Model reference adaptive control of 2-D discrete systems with unbounded variables along two dimensions

Adaptive control is an effective method of controlling unknown dynamical systems. While many research results on one-dimensional (1-D) adaptive control are available, little has been accomplished in the area of 2-D system theory. The main reason is due primarily to the difficult algebra of 2-D systems and the complexity of the underlying theory. In particular, when both independent variables in the 2-D space are unbounded, the problem is very involved. In this paper, we propose a model reference adaptive control scheme for 2-D discrete systems which are described by Roesser state space model and their both independent variables are unbounded. The input of the underlying 2-D system is assigned according to a closed-loop control law incorporating the system state and the reference model state as well as input. In this closed-loop control law, certain feedback gains are fixed, but others are adjustable. Those adjustable feedback gains are updated two-dimensionally subsequently, utilizing the gradient approach and based on the error between the actual system and its corresponding reference model. The stability of the presented 2-D model reference adaptive control (2-DMRAC) system is analyzed.