Fuzzy adaptive control of fractional order chaotic systems with unknown control gain sign using a fractional order Nussbaum gain

Khettab, Khatir; Ladaci, Samir; Bensafia, Yassine

doi:10.1109/jas.2016.7510169

Cited by 44 publications

(31 citation statements)

References 24 publications

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“…Two important and widely applied definitions are Grunwald-Letnikov definition is perhaps the best known due to its most suitability for the realization of discrete control algorithms [1,12]. The Grunwald-Letnikov definition is expresses as [21,[24][25][26][27]:…”

Section: Definition Of Fractional Calculusmentioning

confidence: 99%

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

Bensafia¹,

Khettab²,

Idir³

2018

IJIES

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Abstract:Recently, many research works have focused on fractional order control (FOC) and fractional systems. It has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. In this paper we propose a new approach for robust control by fractionalizing an integer order integrator in the classical PID control scheme and we use the Sub-optimal Approximation of fractional order transfer function to design the parameters of PID controller, after that we study the performance analysis of fractionalized PID controller over integer order PID controller. The implementation of the fractionalized terms is realized by mean of well-established numerical approximation methods. Illustrative simulation examples show that the disturbance rejection is improved by 50%. This approach can also be generalized to a wide range of control methods.

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Section: Definition Of Fractional Calculusmentioning

confidence: 99%

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

Bensafia¹,

Khettab²,

Idir³

2018

IJIES

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“…For system (1), the optimal control problem is to find a control law u(x) that stabilizes (1) and minimizes the performance function defined in (2). In this section, the optimal control problem is addressed under the admissible control policies, whose definition is given as follows.…”

Section: The Nonlinear Infinite-horizon Optimal Control Problemmentioning

confidence: 99%

“…A control u(x) is defined to be admissible with respect to (2) on Ω, denoted as u(x) ∈ U(Ω), if and only if u(x) is continuous with u ∈ Ω u , u(0) = 0, u(x) stabilizes system (1) on Ω, and, ∀x 0 ∈ Ω, V(x 0 ) is finite.…”

Section: Definition 1 (See the Work Of Abu-khalaf And Lewis 57 )mentioning

confidence: 99%

“…The optimal control problems have been studied for more than half a century, and quite a number of methods have been presented, such as fuzzy logic theories [1][2][3][4] and approximation dynamic programming (ADP) algorithms. [5][6][7][8][9][10][11][12][13][14][15][16][17] With the rapid development of intelligent computation technologies in the last several decades, intelligent control methods have been applied in the analysis of nonlinear systems (see the works of Zhang et al, 18 Zhao et al, 19 and Huang and Chung 20 ).…”

Section: Introductionmentioning

confidence: 99%

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Online reinforcement learning for a class of partially unknown continuous‐time nonlinear systems via value iteration

Zhang

et al. 2017

Optim Control Appl Methods

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Summary In this paper, a modified value iteration–based approximate dynamic programming method is proposed for a class of affine nonlinear continuous‐time systems, whose dynamics are partially unknown. The value iteration algorithm is established in an online fashion, and the convergence proof is given. To attenuate the effect caused by the unascertained characteristics of the system dynamics, the integral reinforcement learning scheme is also used. In the proposed approximate dynamic programming method, it is emphasized that the single‐network structure is utilized to estimate the value functions and the control policies. That is, the iteration process is implemented on the actor/critic structure, in which case only the critic NN is required to be identified. Then, the least‐squares scheme is derived for the NN weights updating. Finally, a linear system and a nonlinear system are tested to evaluate the performance of the proposed online value iteration algorithm. Both of the examples show the feasibility and effectiveness of the proposed algorithms.

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“…For the particular case of fractional order chaotic systems, many approaches have been proposed to achieve chaos synchronization, such as PC control [12], nonlinear state observer method [13], adaptive control [14,15] and sliding mode control [16].…”

Section: Introductionmentioning

confidence: 99%

Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Khettab¹,

Bensafia²,

Ladaci³

2017

IJIES

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Abstract:In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PI λ control law with the fractional-order adaptive sliding mode controller in order to eliminate the chattering action in the control signal. Based on Lyapunov theory, the stability analysis of the proposed control strategy is performed for an acceptable synchronization error level. Numerical simulations illustrate the efficiency of the proposed fractional fuzzy adaptive control scheme through the synchronization of two different fractional order chaotic Duffing systems. We show that the introduction of the additional fractional adaptive PI λ control action is able to eliminate the chattering phenomena in the control signal.

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Fuzzy adaptive control of fractional order chaotic systems with unknown control gain sign using a fractional order Nussbaum gain

Cited by 44 publications

References 24 publications

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

Online reinforcement learning for a class of partially unknown continuous‐time nonlinear systems via value iteration

Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

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