论文标题
线性连续时间平均场系统的最佳控制和稳定化延迟
Optimal control and stablilization for linear continuous-time mean-field systems with delay
论文作者
论文摘要
本文研究了具有输入延迟的连续时间平均场系统的最佳控制和稳定问题，这是平均场系统控制和稳定问题的基本发展。有两个主要的贡献：1）据我们所知，本文首先是为这种最佳控制问题建立必要且充分的解决性条件，并通过克服障碍而获得最佳控制器，以至于分离原理不再适合多样化的噪声系统； 2）对于稳定问题，在确切可观察性的假设下，我们严格证明该系统是可以稳定的，并且仅当代数riccati方程具有独特的阳性确定解时。
This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of control and stabilization problems for mean-field systems. There are two main contributions: 1) To the best of our knowledge, the present paper is first to establish the necessary and sufficient solvability condition for this kind of optimal control problem with delay, and to derive an optimal controller through overcoming the obstacle that separation principle no longer holds for multiplicative-noise systems; 2) For the stabilization problem, under the assumption of exact observability, we strictly prove thatthe system is stabilizable if and only if the algebraic Riccati equation has a unique positive definite solution.
