Optimal and Suboptimal Properties of a Two-Time-Scale Control System Using Adaptive Modeling

摘要

Adaptive modeling of plants with unobservable states and unknown dynamics is employed to enable simultaneous estimation of the plant's dynamics and state. A variety of control methods may then be applied; among these is a class of control systems employing two time scales. This class of control systems is considered in the present research effort and is the subject of this report. Given the state and dynamics of the plant, it is possible to estimate the future trajectory of the plant due to present state and present control. The future trajectory of the system error may then be estimated and a control increment may be synthesized to extremize performance indices including these future trajectory data. The report presents the properties of this class of control systems, demonstrates the validity of gradient laws for synthesizing the optimal control and shows the consequences on system dynamics of optimal and suboptimal instrumentation of the control law which this principle yields. The method is generalized to multi-input milti-output plants of unknown dynamics, to performance indices of more general form, and to synthesis of optimal and suboptimal control sequences. The analytical results are supported by analog simulation experiments on a variety of stable and unstable plants. (Author)