Linear controllers for exponential tracking of systems in chained-form

International Journal of Robust and Nonlinear Control

Volumn 10, Issue 4, 2000, Pages 243-263

  Lefeber, E ^a,c   Robertsson, A ^b   Nijmeijer, H ^a,c  

^a UNIVERSITY OF TWENTE   (Netherlands)

^b LUND INSTITUTE OF TECHNOLOGY   (Sweden)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ERROR DETECTION; MOBILE ROBOTS; STATE FEEDBACK; SYSTEM STABILITY;

NON-HOLONOMIC CHAINED FORM CONTROL SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 0034166033     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(20000415)10:4<243::AID-RNC472>3.0.CO;2-P     Document Type: Article

References (42)

1. Astolfi A. Exponential stabilization of nonholonomic systems via discontinuous control. In Proceedings of the Third IFAC Symposium on Nonlinear Control Systems Design (NOLCOS'95), Tahoe City, California, USA, June 1995; 741-746.
2. Astolfi A, Schaufelberger W. State and output feedback stabilization of multiple chained systems with discontinuous control. Systems and Control Letters 1997; 32:49-56.
3. Brockett RW. Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory, Brockett RW, Millman RS, Sussmann HJ (eds.), Birkhäuser, Boston, MA, USA, 1983; 181-191.
4. Byrnes CI, Isidori A. New results and examples in nonlinear feedback stabilization. Systems and Control Letters 1989; 24(12):437-442.
5. Chen M-S. Control of linear time-varying systems by the gradient algorithm. In Proceedings of the 36th Conference on Decision and Control, San Diego, California, USA, December 1997; 4549-4553.
6. Escobar G, Ortega R, Reyhanoglu M. Regulation and tracking of the nonholonomic double integrator: a field-oriented control approach. Automatica 1998; 34(1):125-132.
7. Fierro R, Lewis FL. Control of a nonholonomic mobile robot: backstepping kinematics into dynamics. In Proceedings of the 34th Conference on Decision and Control, New Orleans, LA, USA, December 1995; 3805-3810.
8. Fliess M, Levine J, Martin P, Rouchon P. Design of trajectory stabilizing feedback for driftless flat systems. In Proceedings of the 3rd ECC, Rome, 1995; 1882-1887.
9. Hurwitz A. Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reelen Theilen besitzt. Mathematische Annalen 1895; 46:273-284.
10. Ioannou PA, Sun J. Robust Adaptive Control. Prentice-Hall, Upper Saddle River: New Jersey, USA, 1996.
11. Janković M, Sepulchre R, Kokotović PV. Constructive Lyapunov stabilization of nonlinear cascade systems. IEEE Transactions on Automatic Control 1996; 41(12):1723-1735.
12. Jiang Z-P, Lefeber E, Nijmeijer H. Stabilization and tracking of a nonholonomic mobile robot with saturating actuators. In Proceedings of CONTROLO'98, Third Portuguese Conference on Automatic Control, vol. 1, Coimbra, Portugal, 1998; 315-320.
13. Jiang Z-P, Nijmeijer H. Tracking control of mobile robots: a case study in backstepping. Automatica 1997; 33(7):1393-1399.
14. Jiang Z-P, Nijmeijer H. Observer-controller design for nonholonomic systems. In New Trends in Nonlinear Observer Design, Nijmeijer H, Fossen TI, (eds.), Lecture Notes in Control and Information Sciences, Springer; London, 1999.
15. Jiang Z-P, Nijmeijer H. A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Transactions on Automatic Control 1999; 44(2):265-279.
16. Kailath T. Linear Systems. Prentice-Hall; Englewood Cliffs, New Jersey 1980.
17. Kanayama Y, Kimura Y, Miyazaki F, Noguchi T. A stable tracking control scheme for an autonomous mobile robot. In Proceedings IEEE International Conference on Robotics and Automation 1990; 384-389.
18. Kern G. Uniform controllability of a class of linear time-varying systems. IEEE Transactions on Automatic Control 1982; 27(1):208-210.
19. Khalil HK. Nonlinear Systems. (2nd edn). Prentice-Hall; Upper Saddle River, New Jersey, USA, 1996.
20. Koditschek DE. Adaptive techniques for mechanical systems. In Proceedings of the 5th Yale Workshop on Adaptive Systems, New Haven; CT, 1987; 259-265.
21. Kolmanovsky I, McClamroch NH. Developments in nonholonomic control problems. IEEE Control Systems Magazine 1995; 16(6):20-36.
22. Krstić M, Kanellakopoulos I, Kokotović P. Nonlinear and Adaptive Control Design. Series on Adaptive and Learning Systems for Signal Processing, Communications, and Control, Wiley; New York, 1995.
23. LaSalle JP. Some extensions of Lyapunov's second method. IRE Transactions on Circuit Theory 1960; 7(4):520-527.
24. Lefeber E, Robertsson A, Nijmeijer H. Output feedback tracking of nonholonomic systems in chained form. In Stability and Stabilization of Nonlinear Systems, Aeyels D, Lamnabhi-Lagarrigue F, van der Schaft AJ, (eds.), Lecture Notes in Control and Information Sciences, 246 Springer; Berlin, 1999; 183-199.
25. Lefeber E, Robertsson A, Nijmeijer H. Output feedback tracking of nonholonomic systems in chained form. In Proceedings of the 5th European Control Conference, Karlsruhe, Germany, 1999.
26. Mazenc F, Praly L. Adding integrations, saturated controls, and stabilization for feedforward systems. IEEE Transactions on Automatic Control 1996; 41(11):1559-1578.
27. Micaelli A, Samson C. Trajectory tracking for unicycle-type and two-steering-wheels mobile robots. Technical Report 2097, INRIA, 1993.
28. Murray RM, Walsh G, Sastry SS. Stabilization and tracking for nonholonomic control systems using time-varying state feedback. In IFAC Nonlinear control systems design, Fliess M (ed.), Bordeaux, 1992; 109-114.
29. Oelen W, Berghuis H, Nijmeijer H, Canudas de Wit C. Implementation of a hybrid stabilizing controller on a mobile robot with two degrees of freedom. In Proceedings of the 1994 IEEE International Conference on Robotics and Automation, San Diego, California, USA, 1994; 1196-1201.
30. Ortega R. Passivity properties for stabilization of nonlinear cascaded systems. Automatica 1991; 29:423-424.
31. Panteley E, Lefeber E, Loría A, Nijmeijer H. Exponential tracking control of a mobile car using a cascaded approach. In Proceedings of the IFAC Workshop on Motion Control, Grenoble; France, September 1998; 221-226.
32. Panteley E, Loría A. On global uniform asymptotic stability of nonlinear time-varying systems in cascade. Systems and Control Letters 1998; 33(2):131-138.
33. Parks PC. A new proof of the Routh-Hurwitz stability criterion using the second method of Liapunov. Proceedings of the Cambridge Philosophical Society 1962; 58(4):694-702.
34. Rugh WJ. Linear System Theory. (2nd edn.), Information and System Sciences Series. Prentice-Hall; Englewood Cliffs, New Jersey, 1996.
35. Samson C. Control of chained systems application to path following and time-varying point-stabilization of mobile robots. IEEE Transactions on Automatic Control 1995; 40(1):64-77.
36. Samson C, Ait-Abderrahim K. Feedback control of a nonholonomic wheeled cart in cartesian space. In Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento; USA, 1991; 1136-1141.
37. Sørdalen OJ, Egeland O. Exponential stabilization of nonholonomic chained systems. IEEE Transactions on Automatic Control 1995; 40(1): 35-49.
38. Sussmann HJ, Sontag ED, Yang Y. A general result on the stabilization of linear systems using bounded controls. IEEE Transactions on Automatic Control 1994; 39(12):2411-2425.
39. Tsinias J. Sufficient Lyapunov-like conditions for stabilization. Mathematics of Control of Signals and Systems 1989; 2:343-357.
40. Valášek M, Olgac N. Efficient eigenvalue assignment for general linear MIMO systems. Automatica 1995; 31(11):1605-1617.
41. Valášek M, Olgac N. Efficient pole placement technique for linear time-variant SISO systems. IEE Proceedings - Control Theory and Applications 1995; 142(5):451-458.
42. Vidyasagar M. Nonlinear Systems Analysis. (2nd edn), Prentice-Hall; Englewood Cliffs, New Jersey, USA, 1993.