Hongwei Mei · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27579 · open-access PDF
Teori yang ada tentang masalah kontrol optimal stochastic linear-quadratic (LQ) berfokus pada solvabilitas loop terbuka dan loop tertutup. Untuk masalah horizon terbatas, secara luas diterima bahwa dua jenis solvabilitas ini tidak setara secara umum, seperti yang ditunjukkan oleh counterexamples eksplisit. Sebaliknya, mereka bertepatan dalam formulasi horizon infinite standar dengan koefisien konstan di bawah asumsi stabilisasi dan integrasi yang tepat. Dokumen ini bertujuan untuk menantang paradigma yang sudah mapan ini dengan mengembangkan kerangka kerja baru solvabilitas loop tertutup, yaitu generalisasi solvabilitas loop tertutup.
Machine translation (Meta M2M100); the English original follows.
The existing theory of stochastic linear-quadratic (LQ) optimal control problems focuses on open-loop and closed-loop solvability. For finite horizon problems, it is widely accepted that those two types of solvability are not equivalent in general, as demonstrated by explicit counterexamples. In contrast, they coincide in standard infinite-horizon formulations with constant coefficients under suitable stabilizability and integrability assumptions. This paper aims at challenging this well-established paradigm by developing a novel framework of closed-loop solvability, namely generalized closed-
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