Discrete-event dynamic systems: Gradient-based optimal control versus passive adaptive control

Mathematical analysis of discrete event dynamic systems is fraught with difficulty because of the complexity inherent in such systems. Inspite of its analytical intractability it is desired to create a systematic method of controlling a discrete event dynamic system. Such control can have any one of several objectives. For example, it may be desired to optimize system performance or to avoid certain undesirable system states.;Well-established gradient-based optimization methods for analytically tractable systems already exist. It is therefore desirable to apply such methods to discrete event systems; to accomplish this, however, it is necessary to have available some method of deriving gradient estimators for discrete event dynamic systems.;Brute-force gradient estimation methods for discrete event dynamic systems exist; unfortunately, such methods are inefficient because they require extensive computer resources. Perturbation analysis is intended as a method of deriving gradient estimators, that can be efficiently evaluated, for discrete event dynamic systems.;This thesis presents a critical examination of perturbation analysis. It is shown in this thesis that perturbation analysis is based on flawed reasoning in the sense that the theory underlying perturbation analysis is valid only for trivial systems. It is also shown in this thesis that to even think about performing perturbation analysis one must have more information than is required to run a simulation and thus more information than is normally available in a problem of interest.;An alternative method of control of discrete event dynamic systems is proposed. With this new method the only information that is required is that needed to run the simulation and less, i.e., it is unnecessary to know any distribution functions. This new method is called passive adaptive control because the parameters are simply updated to their estimates provided certain conditions are satisfied.;Simulation results show that a crude version of passive adaptive control works for a few simple systems. Some shortcomings of the crude version are discussed in this thesis along with proposals for removing these deficiencies.