Optimal control and stabilization for linear continuous‐time mean‐field systems with delay

This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of systems. There two main contributions: (1) To best authors' knowledge, present is first to establish necessary sufficient solvability condition this kind problem derive analytical form an controller through overcoming obstacle that separation principle no longer holds multiplicative-noise (2) For problem, under assumption exact observability, it strictly proven system stabilizable if only algebraic Riccati equation has a unique positive definite solution.