Abstract
This new research aims to extend the topic of the enlarged controllability of a fractional output linear system. Thus, we characterize the optimal control by two methods, ensuring that the Riemann-Liouville fractional derivative of the final state of the considered system lies between two given functions on a subregion of the evolution domain. Firstly, we transform the considered problem into the saddle point using the Lagrangian multiplier approach. Then, in the second one, we provide the technique of the subdifferential, which allows us to present the cost-explicit formula of the minimum energy control. Moreover, we construct an algorithm of Uzawa type to illustrate the theoretical results obtained through numerical simulations.
Publisher
International Journal of Optimization and Control: Theories and Applications
Subject
Applied Mathematics,Control and Optimization
Reference18 articles.
1. Oldham, K., & Spanier, J. (1974). The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier.
2. El Jai A., & El Yacoubi, S. (1993). On the number of actuators in parabolic system. International Journal of Applied Mathematics and Computer Science, 3(4), 673–686.
3. Zerrik, E. (1994). Controlabilite et observabilite regionales d’une classe de systemes distribues. PhD thesis Perpignan.
4. El Jai, A., Simon, C., & Zerrik, E., Pritchard, J. (1995). Regional controllability of distributed parameter systems. International Journal of Control, 62(6), 1351–1365.
5. Zerrik, E., Boutoulout, A., & El Jai A. (2002). Actuators and regional boundary controllability of parabolic systems. International Journal of Systems Science, 31(1), 73–82.