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Optimal bilinear control of a reparable multi-state system

This work addresses an optimal bilinear control design representing the corrective maintenance for a reparable multi-state system. The primary interest is to optimise the availability of the system, which is defined as the probability that the system is operating properly when it is requested for use. The system model considered in our current work is governed by coupled transport and integro-differential equations. A corrective maintenance policy is represented by the repair rate, which depends on the distributed repair time. The objective is to determine an optimal repair rate that maximises the availability of the system in good mode over a given system running period. This essentially leads to a bilinear control problem set in a nonreflexive Banach space using -optimisation. A rigorous proof of existence of an optimal controller and the first-order necessary conditions of optimality are addressed. Numerical experiments are conducted to demonstrate the theoretical results.