2020, Volume 9
2019, Volume 8
2018, Volume 7
2017, Volume 6
2016, Volume 5
2015, Volume 4
2014, Volume 3
2013, Volume 2
2012, Volume 1

Volume 5, Issue 3, June 2016, Page: 165-168
The Application of Matrix in Control Theory
Yuanyuan Zhang, College of Science, China Three Gorges University, Yichang, China
Received: Jul. 23, 2016;       Published: Jul. 25, 2016
DOI: 10.11648/j.acm.20160503.21      View  4661      Downloads  252
This paper presents a new way to justify the controllability of linear ordinary systems. This way is based on the maximum geometric multiplicity of eigenvalues for the coefficient matrix of the linear ordinary equation. This method is equivalent to other discrimination laws for controllability.
Controllability, Ordinary Differential Equation, Geometric Multiplicity, Eigenvalues
To cite this article
Yuanyuan Zhang, The Application of Matrix in Control Theory, Applied and Computational Mathematics. Vol. 5, No. 3, 2016, pp. 165-168. doi: 10.11648/j.acm.20160503.21
V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems, Academic Press, Boston, 1993, pp. 74-98.
L. C. Evans, An Introduction to Mathematical Optimal Control Theory, Lecture Notes, Department of Mathematics, University of California, Berkeley, 2008, pp. 92-101.
H. O. Fattorini, Infinite Dimensional Linear Control Systems, the Time Optimal and Norm Optimal Control Problems, North-Holland Mathematics Studies 201, Elsevier, 2005, pp. 48-67.
K. Ito and K. Kunisch, “Semismooth newton methods for time-optimal control for a class of ODES”, SIAM J. Control Optim., vol. 48, 2010, pp. 3997-4013.
C. Y. Kaya and J. L. Noakes, “Computations and time-optimal controls”, Optimal Control Applications and Methods, vol.17, 1996, pp.171-185.
C. Y. Kaya and J. L. Noakes, “Computational methods for time-optimal switching controls”, J. Optim. Theory Appl., vol. 117, 2003, pp. 69-92.
J. P. Lasalle, The Time Optimal Control Problem, Contributions to the Theory of Nonlinear Oscillations, Princeton University Press, Princeton, 1960, 1-24.
X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems, Birkhauser, Boston, 1995, pp. 127-135.
P. Lin and G. Wang, “Blowup time optimal control for ordinary differential equations”, SIAM J. Control Optim., vol. 49, 2011, pp. 73-105.
E. Meier and A. E. Bryson, Efficient algorithms for time-optimal rigid spacecraft reorientation problem, Journal of Guidance, Control, and Dynamics, vol. 13, 1990, pp. 859-866.
T. Li and B. Rao. “A note on the exact synchronization by groups for a coupled system of wave equations”, Mathematical Methods in the Applied Sciences, vol. 38, 2015, pp. 241–246.
L. Hu, F. Ji and K. Wang. “Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations”, Chinese Annals of Mathematics, vol.34(4), 2013, pp. 479–490.
B. Z. Guo, D. H. Yang and L. Zhang. “On optimal location of diffusion and related optimal control for null controllable heat equation”, Journal of Mathematical Analysis and Applications, vol. 433(2), 2016, pp. 1333-1349.
M. Chen. “Bang bang property for time optimal control of the korteweg de vries burgers equation”, appl.math. opt., vol. 2, 2016, pp. 1-16.
L. Wang and Q. Yan. “Time Optimal Controls of Semilinear Heat Equation with Switching Control”, Journal of Theory and Applications, vol. 165(1), 2015: 263-278.
L. Wang and Q. Yan. “Bang-bang property of time optimal controls for some semilinear heat equation”, Mathematics, 2015, 31(3): 477–499
Browse journals by subject