GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics

2026-07-01

AI Summary

This work addresses the challenge of accurately characterizing linearization errors in nonlinear and neural network dynamics, which hinders the safety and constraint satisfaction of real-time robust optimal control. The authors propose differentiable, compact, and GPU-parallelizable Linearization Error Bounds (LEBs)—the first certified error bounds for neural network dynamics—augmented with path-dependent Hessian bounds to enhance accuracy. By integrating System Level Synthesis, affine relaxations, and zonotope-based uncertainty propagation, the method generates formally verified reachability tubes and robust feedback policies online. Evaluated in state spaces up to 168 dimensions, the approach achieves real-time computation at up to 67 Hz, significantly reducing both conservatism and computational overhead while preserving formal guarantees.

Abstract

This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction. We develop tight, differentiable, GPU-parallel LEBs for LTV approximations of nonlinear and neural network (NN) dynamics. For analytic dynamics, we introduce path-based Hessian bounds that are tighter than standard interval methods. For NN dynamics, we derive certified LEBs using NN verifier-generated affine relaxations and local Jacobian corrections. We adapt a GPU-parallel system-level synthesis LTV-based robust control solver to be compatible with these LEBs by extending it to handle right-invertible disturbance matrices and non-zero-centered disturbance sets for tight zonotopic uncertainty propagation. Our method, GPUSLS-LEO, enables online optimization of robust feedback policies that account for linearization error, producing tight, formally verified reachable tubes. On complex nonlinear and NN dynamics up to 168 state dimensions, our method can compute robust control policies on the GPU at rates up to 67 Hz, reducing solve times and conservativeness relative to baselines while preserving formal guarantees and real-time performance.

Problem

• linearization error bounds
• robust optimal control
• nonlinear dynamics
• neural network dynamics
• real-time control

Innovation

• linearization error bounds
• GPU-parallel robust control
• neural network dynamics
• system-level synthesis
• zonotopic uncertainty propagation