arXiv:2606.23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Principle optimality system is solved from multiple initial conditions to generate training data consisting of values, gradients, and Hessians of the value function, where Hessian information is obtained from a matrix Riccati equation along optimal trajectories. These quantities augment a weighted least-squares regression over sparse polynomial bases on hyperbolic cross inde
The continuous advancements in AI and computational methods are enabling new approaches to complex mathematical problems that were previously intractable or highly inefficient.
This development proposes a data-driven method for optimal control problems which are foundational to autonomous systems, potentially leading to significant improvements in their efficiency and robustness.
The ability to efficiently approximate value functions using Hessian-augmented supervised learning introduces a new paradigm for solving Hamilton-Jacobi-Bellman PDEs in optimal control.
- · AI researchers
- · Robotics engineers
- · Autonomous systems developers
- · Control theory specialists
- · Traditional numerical methods that are less efficient
- · Systems heavily reliant on suboptimal control strategies
Improved performance and stability in autonomous decision-making systems.
Faster development cycles and deployment of sophisticated AI-driven optimal control solutions across various industries.
Enhanced automation capabilities in complex environments, potentially accelerating progress in areas like advanced manufacturing and autonomous logistics.
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Read at arXiv cs.LG