Third-order strict-feedback chaotic proportion projection synchronization method based on improved pole assignment
A pole configuration and projection technology, which is applied to instruments, adaptive control, control/regulation systems, etc., can solve the problems of modeling uncertainty, inability to proportional projection synchronization control of the pole configuration method, etc., and achieve the effect of good robustness.
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specific Embodiment 1
[0052] The drive system and the response system are isomorphic systems, both of which are Genesio-Tesi chaotic systems. The state equation of the Genesio-Tesi system is:
[0053]
[0054] Among them, f 1 (x)=x 1 2 , when the parameter a 1 =-1, a 2 =-1.1, a 3 When =-0.45, the Genesio-Tesi system will appear chaotic phenomenon. Equation (13) is the driving system. The initial state of the drive system is set to x 1 (0)=0.4,x 2 (0)=0.3,x 3 (0)=-0.4.
[0055] The response system is also a Genesio-Tesi chaotic system, and the controlled response system with modeling uncertainties and external disturbance signals is expressed as:
[0056]
[0057] where f 2 (y)=y 1 2 , b 1 =-1,b 2 =-1.1,b 3 =-0.45, u is the control input, modeling uncertainty is set to △f 2 (y)=0.3sin(0.2y 1 +y 2 ), then d 1 =0.3, the external interference signal is set as d(t)=0.2cos(2t), then d 2 = 0.2. A controlled response system (14) with modeled uncertain and external disturbance s...
specific Embodiment 2
[0069] The drive system and response system are heterogeneous systems, the drive system is Genesio-Tesi chaotic system, and the response system is Coullet chaotic system. The state equation of Genesio-Tesi system adopts formula (13):
[0070]
[0071] Among them, f 1 (x)=x 1 2 , when the parameter a 1 =-1, a 2 =-1.1, a 3 When =-0.45, the Genesio-Tesi system will appear chaotic phenomenon. Equation (13) is the driving system. The initial state of the drive system is set to x 1 (0)=0.5,x 2 (0)=0.2,x 3 (0)=-0.4.
[0072] The response system is a Coullet chaotic system, and the controlled response system with modeling uncertainties and external disturbance signals is expressed as:
[0073]
[0074] where f 2 (y)=-y 1 3 , b 1 =0.8,b 2 =-1.1,b 3 =-0.45, u is the control input, modeling uncertainty is set to △f 2 (y)=0.2sin(y 1 +2y 2 ), then d 1 =0.2, the external interference signal is set as d(t)=0.3sin(3t), then d 2 = 0.3. A controlled response system ...
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