose cost parameters depend on the current state and reference. We propose a single-network residual-corrector architecture: a state-dependent analytic baseline provides initial QP parameters, and the network learns only the corrections needed to match the full NLP solution; the QP is solved by a differentiable interior-point layer, guaranteeing constraint satisfaction for the first control action. The network is trained offline on data generated by an NLP solver using a hybrid loss that combines supervised imitation and KKT-residual penalties. We validate the approach on a three-link planar robotic arm with Cartesian end-effector tracking, demonstrating orders-of-magnitude speedup over the NLP solver while maintaining comparable tracking performance.

Problem

• Nonlinear Model Predictive Control
• real-time optimization
• computational bottleneck
• constrained nonlinear program
• resource-constrained hardware

Innovation

• Amortized MPC
• State-dependent QP
• Residual-corrector architecture
• Differentiable optimization
• Input-affine nonlinear systems