Optimal control design for a reparable multi-state system

In this paper, we consider the problem of optimal distributed control of a multi-state reparable system. A Linear Quadratic Regulator (LQR) design is proposed in order to accelerate the convergence of the system to its steady-state availability under a preassigned rate. The feedback law provides insights into designing the optimal system maintenance strategy. Finite difference is used to approximate the system and numerical experiments are presented to demonstrate the efficacy of the proposed method.