抄録
This paper is concerned with the determination of optimal control laws for a linear time-varying system having the possibility of failure. When the system fails, it will take some time for repair before resuming its normal duty. Here we assume the duration of repair as a random variable with a possibility distribution function.
Some results are obtained for the following cases.
1) The state (failed or renewed) of the system can be continuously monitored or inspected.
2) The state of the system cannot be monitored or inspected.
For the first case the optimal solution can be obtained by extending the results already known. The solution, however, is easily implementable only in case the probability function is exponential. So here we propose a method which gives implementable control laws in more general cases.
For the second case the optimal solution can be obtained by a two-level method.
