Adnan KhanAdnanProduct & AI
San Francisco Bay Area
Get in touch

Source note3 min read

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

Source

arXiv

arxiv.org/abs/2607.01203v1

Read the source

Source

Plain-Language Brief

The paper presents a new method called GPUSLS-LEO for real-time robust optimal control of uncertain nonlinear systems, specifically focusing on systems with linear time-varying (LTV) approximations. This method provides tight, differentiable, GPU-parallel Linearization Error Bounds (LEBs) for LTV approximations of both traditional nonlinear dynamics and neural network dynamics. The paper proposes path-based Hessian bounds for analytic dynamics, and certified LEBs using NN verifier-generated affine relaxations and local Jacobian corrections for neural network dynamics. The method is compatible with a GPU-parallel system-level synthesis LTV-based robust control solver for tight zonotopic uncertainty propagation. The results show that the new method can compute robust control policies on the GPU at rates up to 67 Hz, reducing solve times and conservativeness compared to baselines while preserving formal guarantees and real-time performance.

What the Document Says

  • The paper focuses on real-time robust optimal control for uncertain nonlinear systems.
  • Linear time-varying (LTV) approximations are used to make planning tractable, but require sound Linearization Error Bounds (LEBs) for robust constraint satisfaction.
  • Tight, differentiable, GPU-parallel LEBs are developed for LTV approximations of both nonlinear and neural network dynamics.
  • Path-based Hessian bounds are introduced for analytic dynamics.
  • Certified LEBs are derived using NN verifier-generated affine relaxations and local Jacobian corrections for neural network dynamics.
  • The method is adapted to be compatible with a GPU-parallel system-level synthesis LTV-based robust control solver.
  • The 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 neural network dynamics up to 168 state dimensions, the method can compute robust control policies on the GPU at rates up to 67 Hz.

Key Concepts Mentioned

  • real-time robust optimal control
  • uncertain nonlinear systems
  • linear time-varying (LTV) approximations
  • Linearization Error Bounds (LEBs)
  • nonlinear dynamics
  • neural network dynamics
  • GPU-parallel
  • path-based Hessian bounds
  • NN verifier-generated affine relaxations
  • local Jacobian corrections
  • system-level synthesis LTV-based robust control solver
  • zonotopic uncertainty propagation

Claims Made by the Document

  • The new method can compute robust control policies on the GPU at rates up to 67 Hz.
  • The new method reduces solve times and conservativeness compared to baselines.

Evidence Used

  • Results from complex nonlinear and neural network dynamics up to 168 state dimensions.

Methods / Approach

  • Development of tight, differentiable, GPU-parallel LEBs for LTV approximations.
  • Introduction of path-based Hessian bounds for analytic dynamics.
  • Derivation of certified LEBs using NN verifier-generated affine relaxations and local Jacobian corrections for neural network dynamics.
  • Adaptation of a GPU-parallel system-level synthesis LTV-based robust control solver to handle right-invertible disturbance matrices and non-zero-centered disturbance sets for tight zonotopic uncertainty propagation.

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

The paper does not mention any limitations from the authors. However, as an assistant, I would note that the performance of the method may depend on the specific nonlinear and neural network dynamics being controlled.

Open Questions

  • What are the specific baselines compared to which the new method reduces solve times and conservativeness?
  • How does the new method perform on a wider range of nonlinear and neural network dynamics?

Notes for Future Q&A

May include interpretation. Labeled where it does.

The paper mentions that the method reduces solve times and conservativeness compared to baselines, but it does not specify what these baselines are. Additionally, while the paper shows results for complex nonlinear and neural network dynamics up to 168 state dimensions, it is unclear how the method performs on a wider range of systems.

Raw Abstract / Excerpt

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.