On-line Optimal Control of a Class of Discrete Event Systems with Real-Time Constraints

Authors:
Jianfeng Mao;Christos G. Cassandras
Affiliations:
Division of Systems Engineering and Center for Information and Systems Engineering, Boston University, Brookline, USA 02446;Division of Systems Engineering and Center for Information and Systems Engineering, Boston University, Brookline, USA 02446
Venue:
Discrete Event Dynamic Systems
Year:
2010

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Abstract

We consider Discrete Event Systems (DES) 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 (CTDA) (Mao et al., IEEE Trans Mobile Comput 6(6):678---688, 2007). In the on-line version, random task characteristics (e.g., arrival times) are not known in advance. To bypass this difficulty, worst-case analysis may be used. This, however, does not make use of probability distributions and results in an overly conservative solution. In this paper, we develop a new approach which does not rely on worst-case analysis but provides a "best solution in probability" efficiently obtained by estimating the probability distribution of sample-path-optimal solutions. 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.