Vai ai contenuti. | Spostati sulla navigazione | Spostati sulla ricerca | Vai al menu | Contatti | Accessibilità

| Crea un account

Santesso, Paolo (2008) Topics on switched systems. [Tesi di dottorato]

Full text disponibile come:

[img]
Anteprima
Documento PDF
880Kb

Abstract (inglese)

This thesis presents several results pertaining two rather distinct research topics within the broader area of the so-called "Switched Systems".
The first part of the work features a deep investigation of the structural properties, namely reachability and zero-controllability, of "Positive Switched Systems", both for the discrete-time and the continuous-time case.
All the notation relative to this contribution is defined in Chapter 1. Together with considerations on the motivational aspect, in Chapter 2, the familiar concepts of reachability and zero-controllability are properly defined within the context of positive switched systems. Then, several results are presented, first dealing with the discrete-time case, and subsequently addressing the continuous-time one. More specifically, in Chapter 3, the zero-controllability of a discrete-time positive switched system is proved to be equivalent to the mortality property of the set of system matrices; some sufficient conditions for this property to hold are then provided, together with an algorithm designed to find the correct switching sequence, if any, which is needed to drive any positive state
vector to the zero vector.
In Chapter 4 the reachability issue for discrete-time positive switched systems is addressed. First, the problem is restated into a geometric form, then the property of monomial reachability, known to be equivalent to the reachability for standard (meaning non-switched) positive systems, but only necessary in our setting, is fully explored and characterized.
All the chapters from 5 to 8 tackle with the continuous-time case.
In particular, in Chapter 5 the possibility for a continuous-time positive switched system to be zero-controllable is ruled out.
The reachability issue is first addressed in Chapter 6 where, similarly to the discrete-time case, we investigate the monomial as well as the pattern reachability property, which represent two necessary conditions for the general reachability of the system. Then, in Chapter 7, a useful sufficient condition for the reachability is provided; a geometric equivalent description of a reachable system is also introduced. Finally, further contributions to the problem of finding conditions ensuring the reachability of a continuous-time positive switched system are presented in Chapter 8, where the useful concept of asymptotic exponential cone of a Metzler matrix (an ordered set of Metzler matrices) is first defined and then fully characterized.
Results pertaining to a different stream of research 1 are included in the chapters 9 and 10.
More specifically, in Chapter 9 the case when a traditional Linear Time Invariant plant is controlled by a switching multicontroller whose transfer function may commute among different ones, each of them stabilizing the system, is considered. In particular, we focus our interest on the design of
the function, called Reset Map, ruling the update of the multicontroller state vector at every switching time. It turns out that a proper choice of it may deeply improve the controlled system transient behaviour.
The application of the same principles is then suggested in Chapter 10 in the context of non-switching reset controllers. The result presented within this chapter represents a substantial enhancement with respect to the traditional
approach which is known in the literature under the name of Reset Control Strategy.
The Appendix, besides a series of technical results which are preliminary to those presented in this thesis, features an extensive contribution to the study of the exponential of a Metzler matrix. This topic has been initially addressed as a mathematical mean for solving certain specific problems within
the setting of positive switched systems. Indeed, the analysis of reachability property for continuous-time positive switched systems requires a deep knowledge of the behaviour of these exponential matrices. For this reason, we decided to include the results in the Appendix. However, we believe that they deserve some interest by themselves, as their significance and extension
exceed by far what we needed for their initial application.


Statistiche Download - Aggiungi a RefWorks
Tipo di EPrint:Tesi di dottorato
Relatore:Valcher, Maria Elena
Correlatore:Hespanha, Joao Pedro
Dottorato (corsi e scuole):Ciclo 20 > Scuole per il 20simo ciclo > INGEGNERIA DELL'INFORMAZIONE > AUTOMATICA E RICERCA OPERATIVA
Data di deposito della tesi:Gennaio 2008
Anno di Pubblicazione:Gennaio 2008
Parole chiave (italiano / inglese):Switched systems, positive systems, reachability, controllability, reset control
Settori scientifico-disciplinari MIUR:Area 09 - Ingegneria industriale e dell'informazione > ING-INF/04 Automatica
Struttura di riferimento:Dipartimenti > Dipartimento di Ingegneria dell'Informazione
Codice ID:656
Depositato il:24 Ott 2008
Simple Metadata
Full Metadata
EndNote Format

Bibliografia

I riferimenti della bibliografia possono essere cercati con Cerca la citazione di AIRE, copiando il titolo dell'articolo (o del libro) e la rivista (se presente) nei campi appositi di "Cerca la Citazione di AIRE".
Le url contenute in alcuni riferimenti sono raggiungibili cliccando sul link alla fine della citazione (Vai!) e tramite Google (Ricerca con Google). Il risultato dipende dalla formattazione della citazione.

[1] & M. Saldago A. Feuer, G. Goodwin. Potential benefits of hybrid control for linear time invariant plants. In Proc. of the American Control Conference, pages 2790–2794, 1997. Cerca con Google

[2] Egerstedt. M. & Wardi Y. Azuma, S. Output-based optimal timing control of switched systems. In Hybrid Systems: Computation and Control, pages 64–78. Springer-Verlag, 2006. Cerca con Google

[3] Borrelli F. Morari M. Bemporad, A. Piecewise linear optimal controllers for hybrid systems. In Proceedings of the 2000 American Control Conference, pages 1190–1194, 2000. Cerca con Google

[4] A. Berman and R.J. Plemmons. Nonnegative matrices in the mathematical sciences. Academic Press, New York (NY), 1979. Cerca con Google

[5] V. D. Blondel and J. N. Tsitsiklis. When is a pair of matrices mortal? Information Processing Letters, 63, no. 5:283286, 1997. Cerca con Google

[6] O. Bournez and M. S. Branicky. On matrix mortality in low dimensions. In V. D. Blondel et al., editor, Open Problems in Mathematical Systems Theory, pages 67–70. Springer and Verlag, 1999. Cerca con Google

[7] & Barrat C. H. Boyd, S. P. Linear controller design: Limits of performance. New Jersey: Prentice Hall, 1991. Cerca con Google

[8] Vandenberghe L. Boyd S. Convex Optimization. Cambridge University Press, 2004. Cerca con Google

[9] R. Bru, S. Romero, and E. Sanch´ez. Canonical forms for positive discrete-time linear control systems. Linear Algebra & its Appl., 310:49– 71, 2000. Cerca con Google

[10] R.A. Brualdi and H.J. Ryser. Combinatorial matrix theory. Cambridge Univ.Press, Cambridge (GB), 1991. Cerca con Google

[11] E. Carson and C. Cobelli. Modelling Methodology for Physiology and Medicine. Academic Press, San Diego, 2001. Cerca con Google

[12] J. Clegg. A nonlinear integrator for servomechanisms. Transactions A.I.E.E., 77:41–42, 1958. Cerca con Google

[13] P.G. Coxson and H. Shapiro. Positive reachability and controllability of positive systems. Lin. Alg. Appl., 94:35–53, 1987. Cerca con Google

[14] Branicky M.S. Petterson S. & Lennartson B. De Carlo, R.A. Perspectives and results on the stabilizability of hybrid systems. Proc. of the IEEE, 88 (7):1069 –1082, 2000. Cerca con Google

[15] Paganini F. Dullerud, G. A course in robust control theory. Spriger, 1999. Cerca con Google

[16] M. Egerstedt and M. Babaali. On observability and reachability in a class of discrete-time switched linear systems. In Proc. of the 2005 American Control Conf., pages 1179–1180, Portland, Orgeon, 2005. Cerca con Google

[17] L. Farina and S. Rinaldi. Positive linear systems: theory and applications. Wiley- interscience, Series on Pure and Applied Mathematics, New York, 2000. Cerca con Google

[18] S. Friedland and H. Schneider. The growth of powers of a non-negative matrix. SIAM J. Algebraic Discrete Methods, 1:185–200, 1980. Cerca con Google

[19] G.F. Frobenius. Cerca con Google

[20] S.S. Ge, Z. Sun, and T.H. Lee. Reachability and controllability of switched linear discrete-time systems. IEEE Trans. Aut. Contr., 46, no. 9:1437–1441, 2001. Cerca con Google

[21] D. Hershkowitz, U.G. Rothblum, and H. Schneider. Characterizations and classifications of M-matrices using generalized nullspaces. Linear Algebra and Appl., 109:59–69, 1988. Cerca con Google

[22] D. Hershkowitz, U.G. Rothblum, and H. Schneider. The combinatorial structure of the generalized nullspace of a block triangular matrix. Linear Algebra and Appl., 116:9–26, 1989. Cerca con Google

[23] D. Hershkowitz and H. Schneider. On the generalized nullspace of Mmatrices and Z-matrices. Linear Algebra Appl., 106:5–23, 1988. Cerca con Google

[24] & Morse A. S. Hespanha, J. P. Towards the high performance control of uncertain process via supervision. In Proc. of the 30th annual conf. On information sciences and systems, pages 405–410, 1996. Cerca con Google

[25] J.P. Hespanha and A.S. Morse. Switching between stabilizing controllers. Automatica, 38:1905–1917, 2002. Cerca con Google

[26] R.A. Horn and C.R. Johnson. Matrix Analysis. Cambridge Univ. Press, Cambridge (GB), 1985. Cerca con Google

[27] I. Horowitz and P. Rosenbaum. Non-linear design for cost of feedback reduction in systems with large parameter uncertainty. International Journal of Control, 21:977–1001, 1975. Cerca con Google

[28] J.A. Jacquez. Compartmental analysis in biology and medicine. Elsevier, Amsterdam (NL), 1972. Cerca con Google

[29] H.D. Victory Jr. On nonnegative solutions to matrix equations. SIAM J. Algebraic Discrete Methods, 6:406–412, 1985. Cerca con Google

[30] L.T. Conner Jr. and D.P. Stanford. State deadbeat response and observability in multi-modal systems. SIAM J. Contr. Optimiz., 22(4):630– 644, 1984. Cerca con Google

[31] L.T. Conner Jr. and D.P. Stanford. The structure of the controllable set for multi-modal systems. Linear Algebra & its Appl., 95:171–180, 1987. Cerca con Google

[32] K. Krishnan and I. Horowitz. Synthesis of a non-linear feedback system with significant plant-ignorance for prescribed system tolerances. International Journal of Control, 19:689–706, 1974. Cerca con Google

[33] D. Liberzon. Switching in Systems and Control. Birkhauser, Boston, 2003. Cerca con Google

[34] D. Liberzon and A.S. Morse. Basic problems in stability and design of switched systems. IEEE Contr. Syst. Magazine, 19:59–70, 1999. Cerca con Google

[35] & Antsaklis P. J. Lin, H. Stability and stabilizability of switched linear systems: a short survey of recent results. In Proc. of the 2005 IEEE Int. Symp. on intelligent Control, pages 24–29, Cyprus, 2005. Cerca con Google

[36] & G. Goodwin M. Seron, J. Braslavsky. Fundamental Limitations in Filtering and Control. London: Springer-Verlag, 1997. Cerca con Google

[37] H. Minc. Nonnegative Matrices. J.Wiley & Sons, New York, 1988. Cerca con Google

[38] & Morse A.S. Pait, F.M. A cycling switching strategy for parameteradaptive control. IEEE Transaction on Automatic Control, 39:1172– 1183, 1994. Cerca con Google

[39] B. Piccoli. Hybrid systems and optimal control. In Proc. of the 37th IEEE Conf. on Decision and Control, pages 13–18, 1998. Cerca con Google

[40] C. Hollot Q. Chen and Y. Chait. Bibo stability of a class of reset control system. In Proc. 2000 Conf. Information Sciences and Systems, pages TP8–39, 2000. Cerca con Google

[41] C. Hollot Q. Chen and Y. Chait. Stability and asymptotic performance analysis of a class of reset control systems. In Proc. 39th Conf. Decis. Contr., pages 251–256, 2000. Cerca con Google

[42] D. Richman and H. Schneider. On the singular graph and the Weyr characteristic of an M-matrix. Aequationes Math., 17:208–234, 1978. Cerca con Google

[43] U.G. Rothblum. Algebraic eigenspaces of non-negative matrices. Linear Algebra Appl., 12:281–292, 1975. Cerca con Google

[44] A. Salomaa and M. Soittola. Automata theoretic aspects of formal power series. Springer-Verlag, 1978. Cerca con Google

[45] P. Santesso and M.E. Valcher. On the zero pattern properties and asymptotic behavior of continuous-time positive system trajectories. Linear Algebra and its Applications, 425:283–302, 2007. Cerca con Google

[46] H. Schneider. The elementary divisors associated with 0 of a singular M-matrix. Proc. Edinburgh Math. Sot. Ser. 2, 10:108–122, 1956. Cerca con Google

[47] H. Schneider. The influence of the marked reduced graph of a nonnegative matrix on the jordan form and on related properties: a survey. Linear Algebra and Appl., 84:161–189, 1986. Cerca con Google

[48] N.K. Son and D. Hinrichsen. Robust stability of positive continuous time systems. Numer. Funct. Anal. and Optimiz., 17 (5 & 6):649–659, 1996. Cerca con Google

[49] D.P. Stanford and L.T. Conner Jr. Controllability and stabilizability in multi-pair systems. SIAM J. Contr. Optimiz., 18(5):488–497, 1980. Cerca con Google

[50] G. A. Stewart, G. E. & Dumont. Finite horizon based switching between stabilizing controllers. In Proc. American Control Conference, pages 1550–1556, 2006. Cerca con Google

[51] Z. Sun and D. Zheng. On reachability and stabilization of switched linear systems. IEEE Trans. Aut. Contr., 46, no. 2:291–295, 2001. Cerca con Google

[52] Ge S.S. Sun Z. Switched Linear Systems: control and design. Springer, 2005. Cerca con Google

[53] M.E. Valcher. Controllability and reachability criteria for discrete time positive systems. Int. J. of Control, 65:511–536, 1996. Cerca con Google

[54] Y. Wang, G. Xie, and L. Wang. Reachability of switched discrete-time systems under constrained switching. In Proc. of the 42nd IEEE Conf. on Decision and Control, pages 5765–5770, Maui, Hawaii, 2003. Cerca con Google

[55] M.A. Wicks, P. Peleties, and R.A. De Carlo. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems. European J. of Control, 4, no. 2:140–147, 1998. Cerca con Google

[56] G. Xie and L. Wang. Reachability realization and stabilizability of switched linear discrete-time systems. J. Math. Anal. Appl., 280:209– 220, 2003. Cerca con Google

[57] P.J. Xu, X. & Antsaklis. Optimal control of switched systems via nonlinear optimization based on direct differentiation of value functions. Int. Journal of Control, 75:1406–1426, 2002. Cerca con Google

[58] X. Xu and P.J. Antsaklis. Optimal control of switched systems based on parametrization of the switching instants. IEEE Transactions on Automatic Control, 49, no.1:2–16, 2004. Cerca con Google

Download statistics

Solo per lo Staff dell Archivio: Modifica questo record