Featurized Occupation Measures for Structured Global Search in Numerical Optimal Control
This work addresses a foundational problem in control theory by bridging global and local methods, offering incremental improvements in structured search for nonlinear control applications.
The paper tackles the challenge of unifying global certification and scalable trajectory optimization in numerical optimal control by introducing the Featurized Occupation Measure (FOM), which provides asymptotic consistency and preserves certified lower bounds with error control.
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.