A stochastic linear-quadratic optimal control problem with jumps in an infinite horizon

In this paper, a stochastic linear-quadratic (LQ, for short) optimal control problem with jumps in an infinite horizon is studied, where the state system is a controlled linear stochastic differential equation containing affine term driven by a one-dimensional Brownian motion and a Poisson stochastic martingale measure, and the cost functional with respect to the state process and control process is quadratic and contains cross terms. Firstly, in order to ensure the well-posedness of our stochastic optimal control of infinite horizon with jumps, the $L^2$-stabilizability of our control system with jump is introduced. Secondly, it is proved that the $L^2$-stabilizability of our control system with jump is equivalent to the non-emptiness of the admissible control set for all initial state and is also equivalent to the existence of a positive solution to some integral algebraic Riccati equation (ARE, for short). Thirdly, the equivalence of the open-loop and closed-loop solvability of our infinite horizon optimal control problem with jumps is systematically studied. The corresponding equivalence is established by the existence of a $stabilizing\ solution$ of the associated generalized algebraic Riccati equation, which is different from the finite horizon case. Moreover, any open-loop optimal control for the initial state $x$ admiting a closed-loop representation is obatined

Long Non-Coding RNA TUG1 Attenuates Insulin Resistance in Mice with Gestational Diabetes Mellitus via Regulation of the MicroRNA-328-3p/SREBP-2/ERK Axis

Background Long non-coding RNAs (lncRNAs) have been illustrated to contribute to the development of gestational diabetes mellitus (GDM). In the present study, we aimed to elucidate how lncRNA taurine upregulated gene 1 (TUG1) influences insulin resistance (IR) in a high-fat diet (HFD)-induced mouse model of GDM. Methods We initially developed a mouse model of HFD-induced GDM, from which islet tissues were collected for RNA and protein extraction. Interactions among lncRNA TUG1/microRNA (miR)-328-3p/sterol regulatory element binding protein 2 (SREBP-2) were assessed by dual-luciferase reporter assay. Fasting blood glucose (FBG), fasting insulin (FINS), homeostasis model assessment of insulin resistance (HOMA-IR), HOMA pancreatic β-cell function (HOMA-β), insulin sensitivity index for oral glucose tolerance tests (ISOGTT) and insulinogenic index (IGI) levels in mouse serum were measured through conducting gain- and loss-of-function experiments. Results Abundant expression of miR-328 and deficient expression of lncRNA TUG1 and SREBP-2 were characterized in the islet tissues of mice with HFD-induced GDM. LncRNA TUG1 competitively bound to miR-328-3p, which specifically targeted SREBP-2. Either depletion of miR-328-3p or restoration of lncRNA TUG1 and SREBP-2 reduced the FBG, FINS, HOMA-β, and HOMA-IR levels while increasing ISOGTT and IGI levels, promoting the expression of the extracellular signal-regulated kinase (ERK) signaling pathway-related genes, and inhibiting apoptosis of islet cells in GDM mice. Upregulation miR-328-3p reversed the alleviative effects of SREBP-2 and lncRNA TUG1 on IR. Conclusion Our study provides evidence that the lncRNA TUG1 may prevent IR following GDM through competitively binding to miR-328-3p and promoting the SREBP-2-mediated ERK signaling pathway inactivation