Hongwei Mei · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27579 · open-access PDF
La teoría existente de los problemas de control óptimo lineal-cuadrático estocástico (LQ) se centra en la solubilidad de circuito abierto y circuito cerrado. Para los problemas de horizonte finito, se acepta ampliamente que estos dos tipos de solubilidad no son equivalentes en general, como lo demuestran contraejemplos explícitos. En contraste, coinciden en fórmulas de horizonte infinito estándar con coeficientes constantes bajo asunciones de estabilización y integrabilidad adecuadas. Este artículo tiene como objetivo desafiar este paradigma bien establecido mediante el desarrollo de un nuevo marco de solubilidad de circuito cerrado, a saber, generalizado de circuito cerrado.
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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