Chaos control of fractional order Lü system via RBF neural network sliding mode controller

A RBF neural network sliding mode controller is presented for chaos control of fractional order Lü system with parametric perturbation and external disturbances, which combines the advantages of RBF neural network and sliding mode control. The controller is given based on the output of RBF neural network and the weights of network can be adjusted online according to the sliding mode reaching law. The stability of the controller is analyzed based on the Lyapunov stability theorem. The simulation results illustrate the effectiveness and robustness of the proposed controller.

[1]  Changpin Li,et al.  Chaos in Chen's system with a fractional order , 2004 .

[2]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[3]  Mohammad Saleh Tavazoei,et al.  A necessary condition for double scroll attractor existence in fractional-order systems , 2007 .

[4]  Junguo Lu.  Chaotic dynamics of the fractional-order Lü system and its synchronization , 2006 .

[5]  I. Podlubny.  Fractional differential equations , 1998 .

[6]  Chunguang Li,et al.  Chaos in the fractional order Chen system and its control , 2004 .

[7]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[8]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[9]  Xu Lei,et al.  Chaos in fractional-order Liu system and a fractional-order unified system and the synchronization between them , 2007 .

[10]  Gao Xin,et al.  Chaos and chaotic control in a fractional-order electronic oscillator , 2005 .

[11]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

[12]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[13]  Wajdi M. Ahmad.  Hyperchaos in fractional order nonlinear systems , 2005 .

[14]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.