Iterative Learning Control for Discrete-time MIMO Systems and its' Application in non-Linear Systems and Cooperative Learning Control
Jayawardhana, Rangana N
In this thesis we consider linear, time invariant, multi-input multi-output, causal, dynamical systems in discrete time. The control input and the response output of the system is observed over a nite time and the process is repeated iteratively with a modi ed control. The goal is to improve the control, during its subsequent application, so that the system output eventually tracks an a priori chosen desired signal. We propose a learning control scheme, based on the well known Luenberger Observer, wherein an update dynamics have to be rendered exponentially stable, using a suitable choice of a pole-assigning gain matrix. The proposed observer based learning scheme is modi ed by allowing the gain matrix to vary from one iteration to the next, and the main idea of implementation is Kalman Filter based parameter estimation. Next we introduce a Projection Algorithm based parameter estimation scheme which can be used as an Iterative Learning Control (ILC) update law. The Luenberger Observer, Kalman Filter and Projection Algorithm based iterative learning control updates, can be implemented with a suitable block structure, requiring one to have only partial knowledge of the system parameters. The three schemes are illustrated via simulation, and their convergence rates are compared. As an important application, the algorithm is applied to a 2-link manipulator. This research was motivated by the research carried out in the area of human upper limb stroke rehabilitation in which an Iterative Learning Controller is used to supplement the control signals provided by a defected motor cortex of a stroke patient. The controller is then reduced in strength incrementally allowing the new formation of neuronal links in the patients brain and the control is transfered from the controller to the brain. We try to mimic this behavior of co-operative learning with the use of two iterative learning controllers and prove that such transfer of control is possible between two iterative learning controllers.