| This work considers the performance optimization of systems involving discrete entities competing for the services provided by a limited number of resources. Such systems are found in transportation, computer and communication networks, and manufacturing, and are typically modeled as discrete event dynamic systems (DEDS), or, more generally, as hybrid dynamical systems (HDS).; For DEDS two new performance optimization strategies are proposed. For those whose performance is a function of a controllable parameter vector, an on-line adaptive control scheme is developed. Ile scheme, inspired by classical gain scheduling techniques for nonlinear systems, centers around a lookup table containing the best parameter values to use for different operating conditions. By estimating the instantaneous operating condition and performing a table lookup, the controller is able to adapt to changing operating conditions. The scheme can be used open-loop with a fixed lookup table, or the table can be constructed dynamically for a closed-loop controller. Another DEDS optimization strategy involves the use of calculus of variations (CV) techniques. Except for one other work, CV techniques have not previously been applied to DEDS. Difficulties associated with the nonsmooth ‘ax’ and ‘min’functions which commonly appear in event-driven dynamics, integer state variables, and uncertainty are addressed. While the first two difficulties can be overcome at least for some problems, CV techniques cannot optimally solve problems involving uncertainty. Nevertheless, the approach supplies insights useful for developing controllers that are robust with respect to the uncertainty.; For HDS a new framework combining event-driven dynamics with time-driven dynamics is proposed. The framework which uses “max-plus” recursive equations to describe the event-driven dynamics and differential equations to describe the time-driven dynamics appears useful for modeling many manufacturing systems such as those in steelmaking, food processing, and pharmaceuticals. Optimal control problems trading off demands on the event-driven states against demands on the time-driven states are formulated and simple examples are analyzed using variational techniques. Since the problems generally cannot be solved in closed-form, structural properties of optimal solutions are derived and used to develop quick and efficient numerical algorithms. |
