Adaptive Dynamic Surface Control of a Class of Nonlinear Systems With Unknown Direction Control Gains and Input Saturation

Jian-jun, MA; Zhang, Zhiqiang; Li, Peng

doi:10.1109/tcyb.2014.2334695

Cited by 212 publications

(112 citation statements)

References 42 publications

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“…Remark 8. In the work of Ma et al, 40 the simulation results show that good tracking performance is reached in the case that the amplitude of the control input is over 300. However, the amplitude of control input is less than 40 in the simulation results of this paper.…”

Section: Examplementioning

confidence: 90%

“…This assumption is also given in many existing results. 37,38,40 g i,0 and g i,m are only used for the propose of stability analysis, and their real values are not used in the controller design.…”

Section: Assumptionmentioning

confidence: 99%

“…Since the filtering errors are not considered, a precise performance is hardly tracked with the existing results. [29][30][31]40 By introducing the error compensating variables 1 , 2 , … , n , the effect of ( 2 − 2 ), ( 3 − 3 ), … , ( n − n ) can be eliminated in this paper.…”

Section: The Infringements Of Full State Constraints Can Be Avoidedmentioning

confidence: 99%

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A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

Liu

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.

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Section: Examplementioning

confidence: 90%

Section: Assumptionmentioning

confidence: 99%

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A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

Liu

et al. 2019

Intl J Robust & Nonlinear

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“…To cope with the complexity problem, the dynamic surface control (DSC) approach was proposed by Swaroop et al, which introduces a first-order low pass filter at each design step to prevent the derivative of nonlinear functions. 3 After more than 10 years of development, the DSC design framework has enjoyed widespread applications in various types of dynamical systems, ranging from linear systems, [4][5][6] to strict-/semi-strict feedback uncertain systems, [7][8][9][10][11][12][13] to pure-feedback or nonaffine systems, [14][15][16][17][18] to constrained systems, [19][20][21][22] and to many more complex systems such as fault-tolerant systems, 23,24 stochastic systems, 25,26 and large-scale interconnected systems. [27][28][29][30] Very recently, to deal with the unmodeled dynamics and state constraints, a neural network (NN) DSC approach was proposed for a class of strict-feedback systems in the work of Zhang et al, 31 and later, this method was extended to pure-feedback systems in other work of Zhang et al 32 Xia et al 33 proposed adaptive DSC (ADSC) scheme for stochastic pure-feedback nonlinear systems with state and input unmodeled dynamics.…”

Section: Introductionmentioning

confidence: 99%

An improved adaptive dynamic surface control approach for uncertain nonlinear systems

Zhang

Duan

Hou

2018

Adaptive Control & Signal

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Dynamic surface control (DSC) was developed to eliminate the "explosion of complexity" problem in backstepping procedure. However, as demonstrated in this paper, the obtained results by the existing DSC technique are somewhat conservative, which may pose difficulties in system debugging for realistic applications. This work addresses a modification that yields an improved adaptive DSC approach for tracking control of a class of semi-strict feedback systems. The new method introduces nonlinear adaptive filters instead of the first-order low pass ones to avoid repeatedly differentiating the virtual control signals. Meanwhile, novel flat zone introduced Lyapunov functions, which have dead zones in the prespecified neighborhood of the origin, are employed to design and analyze the improved robust adaptive control law. As a result, the developed control scheme exhibits three distinct features in comparison with the existing DSC strategy as follows: (1) global rather than semiglobal tracking is achieved even in the presence of nonlinear function nonlinearities; (2) the ultimate tracking accuracy can be exactly known before the controller is implemented; and (3) the ranges of the design parameters to guarantee the closed-loop stability and ultimate tracking accuracy can be completely determined a priori, and the design parameters can be freely chosen from the feasible ranges to improve the control performance. Finally, two examples are presented to confirm the effectiveness of the established approach.

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“…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 Dynamic Surface Control of a Class of Nonlinear Systems With Unknown Direction Control Gains and Input Saturation

Cited by 212 publications

References 42 publications

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

An improved adaptive dynamic surface control approach for uncertain nonlinear systems

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

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