Indirect Adaptive Fuzzy Control of SISO Nonlinear Systems With Input–Output Nonlinear Relationship

Zhang, Faxiang; Hua, Jing; Li, Yimin

doi:10.1109/tfuzz.2018.2800714

Cited by 29 publications

(10 citation statements)

References 17 publications

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“…In addition to the dynamic behavior of the model, the optimal control of the model is also an enduring topic. Scholars in various fields have studied the optimal control problem for different models [ 29 – 33 ]. Gashirai applied the optimal control theory to the FMD transmission model and analyzed how to effectively control the disease [ 31 ].…”

Section: Introductionmentioning

confidence: 99%

Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous environment

et al. 2021

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Considering the influence of environmental capacity and forgetting on rumor spreading, we improve the traditional SIR (susceptible–infected–removed) rumor propagation model and give two dynamic models of rumor propagation in heterogeneous environment and homogeneous environment, respectively. The main purpose of this paper is to make a dynamic analysis of rumor propagation models. In the spatial heterogeneous environment, we have analyzed the uniform persistence of the rumor propagation model and the asymptotic behavior of the positive equilibrium point when the diffusion rate of rumor–susceptible tends to zero. In the spatial homogeneous environment, we discuss the stability of rumor propagation model. Further, optimal control and the necessary optimality conditions are obtained by using the maximum principle. Finally, we study the Hopf bifurcation phenomenon through inducing time delay in the reaction–diffusion model. In addition, the existence of Hopf bifurcation is verified and the influence of diffusion coefficients is studied by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous environment

et al. 2021

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“…e proposed method ensures the stability and convergence of the closedloop system and achieves good results in solving the uncertainty and the influence of noise on the system effect. e design method of the interval type-2 T-S indirect adaptive fuzzy controller has been proposed in [29,30]. e rule front of the system is the interval type-2 fuzzy set, and the latter is the exact number, which makes the control method of the structure.…”

Section: Introductionmentioning

confidence: 99%

Type-2 Combined T-S Adaptive Fuzzy Control

Hao

Xia

et al. 2020

Mathematical Problems in Engineering

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For a class of nonlinear systems with a nonlinear relationship between input and output, a fuzzy control method combining interval type-2 and T-S fuzzy controller is proposed based on type-2 fuzzy system theory. In order to ensure its stability, anti-interference ability, and minimum approximation error, this design combines direct, indirect, supervised, and compensation control types to construct the controller. In this way, the structure of the controller not only has the characteristics of the type-2 fuzzy set, which can reduce the uncertainty of rules, but also has a T-S fuzzy model with linear combination of input variables, which can improve the modeling accuracy and reduce the number of rules of the system. By using the Lyapunov synthesis method, the global stability and the convergence of the closed-loop system under the condition that all variables are uniformly bounded are analyzed, and the adaptive laws of the system parameters are given as well. Finally, the effectiveness and superiority of the proposed method are verified by simulation.

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“…22 Therefore, the adaptive SMC method has excellent adaptability to the unknown nonlinear dynamical systems. It is worth mentioning here that, the adaptive control scheme can be divided into the indirect adaptive control 23 , 24 in which the functions of the system model are estimated, and the direct adaptive control 1 , 25 , 26 where the control input is approximated directly. In addition, the second-order SMC method is another way to mitigate the chattering and enhance the control performance.…”

Section: Introductionmentioning

confidence: 99%

Observer based direct adaptive fuzzy second-order-like sliding mode control for unknown nonlinear systems

Liu

Cheng

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part E:

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This work proposes a novel observer based direct adaptive fuzzy second-order-like sliding mode control (SMC) method for a certain class of high order unknown nonlinear dynamical systems with unmeasurable states. An observer is firstly developed to estimate the tracking error vector directly, and the stability of the observer is analyzed based on Meyer-Kalman-Yakubovich (MKY) lemma. Based on the observer, the equivalent control law is approximated by a double-input single-output fuzzy logic system (FLS), in which the observation of the sliding surface and its derivative are applied as the inputs. In addition, an adaptive switching control law is added to mitigate the system chattering and improve the stability of the system. The free parameters of the controller are adjusted online by the adaptive laws that are derived from the Lyapunov stability analysis. Finally, the convergence of the overall closed-loop system is demonstrated, and the simulation examples illustrate the efficacy of the proposed control method.

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Indirect Adaptive Fuzzy Control of SISO Nonlinear Systems With Input–Output Nonlinear Relationship

Cited by 29 publications

References 17 publications

Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous environment

Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous environment

Type-2 Combined T-S Adaptive Fuzzy Control

Observer based direct adaptive fuzzy second-order-like sliding mode control for unknown nonlinear systems

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