Adaptive Backstepping Control for a Class of Nonlinear Systems With Non-Triangular Structural Uncertainties

Cai, Jianping; Chen, Wen; Su, Hongye; Liu, Zhitao; Xing, Lantao

doi:10.1109/tac.2016.2628159

Cited by 86 publications

(40 citation statements)

References 10 publications

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“…Assumption The signal of concern y d is smooth and known in a sufficient manner. Assumption The exterior disturbance d m ( t ) is confined:

|d_{m} (t)| \leq d_{m}^{*},

where

d_{m}^{*}

is a positive constant. Remark The aforementioned assumptions are common and reasonable. Assumption is a common and standard requirement in the available backstepping designs . Assumption , which is introduced in References , can assure that the external disturbances are bounded. Lemma (Young's inequality).…”

Section: System Description and Preparationsmentioning

confidence: 99%

“…Assumption 1 is a common and standard requirement in the available backstepping designs. [2][3][4][5][6] Assumption 2, which is introduced in References 23-25, can assure that the external disturbances are bounded. 13 ).…”

Section: System Descriptionmentioning

confidence: 99%

“…The backstepping control approach is a recursive methodology such that the design of both control laws and their stability analysis are systematic . A robust adaptive control according to the backstepping technique for a category of nonlinear systems containing unknown parameters is proposed in Reference . Adaptive output‐feedback controllers are addressed in References for a category of output constrained uncertain nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

Naderolasli

Hashemi

Shojaei

2020

Adaptive Control & Signal

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Summary An observer‐based adaptive fuzzy backstepping approach is proposed for nonlinear systems with respect to fractional‐order differential equations, unmatched uncertainties, unmeasured states, and actuator faults. The approximation capability of fuzzy logic system and minimal learning parameter approaches are applied to identify uncertain functions in a simultaneous manner. For estimating the unavailable conditions, a fuzzy fractional‐order state‐observer is extended. Applying fault‐tolerant approach in a backstepping design methodology would provide a new fault‐tolerant adaptive fuzzy output‐feedback approach for fractional‐order strict‐feedback systems. This control structure would assure the considered system stability through selection of the appropriate Lyapunov candidate function. Two numerical simulations are run to exhibit the validity herein.

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“…Assumption The signal of concern y d is smooth and known in a sufficient manner. Assumption The exterior disturbance d m ( t ) is confined:

|d_{m} (t)| \leq d_{m}^{*},

where

d_{m}^{*}

Section: System Description and Preparationsmentioning

confidence: 99%

Section: System Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

Naderolasli

Hashemi

Shojaei

2020

Adaptive Control & Signal

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show abstract

“…FLSs can be combined with backstepping design techniques to overcome the mismatched uncertainties problem. At the same time, backstepping control can provide a symmetric framework for controller design, so fuzzy backstepping control schemes have achieved great success in the control field [4,[9][10][11][12][13]. However, backstepping control needs to do repeated differentiations of the virtual control law.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy State Observer-Based Adaptive Dynamic Surface Control of Nonlinear Systems with Time-Varying Output Constraints

Wan

Liu

Zheng³

et al. 2019

Mathematical Problems in Engineering

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In this paper, a new fuzzy dynamic surface control approach based on a state observer is proposed for uncertain nonlinear systems with time-varying output constraints and external disturbances. An adaptive fuzzy state observer is used to estimate the states that cannot be measured in the systems. In our method, a time-varying Barrier Lyapunov Function (BLF) is used to ensure that the output does not violate time-varying constraints. In addition, dynamic surface control (DSC) technology is applied to overcome the problem of “explosion of complexity” in a backstepping control. Finally, the stability and signal boundedness of the system are confirmed by the Lyapunov method. The simulation results show the effectiveness and correctness of the proposed method.

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“…For mismatched uncertainty nonlinear systems, the backstepping control is very effective and has achieved great success. [16][17][18][19][20] Traditional backstepping control needs to do repeated differentiations of the virtual control law of the former subsystem. If there are nonlinear functions in the virtual controllers, repeated differentiations will lead to the problem of ''explosion of complexity'' with the increase in the order of the system.…”

Section: Introductionmentioning

confidence: 99%

Adaptive fuzzy backstepping control for uncertain nonlinear systems with tracking error constraints

Wan

Liu

2019

Advances in Mechanical Engineering

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This article deals with the design of adaptive fuzzy backstepping control for uncertain nonlinear systems in strictfeedback form with tracking error constraints. In this article, a fuzzy system is used to approximate the unknown nonlinear functions and the differential of virtual control law of each subsystem. In order to satisfy the limitation of tracking error constraints, the barrier Lyapunov function is introduced. Moreover, by applying the minimal learning parameters technique, the number of online parameters update for each subsystem is reduced to only 1. The control scheme not only ensures the tracking error is not to transgress the constraint bounds but also solves the problem of ''explosion of complexity'' and greatly reduces the initial control input and the number of the adaptive parameters; this provides the conditions for the practical application. The simulation results show the effectiveness of the proposed method.

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Adaptive Backstepping Control for a Class of Nonlinear Systems With Non-Triangular Structural Uncertainties

Cited by 86 publications

References 10 publications

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

Approximation‐based adaptive fault compensation backstepping control of fractional‐order nonlinear systems: An output‐feedback scheme

Fuzzy State Observer-Based Adaptive Dynamic Surface Control of Nonlinear Systems with Time-Varying Output Constraints

Adaptive fuzzy backstepping control for uncertain nonlinear systems with tracking error constraints

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