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Optimal Control for Stable Solution of Repairable Human-Machine Systems

Author: WangShiKai
Tutor: WangHui；JiaNuo
School: Harbin Normal University
Course: Operational Research and Cybernetics
Keywords: C0- semigroup Solution existence and uniqueness of Asymptotic stability Optimal Control
CLC: O232
Type: Master's thesis
Year: 2010
Downloads: 46
Quote: 1
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Abstract


The article focuses on a class of conventional failure , a hardware error , critical human error repairable system . Repairable systems are an important class of systems reliability theory discussed also the reliability of the main object of study of mathematics for the use of supplementary variables the repairable system created a mathematical model , first of all, the system differential - integral equations of the mathematical model transformed into Volterra integral equation , to prove that the system is non- negative strong solution existence and uniqueness ; weak system of non - negative time depends solution , the system equations are transformed into abstract differential equations in Banach space , and demonstrate that the system operator to generate compressed C0 semigroup , which proved that the system is non - negative time dependence weak existence and uniqueness of solutions , obtained the system weak solution is a strong solution prove the existence and uniqueness of the solution of the mathematical model of the system of the system solution a non - negative , the probabilistic nature of the solution , in line with the actual physical significance . Secondly, the proof of the asymptotic stability of system . first prove 0 the system is simple intrinsic root , the system dynamic solution converges to the steady-state solution of the system on to discuss the system in the strong conditions get C0 semigroup perturbation theorem system dynamic solution converges to the steady-state solution in exponential form . Finally the repair rate μ (x) steady-state solution as a control variable to the norm index function as a measure of standard control variables , minimizing sequence , Banach-Saks-Mazur theorem in functional analysis to arrive at the system optimal control theory and application value method of repairable complex system controllability .

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CLC: > Mathematical sciences and chemical > Mathematics > Control theory, information theory ( mathematical theory ) > Optimal control
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