论文标题
具有不确定重量的二次成本功能的线性随机微分方程的最佳厄乳
Optimal Ergodic Control of Linear Stochastic Differential Equations with Quadratic Cost Functionals Having Indefinite Weights
论文作者
论文摘要
研究了具有二次成本功能的线性随机微分方程，研究了最佳的ergodic控制问题（简称EC问题）。恒定的非均匀项（并非全部为零）出现在状态方程中，这导致了状态非零的渐近极限。在稳定性条件下，对于任何（可允许的）闭环策略，事实证明是一种不变的度量，这使得ergodic成本功能良好定义且EC问题良好。引入了足够的条件，包括允许成本功能的加权矩阵不确定的条件，以解决EC问题的有限性和解决性。在无限范围内，EC问题的溶解度与随机线性二次最佳控制问题的闭环可溶性之间进行了一些比较。引入正则化EC问题用于获得EC问题的最佳值。
An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead to the asymptotic limit of the state non-zero. Under the stabilizability condition, for any (admissible) closed-loop strategy, an invariant measure is proved to exist, which makes the ergodic cost functional well-defined and the EC problem well-formulated. Sufficient conditions, including those allowing the weighting matrices of cost functional to be indefinite, are introduced for finiteness and solvability for the EC problem. Some comparisons are made between the solvability of EC problem and the closed-loop solvability of stochastic linear quadratic optimal control problem in the infinite horizon. Regularized EC problem is introduced to be used to obtain the optimal value of the EC problem.
