Backstepping for nonsmooth systems

Automatica

Volumn 39, Issue 7, 2003, Pages 1259-1265

  Tanner, Herbert G ^a   Kyriakopoulos, Kostas J ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Backstepping; Discontinuous control; Nonholonomic systems; Nonsmooth differential equations

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; INTERFERENCE SUPPRESSION; LYAPUNOV METHODS; ROBUSTNESS (CONTROL SYSTEMS);

NONSMOOTH SYSTEMS;

NONLINEAR CONTROL SYSTEMS;

EID: 0037502816     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(03)00081-5     Document Type: Article

References (29)

1. Astolfi A. Discontinuous control of nonholonomic systems. Systems & Control Letters. 27:1996;37-45.
2. Bloch A., Drakunov S. Stabilization and tracking in the nonholonomic integrator via sliding modes. Systems and Control Letters. 29:1996;91-99.
3. Brockett R. Control theory and singular Riemannian geometry. New directions in applied mathematics. 1981;Springer, Berlin.
4. Campion, G., d'Andrea Novel, B., & Bastin, G. (1991). Modelling and state feedback control of nonholonomic mechanical systems. In Proceedings of the 1991 IEEE conference on decision and control, Brighton, England.
5. Canudas de Wit C., Sordalen O. Exponential stabilization of mobile robots with nonholonomic constraints. IEEE Transactions on Automatic Control. 13(11):1992;1791-1797.
6. Clarke F. Optimization and nonsmooth analysis. 1983;Addison-Wesley, Reading.
7. Fierro, R., & Lewis, F. (1995). Control of a nonholonomic mobile robot: Backstepping kinematics into dynamics. In Proceedings of 34th IEEE conference on decision and control, New Orelans, LA.
8. Filippov A. Differential equations with discontinuous righthand sides. 1988;Kluwer Academic, Dordrecht.
9. Freeman R.A., Kokotović P.V. Design of 'softer' robust nonlinear control laws. Automatica. 29(6):1993;1425-1437.
10. Freeman R.A., Kokotović P.V. Robust nonlinear control design. 1996;Birkhäuser, Basel.
11. Jiang Z.-P. Robust exponential regulation of nonholonomic systems with uncertainties. Automatica. 36:2000;189-209.
12. Jiang Z.-P., Nijmeijer H. Tracking control of mobile robots. A case study in backstepping Automatica. 33(7):1998;1393-1399.
13. Khalil H.K. Nonlinear systems. 1996;Prentice Hall, Englewood Cliffs.
14. Kim, B. M., & Tsiotras, P. (2000). Time-invariant stabilization of a unicycle-type mobile robot: Theory and experiments. In: Proceedings of the IEEE conference on control applications, Ancorage, AL.
15. Kolmanovsky I., McClamroch N. Developments in nonholonomic control problems. IEEE Control Systems. 15:1995;20-36.
16. Kolmanovsky, I., & McClamroch, N. H. (1995b). Application of integrator backstepping to nonholonomic control problems. In: Proceedings of the IFAC symposium on nonlinear control systems design. Tahoe City, CA.
17. Krstić M., Kanellakopoulos I., Kokotović P. Nonlinear and adaptive control design. 1995;Wiley, New York.
18. Laiou M.-C., Astolfi A. Discontinuous control of high-order generalized chained systems. Systems and Control Letters. 37:1999;309-322.
19. Lin W., Pongvuthithum R., Quian C. Control of high-order nonholonomic systems in power chained form using discontinuous feedback. IEEE Transactions on Automatic Control. 47(1):2002;108-115.
20. Luo J., Tsiotras P. Control design for chained-form systems with bounded inputs. Systems & Control Letters. 29:2000;123-131.
21. M'Closkey, R. T., & Murray, R. M. (1994). Extending exponential stabilizers for nonholonomic systems from kinematic controllers to dynamic controllers. In Proceedings of the fourth IFAC symposium on robot control, Capri.
22. Morin, P., & Samson, C. (1996). Application of backstepping techniques to the time-varying exponential stabilization of chained form systems. Technical Report 2792, INRIA Sophia Antipolis.
23. Paden B., Sastry S. A calculus for computing filipov's differential inclusion with application to the variable structure control of robot manipulators. IEEE Transactions on Circuits and Systems. CAS-34(1):1987;73-82.
24. Reyhanoglu A.M.B.M., McClamroch N.H. Control and stabilization of nonholonomic dynamic systems. IEEE Transactions on Automatic Control. 37:1992;1746-1757.
25. Shevitz D., Paden B. Lyapunov stability theory of nonsmooth systems. IEEE Transactions on Automatic Control. 49(9):1994;1910-1914.
26. Tanner, H., & Kyriakopoulos, K. (2002). Discontinuous backstepping for stabilization of nonholonomic mobile robots. In Proceedings of the IEEE international conference on robotics and automation, Washington DC.
27. Tanner, H., Loizou, S., & Kyriakopoulos, K. (2001). Nonholonomic stabilization with collision avoidance for mobile robots. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems, Maui, Hawaii.
28. Tsiotras P., Luo J. Reduced efrort control laws for underactuated rigid spacecraft. AIAA Journal of Guidance, Control, and Dynamics. 20(6):1997;1089-1095.
29. Yang J.-M., Kim J.-H. Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots. IEEE Transactions on Robotics and Automation. 15(3):1999;578-587