On-line optimal control of a class of discrete event systems with real-time constraints

We consider discrete event systems involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint. It has been shown that the off-line version of this problem can be efficiently solved by the critical task decomposition algorithm by J. Mao et al (2007). The on-line version has been dealt with to date using worst-case analysis so as to bypass the complexity of random effects. This approach, however, does not make use of probability distributions and results in an overly conservative solution. In this paper, we develop a new on-line algorithm without relying on worst-case analysis, in which a ¿best solution in probability¿ can be efficiently obtained by estimating the probability distribution of the off-line optimal control. We introduce a condition termed ¿non-singularity¿ under which the best solution in probability leads to the on-line optimal control. Numerical examples are included to illustrate our results and show substantial performance improvements over worst-case analysis.