Robust Adaptive Control for a Class of Nonlinear Systems Using the Backstepping Method

Zouari, Farouk; Saad, Kamel Ben; Benrejeb, Mohamed

doi:10.5772/54932

Cited by 17 publications

(17 citation statements)

References 20 publications

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“…Due to the uncertainty of modeling perturbations, (⋅) should be an adaptive controller to reject the perturbations. In terms of the internal model of uncertain items shown in (22), the controller is devised as…”

Section: Design Of Nonlinear State Feedback Controllermentioning

confidence: 99%

“…Furthermore, the formula (52) holds. For the multivariable nonlinear system (9) and exosystem (10) satisfying the Assumptions (1) to (5), the nonlinear multivariable internal models (18) and (22) and the input feedback control (25) can make the closed-loop system globally uniformly bounded.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…For the disadvantages of the above methods, some scholars attempt to apply modern control theory to improve the capability of harmonics disturbance rejection. The nonlinear control methods, such as repetitive control [13,14], ∞ control [15,16], prediction control [17][18][19], backstepping control [20][21][22], and fuzzy-adaptive control [23][24][25][26], can deal with the nonlinearity and uncertainty of nonlinear models better. However, these preexisting rejection control methods have the following problems more or less.…”

Section: Introductionmentioning

confidence: 99%

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Global Harmonic Current Rejection of Nonlinear Backstepping Control with Multivariable Adaptive Internal Model Principle for Grid-Connected Inverter under Distorted Grid Voltage

Che

et al. 2013

Mathematical Problems in Engineering

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Based on a brief review on current harmonics generation mechanism for grid-connected inverter under distorted grid voltage, the harmonic disturbances and uncertain items are immersed into the original state-space differential equation of grid-connected inverter. A new algorithm of global current harmonic rejection based on nonlinear backstepping control with multivariable internal model principle is proposed for grid-connected inverter with exogenous disturbances and uncertainties. A type of multivariable internal model for a class of nonlinear harmonic disturbances is constructed. Based on application of backstepping control law of the nominal system, a multivariable adaptive state feedback controller combined with multivariable internal model and adaptive control law is designed to guarantee the closed-loop system globally uniformly bounded, which is proved by a constructed Lyapunov function. The presented algorithm extends rejection of nonlinear single-input systems to multivariable globally defined normal form, the correctness and effectiveness of which are verified by the simulation results.

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Section: Design Of Nonlinear State Feedback Controllermentioning

confidence: 99%

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global Harmonic Current Rejection of Nonlinear Backstepping Control with Multivariable Adaptive Internal Model Principle for Grid-Connected Inverter under Distorted Grid Voltage

Che

et al. 2013

Mathematical Problems in Engineering

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“…It is based on the previous system state. A new Control Lyapunov Function (CLF) is constructed by the increase of CLF of the previous step [8]. This procedure calculates allow us to ensure overall system stability.…”

Section: Backstepping Control With Integral Action For Pmsmmentioning

confidence: 99%

“…This technique of non-linear control has been recently developed; it can be effectively used for linearizing a non-linear system in the presence of uncertainties [6][7][8][9].…”

Section: Backstepping Control With Integral Action For Pmsmmentioning

confidence: 99%

Backstepping control with integral action of PMSM integrated according to the MRAS observer

Larbaoui¹,

Belabbes²,

Meroufel³

et al. 2014

IOSRJEEE

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Event‐triggered‐NN control for nonlinear system with unknown gain and disturbance

Chen

Shi

2022

Intl J Robust & Nonlinear

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In this article, the problem of tracking control for nonlinear system with unknown gain and disturbance is studied. First, to compensate for the adverse effects of disturbance, a disturbance observer via sliding‐mode is designed to estimate the disturbance, and the finite‐time convergence of estimation error is ensured under certain conditions. Then, an event‐triggered neural networks controller based on estimated disturbance is presented to achieve tracking control. Among which, the Nussbaum technique is employed to deal with the unknown gain, and the super‐twisting estimator is introduced to estimate the derivative of virtual control input. Then a time‐varying event‐triggered strategy is designed to reduce communication load. Furthermore, the stability analysis shows that the close‐loop signals are bounded, the tracking error converges to a small compact set, and no Zeno phenomenon occurs. Finally, two examples are provided to illustrate the effectiveness of the proposed new design schemes.

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Robust Adaptive Control for a Class of Nonlinear Systems Using the Backstepping Method

Cited by 17 publications

References 20 publications

Global Harmonic Current Rejection of Nonlinear Backstepping Control with Multivariable Adaptive Internal Model Principle for Grid-Connected Inverter under Distorted Grid Voltage

Global Harmonic Current Rejection of Nonlinear Backstepping Control with Multivariable Adaptive Internal Model Principle for Grid-Connected Inverter under Distorted Grid Voltage

Backstepping control with integral action of PMSM integrated according to the MRAS observer

Event‐triggered‐NN control for nonlinear system with unknown gain and disturbance

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