Application of a second order VSC to nonlinear systems in multi-input parametric-pure-feedback form
Kybernetika, Tome 36 (2000) no. 1, pp. 63-75 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, based on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing robustness.
The use of a multi-input control design procedure for uncertain nonlinear systems expressible in multi-input parametric-pure feedback form to determine the control law for a class of mechanical systems is described in this paper. The proposed procedure, based on the well-known backstepping design technique, relies on the possibility of extending to multi-input uncertain systems a second order sliding mode control approach recently developed, thus reducing the computational load, as well as increasing robustness.
Classification : 34H05, 70Q05, 93B12, 93B51, 93C10, 93C35
Keywords: multi-input control design; nonlinear system
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Ferrara, Antonella; Giacomini, Luisa. Application of a second order VSC to nonlinear systems in multi-input parametric-pure-feedback form. Kybernetika, Tome 36 (2000) no. 1, pp. 63-75. http://geodesic.mathdoc.fr/item/KYB_2000_36_1_a6/

[1] Bartolini G., Ferrara A., Giacomini L., Usai E.: A combined backstepping/second order sliding mode approach to control a class of nonlinear systems. In: Proc. IEEE International Workshop on Variable Structure Systems. Tokyo 1996

[2] Bartolini G., Ferrara A., Usai E.: Applications of a suboptimal discontinuous control algorithm for uncertain second order systems. Internat. J. Robust Nonlin. Control 7 (1997), 299–320 | DOI | MR

[3] Bartolini G., Ferrara A., Usai E.: Chattering avoidance by second–order sliding modes control. IEEE Trans. Automat. Control 34 (1998), 2, 241–246 | DOI | MR

[4] Bartolini G., Ferrara A., Usai E., Utkin V. I.: Second order chattering–free sliding mode control for some classes of multi–input uncertain nonlinear systems. In: Proc. of the 6th IEEE Mediterranean Conference on Control and Systems. Alghero 1998

[5] Diong B. M., Medanic J. V.: Simplex–type variable structure controllers for systems with non–matching disturbances and uncertainties. Internat. J. Control 68 (1997), 625–656 | DOI | MR | Zbl

[6] Kanellakopoulos I., Kokotovic P. V., Morse A. S.: Systematic design of adaptive controllers for feedback linearizable systems. IEEE Trans. Automat. Control 36 (1991), 1241–1253 | DOI | MR | Zbl

[7] Kirk D. E.: Optimal control theory. Prentice Hall, Englewood Cliffs, N.J. 1970

[8] Kokotović P. V., Krstić M., Kanellakopoulos I.: Nonlinear and Adaptive Control Design. Wiley, New York 1995

[9] Levant A.: Sliding order and sliding accuracy in sliding mode control. Internat. J. Control 58 (1993), 1247–1263 | DOI | MR | Zbl

[10] Levant A.: Higher order sliding: collection of design tools. In: European Control Conference, Bruxelles 1997

[11] Nam K., Arapostathis A.: A model reference adaptive control scheme for pure-feedback non–linear systems. IEEE Trans. Automat. Control 33 (1988), 803–811 | DOI | MR

[12] Seto D., Annaswamy A. M., Baillieul J.: Adaptive control of a class of nonlinear systems with a triangular structure. IEEE Trans. Automat. Control 39 (1994), 1411–1428 | DOI | MR

[13] Spong M. W., Vidyasagar M.: Robot Dynamics and Control. Wiley, New York 1989

[14] Su R., Hunt L. R.: A canonical expansion for nonlinear systems. IEEE Trans. Automat. Control 31 (1986), 670–673 | DOI | MR | Zbl

[15] Utkin V. I.: Sliding Modes in Control and Optimization. Springer–Verlag, Berlin 1992 | MR | Zbl