The canonical controllers and regular interconnection

We study the control problem from the point of view of the behavioral systems theory. Two controller constructions, called canonical controllers, are introduced. We prove that for linear time-invariant behaviors, the canonical controllers implement the desired behavior if and only if there exists a controller that implements it. We also investigate the regularity of the canonical controllers, and establish the fact that they are maximally irregular. This means a canonical controller is regular if and only if every other controller that implements the desired behavior is regular.

[1]  J. Willems,et al.  Synthesis of dissipative systems using quadratic differential forms: part II , 2002, IEEE Trans. Autom. Control..

[2]  J. C Willems.  Behaviors, Latent Variables, and Interconnections (Special Issue on Mathematical Approaches to System Engineering Expository Articles) , 1999 .

[3]  Jeffrey S. Rosenthal,et al.  Introduction to mathematical systems theory. a behavioral approach [Book Review] , 2002, IEEE Transactions on Automatic Control.

[4]  J. Willems.  Paradigms and puzzles in the theory of dynamical systems , 1991 .

[5]  Harry L. Trentelman,et al.  Stabilization, pole placement, and regular implementability , 2002, IEEE Trans. Autom. Control..

[6]  J. C. Willems.  Behaviors,Latent Variables,and lnterconnections (システム工学への数理的アプローチ特集) , 1999 .

[7]  Jan Willem Polderman.  Sequential continuous time adaptive control: a behavioral approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[8]  A.J. van der Schaft,et al.  Achievable behavior by composition , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  J. Willems.  On interconnections, control, and feedback , 1997, IEEE Trans. Autom. Control..

[10]  Arjan van der Schaft,et al.  Achievable behavior of general systems , 2003, Syst. Control. Lett..

[11]  Jan C. Willems,et al.  Introduction to mathematical systems theory: a behavioral approach, Texts in Applied Mathematics 26 , 1999 .

[12]  Madhu N. Belur,et al.  Control in a behavioral context , 2003 .

[13]  Arjan van der Schaft,et al.  Compatibility of behavior interconnections , 2003, 2003 European Control Conference (ECC).

[14]  Iven Mareels,et al.  A behavioral approach to adaptive control , 1999 .

[15]  Harry L. Trentelman,et al.  The canonical controller and its regularity , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  Johannes Schumacher,et al.  Proceedings of the European Control Conference , 1997 .

[17]  Paula Rocha.  Regular Implementability of nD Behaviors , 2002 .