Adaptive control in the Nabla setting

Neural, Parallel and Scientific Computations

Volumn 16, Issue 2, 2008, Pages 253-272

  Jackson, Billy J ^a  

^a GEORGIA STATE UNIVERSITY   (United States)

Author keywords

Controllability Gramian; Hilger circle; Lyapunov stability; Nabla derivative

Indexed keywords

EID: 49549109579     PISSN: 10615369     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (18)

1. M. Bohner and A. Peterson. Dynamic Equations on Time Scales: An Introduction with Applications. Birk~iuser, Boston, 2001.
2. M. Bohner and A. Peterson. Advances in Dynamic Equations on ~nne Scales. Birkh/iuser, Boston, 2003.
3. J. DaCuhna. Lyapunov Stability, and Floquet Theory for Nonautonomous Linear Dynamic Systems on Time Scales. Ph.D. thesis, Baylor University, 2004.
4. J. DaCutma. Stability for time varying linear dynamic systems on time scales. J. Comput. Appl. Math. 176(2), 381-410, 2005.
5. J.C. Engwerda. Control aspects of linear discrete time-varying systems. International Journal of Control, 48(4):1631-1658, 1988.
6. L. Fausett and K. Murty. Conu'ollability, observability, and realizability criteria on time scale dynamical systems. Nonlinear Studies, 11 (4):627-638, 2004.
7. T. Gard and J. Hoffacker. Asymptotic behavior of natural growth on time scales. Dynamic Systems and Applications, 12 (1 - 2): 131 - 148, 2003.
8. I.A. Gravagne, J.M. Davis, and J.J. DaCuhna. A unified approach to discrete and high-gain adaptive controllers using time scales, submitted.
9. I.A. Gravagne, J.M. Davis, J.J. DaCuhna, and R.J. Marks II. Bandwidth reduction for controller area networks using adaptive sampling. Proc. Int. Conf. Robotics and Automation (ICRA), New Orleans, LA, April 2004, pp. 5250-5255.
10. I.A. Gravagne, J.M. Davis, and R.J. Marks II. How deterministic must a real-time controller be? Proceedings of 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), Alberta Canada, Aug. 2-6 2005, pp. 3856-3861.
11. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results in Mathematics 18 (1990), 18-56.
12. S. Hilger, Ein Masskettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. Ph.D. thesis, Universität Würzburg, 1988.
13. B. Jackson. A General Linear Systems Theory on Time Scales: Transforms, Stability, and Control. Ph.D. thesis, Baylor University, 2007.
14. Y.C. Ho, R.E. Kalman, and K.S. Narendra. Controllability of linear dynamical systems. Contr. Diff. Eqns., 1(1963):189-213.
15. Kalman, R.E. Contributions to the theory of optimal control. Bol. Soc. Mat. Mex. 5(1960):102-119.
16. C. Pötzsche, S. Siegmund, and F. Wirth. A spectral characterization of exponential stability for linear time-invariant systems on time scales. Discrete and Continuous Dynamical Systems, 9(5):1223-1241, September 2003.
17. W. Rugh. Linear System Theory, 2nd edition. Prentice Hall, New Jersey, 1996.
18. L. Weiss. Controllability, realization, and stability of discrete-time systems. SIAM Journal on Control and Optimization, 10(2):230-251, 1972.