Abstract
For the nonholonomic system of in the form of an arbitrary chain, consideration was given to the problem of tracking. Proposed were two classes of two-dimensional controls in the form of linear feedback with provision for delay that maintain convergence of all trajectories of the controlled system to the desired trajectory.
Similar content being viewed by others
References
Brockett, R.W., Asymptotic Stability and Feedback Stabilization, in Differential Geometric Control Theory, Brockett, R.W., Millman, R.S. and Sussmann, H.J., Eds., Boston: Birkhäuser, 1983.
Coron, J.-M., Praly, L., and Teel, A., Feedback Stabilization of Nonlinear Systems: Sufficient Conditions and Lyapunov and Input-Output Techniques, in Trends in Control: A European Perspective, Isidori, A., Ed., London: Springer, 1995.
Ryan, E.P., On Brockett’s Condition for Smooth Stability and Its Necessity in a Context of Nonsmooth Feedback, SIAM J. Control Optim., 1994, vol. 32, no. 6, pp. 1597–1604.
Murray, R.M. and Sastry, S.S., Nonholonomic Motion Planning: Steering Using Sinusoids, IEEE Trans. Automat. Control, 1993, vol. 38, no. 5, pp. 700–716.
Martynenko, Yu.G., Control of Motion of the Mobile Wheeled Robots, Fundam. Prikl. Mat., 2005, vol. 11, no. 8, pp. 29–80.
Kolmanovsky, I.V. and McClamroch, N.H., Developments in Nonholonomic Control Problems, IEEE Control Syst. Mag., 1995, vol. 15, no. 6, pp. 20–36.
Hespanha, J.P. and Morse, A.S., Stabilization of Nonholonomic Integrators via Logic-based Switching, Automatica, 1999, vol. 35, no. 3, pp. 385–393.
Qu, Z., Wang, J., Plaisted, C.E., and Hull, R.A., Global-stabilizing Near-optimal Control Design for Non-holonomic Chained Systems, IEEE Trans. Optim. Control, 2006, vol. 51, no. 9, pp. 1440–1456.
Sedova, N.O., Global Asymptotical Stability and Stabilization in the Nonlinear Cascaded Delay System, Izv. Vyssh. Uchebn. Zaved., Mat., 2008, no. 11, pp. 68–79.
Lefeber, E., Robertsson, A., and Nijmeijer, H., Linear Controllers for Exponential Tracking of Systems in Chained Form, Int. J. Robust Nonlinear Control, 2000, vol. 10, no. 4, pp. 243–264.
Malkin, I.G., Teoriya ustoichivosti dvizheniya (Motion Stability Theory), Moscow: Nauka, 1966.
Panteley, E., Lefeber, E., Loria, A., and Nijmeijer, H., Exponential Tracking Control of a Mobile car Using a Cascaded Approach, in Proc. IFAC Workshop on Motion Control, Grenoble, France, 1998, pp. 221–226.
Hale, J., Theory of Functional Differential Equations, New York: Springer-Verlag, 1977. Translated under the title Teoriya funktsional’no-differentsial’nykh uravnenii, Moscow: Mir, 1984.
Khusainov, D.Ya. and Shatyrko, A.V., Metod funktsii Lyapunova v issledovanii ustoichivosti differentsial’nofunktsional’nykh uravnenii (Method of the Lyapunov Functions in the Studies of Stability of the Differential-Functional Equations), Kiev: Kiev. Univ., 1997.
Sedova, N.O., Degenerate Functions in Studying Asymptotic Stability of the Solutions of Functionally Differential Equations, Mat. Zametki, 2005, vol. 78, no. 3, pp. 468–472.
Jiang, Z.P. and Nijmeijer, H., A Recursive Technique for Tracking Control of Nonholonomic Systems in Chained Form, IEEE Trans. Automat. Control, 1999, vol. 44, no. 2, pp. 265–279.
Author information
Authors and Affiliations
Additional information
Original Russian Text © N.O. Sedova, 2013, published in Avtomatika i Telemekhanika, 2013, No. 8, pp. 138–147.
Rights and permissions
About this article
Cite this article
Sedova, N.O. On the problem of tracking for the nonholonomic systems with provision for the feedback delay. Autom Remote Control 74, 1348–1355 (2013). https://doi.org/10.1134/S0005117913080110
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117913080110