Research Papers

Design of a High Gain Observer Optimization Method for the State Synchronization of Nonlinear Perturbed Chaotic Systems

[+] Author and Article Information
Ines Daldoul

Laboratory of Advanced Systems,
Polytechnic School of Tunisia,
BP. 743,
La Marsa 2078, Tunisia
e-mail: ines.daldoul@gmail.com

Ali Sghaier Tlili

Laboratory of Advanced Systems,
Polytechnic School of Tunisia,
BP. 743,
La Marsa 2078, Tunisia
e-mail: ali.tlili@ept.rnu.tn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 7, 2018; final manuscript received July 30, 2018; published online August 27, 2018. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 13(11), 111004 (Aug 27, 2018) (10 pages) Paper No: CND-18-1148; doi: 10.1115/1.4041084 History: Received April 07, 2018; Revised July 30, 2018

This paper propounds addressing the design of a high gain observer optimization method in order to ensure a reliable state synchronization of nonlinear perturbed chaotic systems. The salient feature of the developed approach lies in the optimization of the high gain observer by using the optimal control theory associated with a proposed numerical algorithm. Thereby, an innovative quadratic optimization criterion is proposed to calculate the required optimal value of the observer setting parameter θ, characterizing the observation gain and corresponding to the minimal value of the cost function, by achieving a compromise between the correction term of the state observer and its observation error. Moreover, the exponential stability of the high gain observer is demonstrated within the Lyapunov framework. The efficacy of the designed approach is highlighted by numerical simulation on two prominent examples of nonlinear perturbed chaotic systems.

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Fig. 1

Flowchart of the proposed optimization algorithm

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Fig. 2

Attractors of the hyperbolic tangent chaotic system (a)  x1(t),x2(t),x3(t) and (b)  x3(t),x1(t),x2(t)

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Fig. 3

Correspondence values between θ and J for the disturbed hyperbolic tangent chaotic system with θ∈{10,…,20} and a step ε=0.01

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Fig. 4

Evolution of x1(t) and their observed x̂1(t) for θ=10,θ=13 and θopt=11.05

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Fig. 5

Evolution of x2(t) and their observed x̂2(t) for θ=10,θ=13 and θopt=11.05

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Fig. 6

Evolution of x3(t) and their observed x̂3(t) for θ=10,θ=13 and θopt=11.05

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Fig. 7

Lorenz system state estimation and its attractor for α=0.3

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Fig. 8

Chen system state estimation and its attractor for α=0.8

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Fig. 9

Lü system state estimation and its attractor for α=1

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Fig. 10

Evolution of x1(t) and their observed states for θ=1.1,θ=5 and θopt=3.5

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Fig. 11

Evolution of x2(t) and their observed states for θ=1.1,θ=5 and θopt=3.5

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Fig. 12

Evolution of x3(t) and their observed states for θ=1.1,θ=5 and θopt=3.5



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