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Iterative design of time-varying stabilizers for multi-input systems in chained form. (English) Zbl 0866.93084

Summary: This paper proposes an alternative solution to the global stabilization of nonholonomic multi-input chained form systems investigated in recent contributions. A systematic design, which is reminiscent of integrator backstepping methods, is presented to generate a new class of smooth time-varying dynamic stabilizers. The proof of stability is straightforward and the algorithm finds its application in adaptive control of nonholonomic systems and tracking control of a mobile robot.

MSC:

93D15 Stabilization of systems by feedback
70F25 Nonholonomic systems related to the dynamics of a system of particles
93C85 Automated systems (robots, etc.) in control theory
93C99 Model systems in control theory
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[1] Brockett, R. W., Asymptotic stability and feedback stabilization, (Brockett, R. W.; Millman, R. S.; Sussmann, M. J., Differential Geometric Control Theory (1983)), 181-191 · Zbl 0528.93051
[2] Bushnell, L.; Tilbury, D.; Sastry, S., Steering three-input chained form nonholonomic systems using sinusoids: The fire truck example, (Proc. 2nd European Control Conf. (1993)), 1432-1437
[3] Byrnes, C. I.; Isidori, A., New results and examples in nonlinear feedback stabilization, Systems Control Lett., 12, 437-442 (1989) · Zbl 0684.93059
[4] Coron, J.-M., Global asymptotic stabilization for controllable systems without drift, Math. Control. Signals Systems, 5, 295-312 (1992) · Zbl 0760.93067
[5] Jiang, Z. P.; Pomet, J.-B., Combining backstepping and time-varying techniques for a new set of adaptive controllers, (Proc. 33rd IEEE Conf. Decision Control. Proc. 33rd IEEE Conf. Decision Control, Florida (1994)), 2207-2212
[6] Jiang, Z. P.; Pomet, J.-B., Backstepping-based adaptive controllers for uncertain nonholonomic systems, (Proc. 34th IEEE Conf. Decision Control. Proc. 34th IEEE Conf. Decision Control, New Orleans (1995)), 1573-1578
[7] Jiang, Z. P.; Nijmeijer, H., Tracking control of mobile robots: a case study in backstepping, (Memorandum 1321 (April 1996), Department of Applied Mathematics, University of Twente) · Zbl 0882.93057
[8] Kokotović, P. V., The joy of feedback: nonlinear and adaptive, Control Systems Magazine, 12, 7-17 (1992)
[9] Kolmanovsky, I.; McClamroch, N. H., Applications of integrator backstepping to nonholonomic control problems, Prep. IFAC NOLCOS’95, 753-758 (1995), California
[10] LaSalle, J.-P., Stability theory for ordinary differential equations, J. Differential Equations, 4, 57-65 (1968) · Zbl 0159.12002
[11] M’Closkey, R.; Murray, R., Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback, (Proc. 33rd IEEE Conf. Decision Control. Proc. 33rd IEEE Conf. Decision Control, Florida (1994)), 1317-1322
[12] Murray, R. M.; Sastry, S., Nonholonomic motion planning: steering using sinusoids, IEEE Trans. Automat. Control, 38, 700-716 (1993) · Zbl 0800.93840
[13] 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
[14] Samson, C., Control of chained systems. Application to path following and time-varying point-stabilization of mobile robots, IEEE Trans. Automat. Control, 40, 64-77 (1995) · Zbl 0925.93631
[15] Sørdalen, O. J.; Egeland, O., Exponential stabilization of nonholonomic chained systems, IEEE Trans. Automat. Control, 40, 35-49 (1995) · Zbl 0828.93055
[16] Teel, A.; Murray, R.; Walsh, G., Nonholonomic control systems: from steering to stabilization with sinusoids, Internat. J. Control, 62, 849-870 (1995) · Zbl 0837.93062
[17] Tsinias, J., Sufficient Lyapunov-like conditions for stabilization, Math. Control Signals Systems, 2, 343-357 (1989) · Zbl 0688.93048
[18] Walsh, G. C.; Bushnell, L. G., Stabilization of multi input chained form control systems, Systems Control Lett., 25, 227-234 (1995) · Zbl 0877.93100
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