Adaptive robust backstepping control for a class of uncertain dynamical systems using neural networks

Wang, Yuchao; Wu, Hansheng

doi:10.1007/s11071-015-2093-2

Cited by 34 publications

(30 citation statements)

References 39 publications

(61 reference statements)

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“…Recently, many researchers are dedicated to handling the control problem of uncertain nonlinear system by combining the back-stepping technique and universal function approximators, that is, neural networks (NNs), [6][7][8][12][13][14][15][16][17][18] and fuzzy logic systems (FLSs). [19][20][21] However, most of approximation-based back-stepping control techniques focus on strict feedback nonlinear systems [6][7][8][12][13][14][19][20][21] or pure feedback nonlinear systems without the consideration of prescribed performance, [15][16][17][18] and less attention was paid to approximation-based prescribed performance back-stepping control for pure feedback nonlinear systems. In addition, the existing approximation-based back-stepping controllers for pure feedback nonlinear systems remain the problems of approximation errors, "explosion of complexity" and algebraic loop.…”

Section: Discussionmentioning

confidence: 99%

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Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

Chen

Yang

2020

Adaptive Control & Signal

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Summary In this study, an adaptive output feedback control with prescribed performance is proposed for unknown pure feedback nonlinear systems with external disturbances and unmeasured states. A novel prescribed performance function is developed and incorporated into an output error transformation to achieve tracking control with prescribed performance. To handle the unknown non‐affine nonlinearities and avoid the algebraic loop problem, the radial basis function neural network (RBFNN) is adopted to approximate the unknown non‐affine nonlinearities with the help of Butterworth low‐pass filter. Based on the output of the RBFNN, the coupled design between sate observer and disturbance observer is presented to estimate the unmeasured states and compounded disturbances. Then, the adaptive output feedback control scheme is proposed for unknown pure feedback nonlinear systems, where a first‐order filter is introduced to tackle with the issue of “explosion of complexity” in the traditional back‐stepping approach. The boundedness and convergence of the closed‐loop system are proved rigorously by utilizing the Lyapunov stability theorem. Finally, simulation studies are worked out to demonstrate the effectiveness of the proposed scheme.

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Section: Discussionmentioning

confidence: 99%

“…Proof. Based on (10), (11), (12) and the properties of Γ( ), the proof can be derived easily, and thus it is omitted here due to the limited space. ▪…”

Section: Lemma 2 (2) For the Nonlinear Systemmentioning

confidence: 99%

Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

Chen

Yang

2020

Adaptive Control & Signal

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“…To address this problem, as universal approximators, fuzzy logic systems or neural networks have been introduced to approximate the unknown functions [10][11][12][13]. Many adaptive robust state or output feedback controllers have been developed based on fuzzy logic systems or neural networks [14][15][16][17][18][19][20]. However, the problem of 'explosion of terms' was not taken into account, which made the controller design process cumbersome.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Surface Control Using Fuzzy Logic Systems for Uncertain, Strict‐feedback, Nonlinear Systems with Unknown Control Directions

Shi

Chen

2019

IEEJ Transactions Elec Engng

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This paper proposes an adaptive tracking control design procedure for a class of uncertain, strict-feedback, nonlinear systems in the presence of unknown structure uncertainties, external disturbances, and unknown control directions. To stabilize the systems, fuzzy logic systems are utilized to approximate the unknown structure uncertainties, and the weight matrices and the upper bounds of approximation errors of fuzzy logic systems are not supposed to be known a priori. Then, to avoid the problem of 'explosion of terms', a dynamic surface control approach is employed by introducing a first-order low-pass filter. Furthermore, the issue of unknown control directions is solved by inserting the Nussbaum function. In addition, the projection operator is applied in the adaptation laws to guarantee the boundedness of the estimated parameters. Finally, simulation results are presented to show the validity of the proposed control strategy.

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] In spite of highly rich literature, it is surprising to notice that a Lyapunov function is required to obtain the virtual control law and the parameter updated law at each step of the design. In general, backstepping algorithm is taken as a core for control design of nonlinear systems in strict feedback form and is combined with other techniques like adaptive control, fuzzy or neural network control, and sliding mode control to yield some new control methods for both academic and industrial communities.…”

Section: Introductionmentioning

confidence: 99%

“…In general, backstepping algorithm is taken as a core for control design of nonlinear systems in strict feedback form and is combined with other techniques like adaptive control, fuzzy or neural network control, and sliding mode control to yield some new control methods for both academic and industrial communities. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] In spite of highly rich literature, it is surprising to notice that a Lyapunov function is required to obtain the virtual control law and the parameter updated law at each step of the design. As the dimension of systems increases, backstepping implementation becomes increasingly complex.…”

Section: Introductionmentioning

confidence: 99%

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

Zhang

Huang

et al. 2017

Adaptive Control & Signal

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This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding-based technique. As an attractive alternative of the adaptive backstepping method, this bottom-up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower-order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results. KEYWORDS adaptive control, filters, input saturation, mapping filtered forwarding control, uncertain nonlinear systems 248 ;32:248-264. ZHANG ET AL. 249error as z =θ − θ + β(x), where β(x) is a continuous term, and utilizing the uncertainty equivalence principle to design parameter update laws for lower triangular systems. Although researchers used this method to design parameter update laws in some practical systems, the achievements strictly depend on an assumption satisfying the partial differential inequality to obtain β(x). 20,21 In essence, the solvability of this inequality strongly relies on the structure of the regressor, and as system order increases, the implementation will be limited. Therefore, it could not be feasible to achieve I&I adaptive stabilization for high-order nonlinear systems with extended matching uncertainties. 22,23 Furthermore, control input saturation severely limits system performance in many physical systems, giving rise to undesirable properties or leading instability. 24,25 The hyperbolic tangent function is used to approximate the saturated nonlinearity, 12 where the approximated error is considered as an augmented external disturbance. Although this algorithm is easy to be carried out, the problem of the definition domain of artanh(·) is encountered while tuning controller gains. It can be shown that the bound of the nonlinear function we derive must be restricted to (−1, 1). 26 The problem of the controller design for the nonlinear systems with input saturation and parametric uncertainties has not been addressed adequately under a mapping filtered forwarding-based framework.In this paper, we will study the robust adaptive control design for nonlinear systems subject to input saturation and uncertainties under the mapping filtered forwarding-based framework. A new bottom-up control scheme from a manifold's perspective, namely, mapping filtered adaptive forwarding, which consists of virtual control laws and parameter updated laws, will be presented. With the proposed controller architecture, manifolds are guaranteed to be insensitive to uncertainties, and the iss...

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Adaptive robust backstepping control for a class of uncertain dynamical systems using neural networks

Cited by 34 publications

References 39 publications

Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

Adaptive neural prescribed performance output feedback control of pure feedback nonlinear systems using disturbance observer

Dynamic Surface Control Using Fuzzy Logic Systems for Uncertain, Strict‐feedback, Nonlinear Systems with Unknown Control Directions

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

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