One Type Of Degradation Of Complex Repairable Systems The Optimal Control Solution

Repairable system is composed of a number of one or more repair parts and equipment (mechanic), with repair of defective parts to repair equipment, repair work can continue after the system is discussed in reliability theory, an important class of systems, but also the reliability of important study of mathematics. The system is characterized by a number of parts and components of one or more repair facilities. If failure, its maintenance, repair parts after the sustainable implemen-tation of the command. In this paper, proved that the system of non-negative dynamic existence and uniqueness of solutions on the basis of asymptotic stability and further through a system of indicators as a measure of functional controllability criteria for a class of solutions of complex repairable deteriorating system, the prob-ability distribution of the expected optimal control problem. Methods for the use of additional variables repairable system established by the mathematical model of the problem space into a Banach Cauchy using the issue of abstract to describe the system, through the transformation, the differential equation into a convolution-type Volterra integral equation form, the use of functional analysis in the mapping principle and fixed point theorem proving system is the only non-negative strong solution, based on C0-semigroup theory to prove the system operator generates a positive compression semigroup, and thus prove that the system has a unique time-dependent non-negative weak solution, strong solution is both a weak solu-tion, prove the existence and uniqueness of solutions.0 in the show is its simple eigenvalue, its eigenvector is the steady-state solutions of the system on the basis of the asymptotic stability of the system; in the proof of asymptotic stability of the system, the known system of non-negative time dependent solution of the steady-state solution approach, the proof of the stability of the system; Finally, select the norm index of functional controllability as a measure of the system, minimizing sequence of the method used to obtain the optimal control element;...