Optimal synchronization of two different in‐commensurate fractional‐order chaotic systems with fractional cost function |
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| Authors: | Reza Behinfaraz Mohammadali Badamchizadeh |
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| Affiliation: | Faculty of Electrical and Computer Engineering, Department of Control Engineering, University of Tabriz, Tabriz, Iran |
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| Abstract: | This article investigates the optimal synchronization of two different fractional‐order chaotic systems with two kinds of cost function. We use calculus of variations for minimizing cost function subject to synchronization error dynamics. We introduce optimal control problem to solve fractional Euler–Lagrange equations. Optimal control signal and minimum time of synchronization are obtained by proposed method. Examples show the optimal synchronization of two different systems with two different cost functions. First, we use an ordinary integer cost function then we use a fractional‐order cost function and comparing the results. Finally, we suggest a cost function which has the optimal solution of this problem, and we can extend this solution to solve other synchronization problems. © 2016 Wiley Periodicals, Inc. Complexity 21: 401–416, 2016 |
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| Keywords: | optimal synchronization fractional‐order chaotic system Euler– Lagrange equations fractional cost function |
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