Achievable behavior of general systems

A basic question in systems and control theory concerns the characterization of the set of all achievable closed-loop systems for a given plant system and a controller system to be designed. This problem is addressed in a general behavioral context. Sufficient, and often necessary, conditions for a behavior to be achievable are given, and for any achievable behavior a canonical controller is defined. The results generalize previously obtained results obtained for finite-dimensional linear systems. The application to nonlinear differential systems is outlined.

[1]  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).

[2]  J. Polderman.  Proper Elimination of Latent Variables , 1993 .

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

[4]  Arjan van der Schaft,et al.  Perspectives in control theory , 1990 .

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

[6]  A. Schaft.  Transformations of nonlinear systems under external equivalence , 1989 .

[7]  Anton A. Stoorvogel,et al.  A behavioral approach to the H ∞ optimal control problem , 1997 .

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

[9]  H. Narayanan.  Some applications of an Implicit Duality Theorem to connections of structures of special types including Dirac and reciprocal structures , 2002, Syst. Control. Lett..

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

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

[12]  Jan Willem Polderman,et al.  Proper elimination of latent variables , 1993 .

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

[14]  A. Schaft.  Transformations and representations of nonlinear systems , 1990 .

[15]  Harry L. Trentelman,et al.  The mathematics of systems and control: from intelligent control to behavioral systems , 1999 .