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International Journal of Differential Equations
Volume 2010 (2010), Article ID 461048, 16 pages
Time-Optimal Control of Systems with Fractional Dynamics
Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical and Computer Engineering, Utah State University, 41260 Old Main Hill, Logan, UT 84322-4160, USA
Received 1 August 2009; Accepted 5 December 2009
Academic Editor: Wen Chen
Copyright © 2010 Christophe Tricaud and YangQuan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [17 citations]
The following is the list of published articles that have cited the current article.
- Raj Kumar Biswas, and Siddhartha Sen, “Fractional Optimal Control Problems With Specified Final Time,” Journal of Computational and Nonlinear Dynamics, vol. 6, no. 2, pp. 021009, 2011.
- M. Mehedi Hasan, Xiangqing W. Tangpong, and Om Prakash Agrawal, “Fractional optimal control of distributed systems in spherical and cylindrical coordinates,” Journal Of Vibration And Control, vol. 18, no. 10, pp. 1506–1525, 2012.
- A. Dzielinski, and P. M. Czyronis, “Fixed final time and free final state optimal control problem for fractional dynamic systems - linear quadratic discrete-time case,” Bulletin of The Polish Academy of Sciences-Technical Sciences, vol. 61, no. 3, pp. 681–690, 2013.
- Dariusz Idczak, and Rafał Kamocki, “Fractional differential repetitive processes with Riemann–Liouville and Caputo derivatives,” Multidimensional Systems and Signal Processing, 2013.
- Raj Kumar Biswas, and Siddhartha Sen, “Free final time fractional optimal control problems,” Journal of the Franklin Institute, 2013.
- A. G. Butkovskii, S. S. Postnov, and E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. II. Fractional dynamic systems: Modeling and hardware implementation,” Automation and Remote Control, vol. 74, no. 5, pp. 725–749, 2013.
- Mohammad Amin Rahimian, “Optimal Tuning for Fractional-Order Controllers: An Integer-Order Approximating Filter Approach,” Journal of Dynamic Systems Measurement and Control, vol. 135, no. 2, pp. 021017, 2013.
- Antonio Flores Tlacuahuac, and Lorenz T Biegler, “Optimization of Fractional Order Dynamic Chemical Processing Systems,” Industrial & Engineering Chemistry Research, pp. 131231141208004, 2013.
- Shakoor Pooseh, Ricardo Almeida, and Delfim Torres, “Fractional order optimal control problems with free terminal time,” Journal of Industrial and Management Optimization, vol. 10, no. 2, pp. 363–381, 2013.
- Rafal Kamocki, “Pontryagin maximum principle for fractional ordinary optimal control problems,” Mathematical Methods in The Applied Sciences, vol. 37, no. 11, pp. 1668–1686, 2014.
- Rafal Kamocki, “On the existence of optimal solutions to fractional optimal control problems,” Applied Mathematics and Computation, vol. 235, pp. 94–104, 2014.
- Necati Ozdemir, and Derya Avci, “Optimal control of a linear time-invariant space-time fractional diffusion process,” Journal of Vibration and Control, vol. 20, no. 3, pp. 370–380, 2014.
- Jing Bai, Guoguang Wen, Ahmed Rahmani, Xing Chu, and Yongguang Yu, “Consensus with a reference state for fractional-order multi-agent systems,” International Journal of Systems Science, pp. 1–13, 2015.
- Ivan Matychyn, and Viktoriia Onyshchenko, “Time-Optimal Control Of Fractional-Order Linear Systems,” Fractional Calculus And Applied Analysis, vol. 18, no. 3, pp. 687–696, 2015.
- Yiheng Wei, Bin Du, Songsong Cheng, and Yong Wang, “Fractional Order Systems Time-Optimal Control and Its Application,” Journal of Optimization Theory and Applications, 2015.
- Jing Bai, Guoguang Wen, Ahmed Rahmani, and Yongguang Yu, “Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay,” International Journal of Systems Science, pp. 1–13, 2015.
- Samaneh Soradi Zeid, Ali Vahidian Kamyad, Sohrab Effati, Seyed Ali Rakhshan, and Soleiman Hosseinpour, “Numerical solutions for solving a class of fractional optimal control problems via fixed-point approach,” SeMA Journal, 2017.