Optimal Control Of A Parallel Repairable System With Tow Non-idential Units

In recent years，theoretical study of the repairable system is concerned by moreand more scholars，and have achieved fruitful results. Repairable system means asystem constitutesa system component failure or deterioration through various re-pair means to restorefunction.By analyzing the status of repairable system modelconcepts and theories of therepairable system，and on this basis，the repairablesystem model-based analysis methods parallel repairable system with two difer-ent components，for examplesystemsolution existence and uniqueness，stability，exponential stability，optimal control and other issues were discussed in detail. Inthis paper，the following aspects of two diferent components in parallel repairablesystem.Study on the existence and uniqueness of solution of the system.The integraldiferential equations that describe the repairable system into Volterra operator e-quations in Banach space. By using functional analysis method，prove the unique-ness of the solution. studies of the system P (T) at time T lower bound problem.Using the theory of functional analysis，the existence and uniqueness of the solutionthrough the system，P (T) be in time T lower bound on the specifc value.Seccond,Study on the stability of the solution of the system. Based on the analysis of thespectral properties of the operator，the spectrum of an operator in the complexplane of the left half plane，the imaginary axis point except0are in the solutionset.0is corresponding to the operator and its adjoint operator with geometric mul-tiplicit and algebraic multiplicity1eigenvalue，eigenvalue and the correspondingeigenvector is the stationary solution of the system.And the0eigenvalues of thecorresponding eigenvector is positive, so the system has steady state solution.Studyof the solution of the system reliability. The system failure rate and repair rateis assumed to be constant, can launch p0(t) is a decreasing function，namely thereliability of certifcate.Research on the solution of the system exponential stabil-ity. The repairable system of essential spectrum of bounded disturbance changesafter research，demonstrate the system dynamic solution under the condition ofstrong exponentially converge to the stationary solution of the system. Finally, the indicator functions of the norm as a standard measurement system control ability,optimal control system solutions.