GPU-Parallel Linearization Error Bounds for Real-Time Robust Optimal Control of Nonlinear and Neural Network Dynamics
arXiv:2607.01203v1 Announce Type: cross 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-gene
The increasing complexity of AI and robotic systems, especially with the integration of neural networks, necessitates robust control methodologies that can operate in real-time while guaranteeing performance and safety.
This development allows for more reliable and performant autonomous systems by providing tighter and certifiable error bounds, enabling complex AI models to be deployed in safety-critical applications.
The ability to accurately and rapidly quantify linearization errors for both traditional nonlinear and neural network dynamics will significantly enhance the trustworthiness and real-time capabilities of advanced optimal control systems.
- · Autonomous vehicle manufacturers
- · Robotics companies
- · AI algorithm developers
- · Defence contractors
- · Companies relying on less robust control methods
- · Developers limited by computational constraints for control
More widespread and safer deployment of AI-driven autonomous systems in physical environments.
Increased competition and innovation in sectors requiring high-assurance real-time control, such as industrial automation and aerospace.
Potential for new regulatory frameworks and certification standards to emerge for AI control systems, based on these quantifiable guarantees.
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Read at arXiv cs.LG