Computational Algebra techniques for linear dynamical systems over rings: State Estimations Problems

Linear delay differential systems can be modeled as systems with coefficients in a suitable ring, so that several design problems can be solved using a geometric approach. To practically compute the solutions obtained for systems over a ring, Computational Algebra techniques must be used. The freely available software CoCoA is an efficient tool and easy to effectively implement the needed algorithms. The paper describes in details how the algorithms contained in the package “control.cpkg” can be used to practically solve State Estimations Problems for delay differential systems.

[1]  Massimo Caboara,et al.  Efficient algorithms for ideal operations , 1998 .

[2]  Christopher I. Byrnes,et al.  Algebraic and geometric methods in linear systems theory , 1980 .

[3]  J. Pearson.  Linear multivariable control, a geometric approach , 1977 .

[4]  Carlo Traverso,et al.  Efficient algorithms for ideal operations (extended abstract) , 1998, ISSAC '98.

[5]  Anna Maria Perdon,et al.  Systems over a Principal Ideal Domain. A Polynomial Model Approach , 1982 .

[6]  Anna Maria Perdon,et al.  Systems over rings: Geometric theory and applications , 2000 .

[7]  Massimo Caboara,et al.  Algorithms for Geometric Control of Systems Over Rings , 2003 .

[8]  G. Conte,et al.  Noninteracting control problems for delay-differential systems via systems over rings , 1997 .

[9]  Harald K. Wimmer,et al.  (C, A)-Invariance of Modules over Principal Ideal Domains , 2000, SIAM J. Control. Optim..

[10]  John W. Bunce,et al.  Linear Systems over Commutative Rings , 1986 .

[11]  Khalid Ali,et al.  Proof , 2006, BMJ : British Medical Journal.

[12]  Anna Maria Perdon,et al.  GEOMETRIC DESIGN OF OBSERVERS FOR LINEAR TIME-DELAY SYSTEMS , 2006 .

[13]  Anna Maria Perdon,et al.  The block decoupling problem for systems over a ring , 1998, IEEE Trans. Autom. Control..

[14]  R. E. Kalman,et al.  Mathematical system theory : the influence of R.E. Kalman : a festschrift in honor of professor R.E. Kalman on the occasion of his 60th birthday , 1991 .

[15]  Massimo Caboara,et al.  Efficient algorithms for geometric control of systems over rings , 2006 .

[16]  Paul M. Frank,et al.  Issues of Fault Diagnosis for Dynamic Systems , 2010, Springer London.

[17]  Eduardo Sontag.  Linear Systems over Commutative Rings. A Survey , 1976 .

[18]  P. Picard.  Sur l'observabilite et la commande des systemes lineaires a retards, modelises sur un anneau , 1996 .

[19]  Anna Maria Perdon,et al.  The Disturbance Decoupling Problem for Systems Over a Ring , 1995 .

[20]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[21]  Lcgjm Luc Habets,et al.  Algebraic and computational aspects of time-delay systems , 1994 .

[22]  A. Perdon,et al.  Unknown Input Observers and Residual Generators for Linear Time Delay Systems , 2006 .

[23]  Anna Maria Perdon,et al.  An efficient computation of the solution of the block decoupling problem with coefficient assignment over a ring , 1999, Kybernetika.