Performance-adaptive renewal policies for linear systems

The design of systems with a component subject to failure may include a discrete renewal capability to counter the degradation in performance caused by improper operation of the failed component. A solution is presented to the problem of determining the optimal use of available renewal capability for first-order time-varying linear systems with a quadratic performance index, using an exponential model of component failure. The solution is extended quasi optimally to linear systems of arbitrary order. The renewal policy determined is performance-adaptive in the sense that it depends on the failure and renewal histories of the system and on their relation to future operating requirements. The renewal policy is determined with respect to other control variables to insure overall optimal performance. A discrete stage variable is introduced to specify the system operating condition. The optimal control and renewal policy within each stage is specified by a pair of Riccati equations whose solutions are precomputed. The method avoids quantization of continuous-valued state variables, thereby lessening the effects of the curse of dimensionality.