Artículos de revistas
Computation Of Contractive Polyhedra For Discrete-time Linear Systems With Saturation Controls
Registro en:
International Journal Of Control. , v. 75, n. 16, p. 1311 - 1320, 2002.
207179
10.1080/0020717021000023744
2-s2.0-0037126495
Autor
Milani B.E.A.
Institución
Resumen
This paper deals with computational aspects of characterization and construction of polyhedral γ-contractive sets with respect to discrete-time linear systems with saturating feedback control inputs. Using a piecewise-affine model of the saturating closed-loop system, new necessary and sufficient algebraic condition for convex closed polyhedra be γ-contractive is derived. Based on linear programming formulation of this condition, an effective procedure is proposed for construction of as large as possible γ-contractive convex polyhedra for estimation of the region of asymptotic stability of origin. The procedure starts with a γ-contractive polyhedron, possibly contained in the region of linear control, and progressively expands it non-homothetically over the region of non-linear saturated control. The proposed approach is less conservative and computationally much more efficient than previously published ones. 75 16 1311 1320 Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., (1990) Linear Programming and Network Flows, , (New York: Wiley) Bemporad, A., Torrisi, F.D., Morari, M., Optimization-based verification and stability characterization of piecewise affine and hybrid systems (2000) Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, 1790, pp. 45-58. , Proceedings of the 3rd International Workshop on Hybrid Systems: Computation and Control, Pittsburg, PA, In B. H. Krogh and N. Lynch (eds) Blanchini, F., Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions (1994) IEEE Transactions on Automatic Control, 39, pp. 428-433 Blanchini, F., Set invariance in control: A survey (1999) Automatica, 35, pp. 1747-1768 Chiang, H., Thorp, J.S., Stability regions of nonlinear dynamical systems: A constructive methodology (1989) IEEE Transactions on Automatic Control, 34, pp. 1229-1241 Dorea, C.E.T., Hennet, J.C., (A, B)-invariant polyhedral sets of linear discrete-time systems (1999) Journal of Optimization Theory and Applications, 103, pp. 521-542 Gilbert, E.G., Tan, K.T., Linear systems with state and control constraints: The theory and application of maximal output admissible sets (1991) IEEE Transactions on Automatic Control, 36, pp. 1008-1019 Gomes Da Silva J.M., Jr., Tarbouriech, S., Polyhedral regions of local stability for discrete-time linear systems with saturating controls (1999) IEEE Transactions on Automatic Control, 44, pp. 2081-2085 Hennet, J.C., Une extension du lemme de Farkas et son application au probleme de regulation linéaire sous contraintes (1989) Comptes-Rendus de l'Académie des Sciences, 308, pp. 415-419. , Série I Johansson, M., Rantzer, A., Computation of piecewise quadratic Lyapunov functions for hybrid systems (1998) IEEE Transactions on Automatic Control, 43, pp. 555-559 Kantner, M., Robust stability of piecewise linear discrete time systems (1997) Proceedings of the 1997 American Control Conference, Albuquerque, NM, pp. 1241-1245 Milani, B.E.A., Contractive polyhedra for discrete-time linear systems with saturating controls (1999) Proceedings of the 38th Conference on Decision and Control, Phoenix AZ, USA, pp. 2039-2044 Milham, C.B., Fast feasibility methods for linear programming (1976) OPSEARCH, 13, pp. 198-204 Slotine, J.E., Li, W., (1981) Applied Nonlinear Control, , (Englewood Cliffs, NJ: Prentice-Hall) Tarbouriech, S., Gomes Da Silva J.M., Jr., Admissible polyhedra for discrete-time linear systems with saturating controls (1997) Proceedings of the 1997 American Control Conference, Albuquerque, NM, pp. 3915-3919 Vassilaki, M., Hennet, J.C., Bitsoris, G., Feedback control of linear discrete-time systems under state and control constraints (1988) International Journal of Control, 47, pp. 1727-1735 Verriest, E.I., Pajunen, G.A., Quadratically saturated regulator for constrained linear systems (1996) IEEE Transactions on Automatic Control, 41, pp. 992-995 Wright, J.S., (1997) Primal-Dual Interior-Point Methods, , (Philadelphia, PA: SIAM)