Regional Controllability and Minimum Energy Control of Delayed Caputo Fractional-Order Linear Systems

被引:0
作者
Karite, Touria [1 ]
Khazari, Adil [2 ]
Torres, Delfim F. M. [3 ]
机构
[1] Sidi Mohamed Ben Abdellah Univ, Natl Sch Appl Sci, Dept Elect Engn & Comp Sci, Lab Engn Syst & Applicat, Ave My Abdallah Km 5 Route Imouzzer, Fes BP 72, Morocco
[2] Sidi Mohamed Ben Abdellah Univ, Natl Sch Commerce & Management, Lab Anal Math & Applicat, Fes BP 1796, Morocco
[3] Univ Aveiro, Ctr Res & Dev Math & Applicat CIDMA, Dept Math, P-3810193 Aveiro, Portugal
关键词
regional controllability; fractional-order systems; Caputo derivatives; control delays; optimal control; minimum energy; STABILITY; EQUATIONS;
D O I
10.3390/math10244813
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.
引用
收藏
页数:16
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