1 An attainable set - based approach to schedule robustness analysis in continuous time

Schedules are executed under dynamic and uncertain environments. Even though considerable advancements have been achieved in the analysis of schedule robustness, the studies on dynamic system theory are quite rare in this domain. In this paper, we develop a new method for robustness analysis of those schedules that are formulated in continuous time in the state-space domain. The developed method is based on attainable sets. The technical development and approximation of attainable sets are presented. A robustness index is developed on the basis of the minimax regret approach, and it can be used as an additional indicator for decision-makers regarding the trade-off “performance vs. robustness”. With the presented results, it becomes possible to obtain attainable sets for interval data with no a priori information about perturbation impacts, i.e., for non-stationary perturbations. We conclude that attainable sets may be favourable to obtain estimations of schedule performance attainability and degradation. Attainable sets allow to consider perturbations and schedule performance as time functions. Perturbation functions may be set up for different uncertainty scenarios, including interval perturbations with fully unpredictable disruptions. Besides, the application of attainable sets can help in implementing a direct interconnection with the adaptation models which are widely described in control terms in order to design rescheduling algorithms in the state-space form with desired closed-loop properties.