Featurized Occupation Measures for Structured Global Search in Numerical Optimal Control
🤖 AI Summary
This work addresses the limitations of global methods such as Hamilton–Jacobi–Bellman (HJB) equations, which suffer from the curse of dimensionality, and trajectory optimization approaches, which lack global guarantees in numerical optimal control. To bridge this gap, the paper proposes the Featurized Occupation Measure (FOM) framework, which unifies trajectory search and HJB-type global verification through a finite-dimensional dual formulation. By leveraging approximate HJB subsolutions as intrinsic dual certificates to guide optimization, FOM establishes—for the first time—a certifiable and reusable mechanism for computing global lower bounds. The framework exhibits robustness under time translation and model perturbations and employs structured function approximation to ensure controllable error and computational complexity. Theoretically, FOM is shown to be asymptotically consistent with the infinite-dimensional occupation measure formulation, offering a principled balance of global optimality, scalability, and rigorous guarantees in nonlinear control.
Application Category
📝 Abstract
Numerical optimal control is commonly divided between globally structured but dimensionally intractable Hamilton-Jacobi-Bellman (HJB) methods and scalable but local trajectory optimization. We introduce the Featurized Occupation Measure (FOM), a finite-dimensional primal-dual interface for the occupation-measure formulation that unifies trajectory search and global HJB-type certification. FOM is broad yet numerically tractable, covering both explicit weak-form schemes and implicit simulator- or rollout-based sampling methods. Within this framework, approximate HJB subsolutions serve as intrinsic numerical certificates to directly evaluate and guide the primal search. We prove asymptotic consistency with the exact infinite-dimensional occupation-measure problem, and show that for block-organized feasible certificates, finite-dimensional approximation preserves certified lower bounds with blockwise error and complexity control. We also establish persistence of these lower bounds under time shifts and bounded model perturbations. Consequently, these structural properties render global certificates into flexible, reusable computational objects, establishing a systematic basis for certificate-guided optimization in nonlinear control.
Problem
Research questions and friction points this paper is trying to address.
numerical optimal control
Hamilton-Jacobi-Bellman
global search
trajectory optimization
occupation measures
Innovation
Methods, ideas, or system contributions that make the work stand out.
Featurized Occupation Measure
Hamilton-Jacobi-Bellman
certificate-guided optimization
occupation measures
numerical optimal control
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