Simultaneous identification and control of discrete time single input single output systems - Saratchandran, P (1978)
﻿ This thesis is concerned with suboptimal adaptive control of discrete linear stochastic processes whose parameters are unknown. The suboptimal adaptive controllers considered are (i) Open Loop Feedback Optimal (OLFO) controller, (ii) self-tuning controller, and (iii) optimal k step ahead controller. Two more controllers, certainty about parameter (CAP) controller and no learning (NOL) controller, that provide bounds on the performance of these adaptive controllers are also considered. Performance of these controllers have been evaluated for a first order process through monte-carlo simulations. Simulation of OLFO controller together with the bounding controllers for the first order process when there is only one unknown parameter revealed that OLFO controller is unsuitable to control unstable processes and would be an unwise choice even for controlling stable processes. Selftuning and OK controllers have been simulated for the first order process with all the parameters unknown. Three cases for the unknown parameters have been considered. They are: (i) constant unknown parameters (ii) slowly time-varying unknown parameters and (iii) rapidly time-varying unknown parameters. Simulation results showed that in certain regions of the unknown parameter space the cost produced by self tuning controller and OK controller are very similar, in certain regions the OK controller produces lesser cost than the self-tuning controller and in certain other regions both controllers perform very badly. But self-tuning controller always took only half as much computing time as OK controller. A necessary condition for convergence of OK controller to a linear constant parameter controller having the same functional form as CAP controller is found out using the ideas of uniform complete observability. For a first order process under OK controller the only occasion the condition would be violated is when there is 'turn-off'. Finally, it is shown that using the combined state/parameter estimator in the place of extended Kalman filter the computational requirement of OK controller can be reduced. For the first order process, OK controller with the combined estimator took only sixty percent as much computing time as the OK controller with extended Kalman filter without any appreciable deterioration in the performance.