Optimal control of a class of real-time computational systems

In many computational systems, tasks comprising numerical or symbolic data arrive at a processor periodically. Processing of the $i\sp{th}$ task has to stop before processing of the ($i$ + 1)$\sp{th}$ task begins, causing a hard constraint on $T\sb{p}(i)$: the time needed for complete processing of the $i\sp{th}$ task. Failing to meet this constraint means the processing is aborted and the output is deemed totally inaccurate or useless. To improve the probability of making real time, $T\sb{p}(i)$ may be reduced by approximating the data or the processing algorithms. Since approximation also reduces output accuracy, an overall objective function is constructed that merges the real-time constraint with the objective of accuracy, maximization of which yields the optimal level of approximation. An Object Recognizer is chosen as an example where image resolution is the method of approximation. The optimal policy for this example is discussed in detail with the help of a simulation