MASSACHUSETTS INST OF TECH CAMBRIDGE ELECTRONIC SYSTEMS LAB
The control of linear systems with incomplete information is considered where the unknown disturbances andor random parameters are assumed to satisfy some statistical laws. The observer theory for linear systems is developed which generalizes the concepts due to Kalman and Luenberger pertaining to the design of linear systems which estimate the state of a linear plant on the basis of both noise-free and noisy measurements of the output variables. The separation theorem for linear system is then extended for such observers- estimators. The problem of controlling a linear system with unknown gain is then considered. An open-loop-feedback-optimal control algorithm is developed which seems to be computationally feasible. Existence of such suboptimal control scheme is proved under the assumption that the uncertainties in the unknown gail will not grow in time. Convergence of such suboptimal control system to the truly optimal control system is considered. A computer program is developed to study the control of a variety of third order systems with known poles but unknown zeroes. The experimental results serve to provide more insights into the structure and behavior of the open-loop-feedback-optimal control systems.