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Output feedback exponential stabilization of uncertain chained systems. (English) Zbl 1119.93057
Summary: This paper deals with chained form systems with strongly nonlinear disturbances and drift terms. The objective is to design robust nonlinear output feedback laws such that the closed-loop systems are globally exponentially stable. The systematic strategy combines the input-state-scaling technique with the so-called backstepping procedure. A dynamic output feedback controller for general case of uncertain chained system is developed with a filter of observer gain. Furthermore, two special cases are considered which do not use the observer gain filter. In particular, a switching control strategy is employed to get around the smooth stabilization issue (difficulty) associated with nonholonomic systems when the initial state of system is known.

93D15Stabilization of systems by feedback
93C15Control systems governed by ODE
Full Text: DOI
[1] Brockett, W.: Asymptotic stability and feedback stabilization. Differential geometric control theory, 181-191 (1983)
[2] Kolmanovsky, I.; Mcclamroch, N. H.: Developments in nonholonomic control problems. IEEE control systems magazine 15, No. 6, 20-36 (1995)
[3] Astolfi, A.: Discontinuous control of nonholonomic systems. Systems control lett. 27, 37-45 (1996) · Zbl 0877.93107
[4] Astolfi, A.; Schaufelberger, W.: State and output feedback stabilization of multiple chained systems with discontinuous control. Proceedings of 35th IEEE conference on decision and control, 1443-1447 (December 1996) · Zbl 0901.93058
[5] Bloch, A.; Reyhanoglu, M.; Mcclamroch, N. H.: Control and stabilization of nonholonomic dynamic systems. IEEE trans. Automat. control 37, 1746-1757 (1992) · Zbl 0778.93084
[6] De Wit, C. Canudas; Sordalen, O. J.: Exponential stabilization of mobile robots with nonholonomic constraints. IEEE trans. Automat. control 37, 1791-1797 (1992) · Zbl 0778.93077
[7] Reyhanoglu, M.; Cho, S.; Mcclamroch, N. H.; Kolmanovsky, I.: Discontinuous feedback control of a planar rigid body with an underactuated degree of freedom. Proceedings of 37th IEEE conference on decision and control, 433-438 (December 1998)
[8] Rui, C.; Reyhanoglu, M.; Kolmanovsky, I.; Cho, S.; Mcclamroch, N. H.: Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system. Proceedings of the 36th IEEE conference on decision and control, 3998-4003 (December 1997)
[9] Fliess, M.; Levine, J.; Martin, P.; Rouchon, P.: Flatness and defect of nonlinear systems: introductory theory and examples. Internat. J. Control 61, 1327-1361 (1995) · Zbl 0838.93022
[10] Jiang, Z. P.: Iterative design of time-varying stabilizers for multi-input systems in chained form. Systems control lett. 28, 255-262 (1996) · Zbl 0866.93084
[11] Kolmanovsky, I.; Mcclamroch, N. H.: Hybrid feedback laws for a class of cascaded nonlinear control systems. IEEE trans. Automat. control 41, 1271-1282 (1996) · Zbl 0862.93048
[12] M’closkey, R.; Murray, R.: Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE trans. Automat. control 42, No. 5, 614-628 (1997) · Zbl 0882.93066
[13] Murray, R. M.; Sastry, S.: Nonholonomic motion planning: steering using sinusoids. IEEE trans. Automat. control 38, No. 5, 700-716 (1993) · Zbl 0800.93840
[14] Pomet, J. B.: Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift. Systems control lett. 18, 147-158 (1992) · Zbl 0744.93084
[15] Sordalen, O. J.; Egeland, O.: Exponential stabilization of nonholonomic chained systems. IEEE trans. Automat. control 40, 35-49 (1995) · Zbl 0828.93055
[16] Tilbury, D.; Murray, R. M.; Sastry, S.: Trajectory generation for the n-trailer problem using Goursat normal form. IEEE trans. Automat. control 40, 802-819 (1995) · Zbl 0826.93046
[17] Jiang, Z. P.: Robust exponential regulation of nonholonomic systems with uncertainties. Automatica 36, 189-209 (2000) · Zbl 0952.93057
[18] Do, K. D.; Pan, J.: Adaptive global stabilization of nonholonomic systems with strong nonlinear drifts. Systems control lett. 46, 195-205 (2002) · Zbl 0994.93055
[19] Marchand, N.; Alamir, M.: Discontinuous exponential stabilization of chained form systems. Automatica 39, 343-348 (2003) · Zbl 1011.93534
[20] Huo, W.; Ge, S. S.: Exponential stabilization of non-holonomic systems: an ENI approach. Internat. J. Control 74, No. 15, 1492-1500 (2001) · Zbl 1017.93021
[21] Ge, S. S.; Sun, Z.; Lee, T. H.; Spong, M. W.: Feedback linearization and stabilization of second-order non-holonomic chained systems. Internat. J. Control 74, No. 14, 1383-1392 (2001) · Zbl 1026.93047
[22] Luo, J.; Tsiotras, P.: Exponentially convergent control laws for nonholonomic systems in power form. Systems control lett. 35, 87-95 (1998) · Zbl 0909.93029
[23] Xi, Z.; Feng, G.; Jiang, Z.; Cheng, D.: A switching algorithm for global exponential stabilization of uncertain chained systems. IEEE trans. Automat. control 48, No. 10, 1793-1798 (2003)
[24] Astolfi, A.; Schaufelberger, W.: State and output feedback stabilization of multiple chained systems with discontinuous control. Systems control lett. 32, 49-56 (1997) · Zbl 0901.93058
[25] Ge, S. S.; Wang, Z.; Lee, T. H.: Adaptive stabilization of uncertain nonholonomic systems by state and output feedback. Automatica 39, 1451-1460 (2003) · Zbl 1038.93079
[26] Krstić, M.; Kanellakopoulos, I.; Kokotović, P. V.: Nonlinear and adaptive control design. (1995) · Zbl 0763.93043
[27] Sontag, E. D.: Comments on integral variants of ISS. Systems control lett. 34, 93-100 (1998) · Zbl 0902.93062
[28] Praly, L.; Kanellakopoulos, I.: Output feedback asymptotic stabilization for triangular systems linear in the unmeasured state components. Proceedings of the 39th IEEE conference on decision and control, 2466-2471 (December 2000)
[29] Ikeda, M.; Maeda, H.; Kodama, S.: Stabilization of linear systems. SIAM J. Control 10, No. 4, 716-729 (1972) · Zbl 0244.93049
[30] Besancon, G.; De Leon-Morales, J.; Huerta-Guevara, O.: On adaptive observers for state affine systems and application to synchronous machines. Proceedings of the 42nd IEEE conference on decision and control, 2192-2197 (December 2003)
[31] P. Morin, J.B. Pomet, C. Samson, Developments in time-varying feedback stabilization of nonlinear systems, Preprints of Nonlinear control systems design symposium (NOLCOS’98), vol. 1/2, 1998, pp. 587 -- 594.