Learning control of uncertain dynamical systems with specified iterative initial conditions

Abstract

This thesis reports the learning control techniques for different types of dynamical systems with specified iterative initial conditions. The developed learning control methods of the research have bestowed the control capabilities on dynamical systems. Two-Dimensional (2-D) system theory has provided a new dimension for investigation of the learning control systems. In this thesis, the existing 2-D system theory based Iterative Learning Control (ILC) techniques are further investigated for linear time-variant discrete systems with fixed iterative initial errors. By exploiting the convergent property of 2-D linear time-variant discrete systems with only one independent variable, a kind of ILC approach in the basis of the 2-D system theory is presented for linear time-variant discrete systems. In the case of zero iterative initial error, the existing 2-D system theory based ILC techniques for linear continuous systems are extended to linear continuous systems with time-delays, including time-delays in state and time-delays in input. The strategy is to reconstruct the derived ILC error equations of linear continuous time-delay systems in the compact form of the 2-D linear continuous-discrete Roessor’s model. Consequently, convergent ILC rules with necessary and sufficient conditions are derived according to the property of 2-D linear continuous-discrete systems. A new type of 2-D linear inequalities is developed to deal with the ILC problem of nonlinear dynamic systems. Convergence and robustness of the proposed ILC rule in the sense of the sup norm are derived for a class of nonlinear discrete-time systems with multiple input delays. It is shown that the ILC tracking errors are bounded in the presence of state, output disturbances and initial state uncertainty. As these disturbances and uncertainty satisfy the required conditions, the ILC tracking errors can even be driven to zero. Non-fixed iterative initial condition remains a significant and open issue for ILC research. Accordingly, a new ILC method with initial rectifying action for nonlinear continuous multivariable systems is presented in the thesis. Unlike general ILC techniques, the proposed ILC approach allows initial outputs of an ILC system at different iterations to fluctuate randomly around the initial value of the desired output. The output tracking error beyond the initial time interval can be driven to a residual set whose size depends on the estimation error of the input matrix. Repetitive Learning Control (RLC) is another type of learning control approach which is different from ILC in the iterative initial condition and the tracking trajectory. A Quasi-Sliding Mode (QSM) based RLC method is proposed for tackling Multiple-Input Multiple-Output (MIMO) nonlinear continuous-time systems with matching system uncertainties and exogenous disturbances. The proposed RLC method is able to perform rejection of periodic exogenous disturbances as well as tracking of periodic reference trajectories. It ensures a robust system stability when the controlled system is subject to non-periodic uncertainties and disturbances.

Date of Award	16 Jul 2007
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Kin Lim John HO (Supervisor)