Trajectory control and interconnection of 1D and nD systems (Q2719155)

The authors show that control can be looked upon from two points of view: as regular interconnection of systems and as the ability to drive trajectories. Thus, for one-dimensional linear time-invariant systems, the ability to obtain a given subsystem by regular interconnection is equivalent to the ability to derive any trajectory in that subsystem. An exposition of the theory of regular interconnection for one-dimensional and \(n\)-dimensional systems is made, together with the recently discovered equivalence to feedback interconnection. Moreover, they give an algorithm for testing achievability for regular interconnection and constructing a controller.NEWLINENEWLINENEWLINENext, the authors define the notion of set-controllability, which describes the ability to concatenate any trajectory of a given behavior with some trajectory of a prescribed subset. They characterize set-controllability and show the relationship between it and regular interconnection. The regular interconnection of extended behaviors obtained by introducing latent or auxiliary variables is presented. This is named ``regular extended interconnection''. A main result is obtained, namely, that achievability of a given subbehavior by regular extended interconnection is equivalent to set-controllability to that subbehavior in both the one-dimensional and \(n\)-dimensional cases.