GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics
2026-07-01 • Artificial Intelligence
Artificial IntelligenceMachine LearningRobotics
AI summaryⓘ
The authors study how to control complex systems that change over time and have uncertain behavior. They create a fast and precise way to estimate errors when simplifying these systems to make planning easier. Their method works for systems described by equations and neural networks, using a special computing setup to quickly find safe ways to control the system in real time. This approach helps generate reliable control plans even when the system is very complicated, running much faster and with fewer errors than previous methods.
Robust controlNonlinear systemsLinear time-varying (LTV) approximationsLinearization error bounds (LEBs)Neural network dynamicsGPU parallel computingHessian boundsAffine relaxationsZonotopic uncertaintyOnline optimization
Authors
Jeffrey Fang, Keyi Shen, Anutam Srinivasan, Glen Chou
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.