论文标题
无限尺寸随机线性系统的功能分析方法
A functional analytic approach to infinite dimensional stochastic linear systems
论文作者
论文摘要
在本文中，我们研究具有无界控制和观察算子的无限维度随机系统。首先，使用半群方法，我们又一次介绍了[Siam J. Control Optim。，53（2015），第3457---3482页中所处理的系统的适当性。我们进一步证明了此类系统的确切可控性的结果。其次，我们提出了常数公式的新变化，用于使用可允许的运营商的Yosida扩展的概念，用于扰动抽动的抽象随机库奇问题的轻度解决方案。第三，我们证明了扰动边界控制系统的适当性。第四，我们将此结果应用于具有延迟，控制和观察部件的一般类随机系统。最后，我们研究了可允许的观察算子和半线性随机系统的确切可观察性。
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM J. Control Optim., 53 (2015), pp. 3457--3482]. We further prove a result on the exact controllability of such systems. Second, we propose a new variation of constants formula for mild solutions of perturbed abstract stochastic Cauchy problems using the concept of Yosida extensions of admissible operators. Third, we prove the well-posedness of perturbed boundary control systems. Fourth, we apply this result to a general class of stochastic systems with delays in the state, control, and observation parts. Finally, we study admissible observation operators and exact observability for semilinear stochastic systems.
