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State and output feedback stabilization of multiple chained systems with discontinuous control. (English) Zbl 0901.93058

Summary: The problem of state and output feedback stabilization of nonholonomic multiple chained systems is addressed and solved using a particular class of discontinuous control laws. The obtained control laws are relatively simple, compared with others existing in the current literature, and guarantee exponential convergence of the closed-loop system. A simulation example, showing the main features of the proposed controllers, is enclosed.

MSC:

93D15 Stabilization of systems by feedback
70F25 Nonholonomic systems related to the dynamics of a system of particles
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[1] Astolfi, A., Asymptotic stabilization of nonholonomic systems with discontinuous control, (Ph.D. Thesis (1995), Eidgenössische Technische Hochschule) · Zbl 0877.93107
[2] Astolfi, A., Exponential stabilization of nonholonomic systems via discontinuous control, (Proc. Symp. on Nonlinear Control System Design. Proc. Symp. on Nonlinear Control System Design, Lake Tahoe, CA (1995)), 741-746
[3] Astolfi, A., Discontinuous control of nonholonomic systems, Systems Control Lett., 27, 37-45 (1996) · Zbl 0877.93107
[4] Astolfi, A., Extending discontinuous stabilizers for nonholonomic systems from kinematic controllers to dynamic controllers, (MTNS. MTNS, St. Louis, Missouri (1996)), Invited Session: Control of Locomotion
[5] Bushnell, L. G.; Tilbury, D. M.; Sastry, S. S., Steering threeinput chained form nonholonomic systems using sinusoids: the Fire Truck example, Internat. J. Robotics Res., 14, 4, 366-381 (1995)
[6] Gurvits, L., Averaging approach to nonholonomic motion planning, (Proc. Internat. Conf. on Robotics and Automation. Proc. Internat. Conf. on Robotics and Automation, Nice, France (1992), IEEE: IEEE New York), 2541-2546
[7] Kolmanovsky, I.; McClamroch, N. H., Developments in nonholonomic control problems, IEEE Control Systems, 15, 20-36 (1995)
[8] Murray, R. M., Control of nonholonomic systems using chained form, (Dynamic and Control of Mechanical Systems, The Falling Cat and Related Problems (1991), The Field Institute for Research in Mathematical Sciences) · Zbl 0788.70018
[9] Sontag, E. D., Feedback stabilization of nonlinear systems, (Robust Control of Linear Systems and Nonlinear Control (1990), Birkhäuser: Birkhäuser Basel), 61-81 · Zbl 0735.93063
[10] Sørdalen, O. J., Feedback control of nonholonomic mobile robots, (Ph.D. Thesis (1993), The Norwegian Institute of Technology) · Zbl 0828.93055
[11] Teel, A. R.; Murray, R. M.; Walsh, G., Nonholonomic control systems: from steering to stabilization with sinusoids, Internat. J. Control, 62, 849-870 (1995) · Zbl 0837.93062
[12] Tilbury, D. M.; Chelouah, A., Steering a three-input nonholonomic system using multi-rate controls, (Proc. 2nd European Control Conference. Proc. 2nd European Control Conference, Groningen, The Netherlands (1993)), 1428-1431
[13] Tilbury, D. M.; Sastry, S. S., The multi-steering \(n\)-trailer system: a case study of Goursat normal forms and prolongations, (Proc. Symp. on Nonlinear Control System Design. Proc. Symp. on Nonlinear Control System Design, Lake Tahoe, CA (1995)), 555-560 · Zbl 0833.93042
[14] Tilbury, D. M.; Sørdalen, O. J.; Bushnell, L. G.; Sastry, S. S., A multi-steering trailer system: conversion into chained form using dynamic feedback, IEEE Trans. Robotics Automat., 11, 6, 807-818 (1995)
[15] Walsh, G. C.; Bushnell, L. G., Stabilization of multiple input chained form control systems, Systems Control Lett., 25, 227-234 (1995) · Zbl 0877.93100
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