On adaptive control of interconnected systems with unknown interconnections

First, the authors consider a set of linear minimum-phase systems with y_i(t) as output, u_i(t) as control of the i-th system (i=1, ..., N), and no system interconnection. The control goal for the i-th system is defined by the relations: y_i(t)→y¯_i(t), as t→∞, |u|⩽ constant, where y¯_i(t) are given bounded reference processes. Coefficients of these systems are assumed to be unknown. The authors discuss methods of adaptive control for solution of this problem. They then extend the theory to systems of two interconnected two-mass objects, specifically inverted pendulums on controlled carts. Finally, they consider the case when movements of the carts occur on the same line