Applied and Computational Mathematics
Volume 6, Issue 4, August 2017, Pages: 185-188
Received: Jul. 19, 2017;
Published: Jul. 19, 2017
Views 1847 Downloads 103
Yuanyuan Zhang, College of Science, China Three Gorges University, Yichang, China
Time optimal control problems of ordinary differential equations have been of great interest for decades due to their practical applications. There are mainly two ways to compute optimal times. The first one is the Switching Time Optimization method, where the switching time is taken as extra unknowns and the optimization problems is solved by nonlinear programming technique. The second one is based on the first order necessary condition for optimal control. In this paper, we extend the numerical method given in  for the computation of the optimal time for the time optimal control problems. In the end some examples are provided to show the efficiency of the numerical method.
Research on the Application of Numerical Method in Control Theory, Applied and Computational Mathematics.
Vol. 6, No. 4,
2017, pp. 185-188.
X. Lu, L. Wang and Q. Yan, “Computation of Time Optimal Control Problems governed by Linear Ordinary Differential Equations”, Journal of Scientific Computing, 2017, pp. 1-25.
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.