Adaptive robust dynamic surface asymptotic tracking for uncertain strict-feedback nonlinear systems with unknown control direction

Shi, Wenrui; Hou, Ming; Hao, Mingrui

doi:10.1016/j.isatra.2021.04.009

Cited by 17 publications

(8 citation statements)

References 58 publications

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“…where l i > 0, θ * i = max β * i 2 with θi being the estimation of θ * i . Submitting (25) into (24), it is obtained easily that:…”

Section: Adaptive Elm Control Methods Designmentioning

confidence: 99%

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Adaptive Dynamic Surface Control for a Class of Time Delay Nonlinear Systems with Extreme Learning Machine

jingyang

Liu

2022

Preprint

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This paper is aimed at investigating the problem of adaptive track- ing control for a class of strict-feedback nonlinear systems with unknown ex- ternal disturbance and time delay. First of all, the original system state equa- tion is transformed into a new form of state equation by coordinate trans- formation. In the next part, extreme learning machine is applied to approx- imate the unknown functions which exist in the whole system states. Based on this, adaptive dynamic surface controller is invented to cope with the dif- ferential explosion problem. In addition, the combination of the control law and the compensation signal of the filter improves the accuracy performance. Lyapunov-Krasovskii functional is introduced to handle the influence of time delay successfully. Subsequently, all signals of the whole closed-loop system can be ultimately uniformly bounded through a series of proofs. In the end, simulation examples are presented to verify the feasibility and effectiveness of the proposed algorithm.

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“…where l i > 0, θ * i = max β * i 2 with θi being the estimation of θ * i . Submitting (25) into (24), it is obtained easily that:…”

Section: Adaptive Elm Control Methods Designmentioning

confidence: 99%

“…In all the control schemes described above, the large-scale parallelism and fast adaptability of NN or FL implementations provide the impetus for further research on dynamic problems involving unknown smooth nonlinear functions [23,24]. In practical applications, some systems that need to be approximated are time-varying.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Dynamic Surface Control for a Class of Time Delay Nonlinear Systems with Extreme Learning Machine

jingyang

Liu

2022

Preprint

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“…The main technical obstacle in the design for stochastic systems is that the Itb o stochastic differentiation involves not only the gradients but also the higher order Hessian terms ð1=2ÞTrfg T ð∂ 2 V =∂x 2 Þgg. In order to handle the Hessian terms conveniently, in the most existing results, the authors used the quartic functions ð1=4Þz 4 to analyze the stability of the systems. In addition, for the stochastic tracking problem, in references 34 and 35, the controllers are designed by using the quadratic Lyapunov function under a risk-sensitive cost criterion.…”

Section: Controller Designmentioning

confidence: 99%

“…In the past decades, the adaptive fuzzy or neural network (NN) control design for uncertain stochastic nonlinear systems has received increasing attention, such as [1][2][3][4]39 many fuzzy problems can be effectively solved by either the homotopy perturbation method 5 or the variational iteration method, 6 both methods were proposed by Chinese mathematician, Dr. Ji-Huan He. 7 Based on Itô stochastic differential equation and backstepping design technique, many adaptive fuzzy control design results obtained for deterministic nonlinear systems were extended to those stochastic nonlinear systems, for example, references.…”

Section: Introductionmentioning

confidence: 99%

Adaptive tracking control for a class of stochastic nonlinearly parameterized systems with time-varying input delay using fuzzy logic systems

Yue

Gong

2022

Journal of Low Frequency Noise, Vibration and Active Control

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This paper addresses the problem of adaptive tracking control for a class of stochastic nonlinear systems with time-varying input delays, and the nonlinear functions of the systems are with not only the unknown parameters but also the unknown state time-varying delays, which is different from the previous work. In this paper, through a state transformation, the system can be easily transformed into a system without the time-varying input delay; the appropriate Lyapunov–Krasovskii functionals are used to compensate the unknown time-varying delay terms, and the quadratic functions instead of the quartic functions often utilized in the existing results are used as Lyapunov functions to analyze the stability of systems and the hyperbolic tangent functions are introduced to deal with the Hessian terms. Fuzzy logic systems (FLSs) in Mamdani type are used to approximate the unknown nonlinear functions. Then, based on the backstepping technique, the adaptive fuzzy controller is designed. The three main advantages of the developed scheme are that (i) unlike the existing results which deal with the nonlinearly parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS; (ii) the number of the adjusted parameters only depend on the order of the investigated systems, which can reduce the computational burden greatly; and (iii) the existence of the time-varying input delay such that the controller design becomes much more difficult, and in this paper, it can be dealt with by using an appropriate state transformation. It is proven that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded in probability, whereas the tracking error converges to a small neighborhood of the origin. Finally, simulation results are provided to show the effectiveness of the proposed approach.

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“…From then on, there have been many outstanding results based on the principle of the DSC method. [6][7][8][9][10][11] In Reference 7, an adaptive neural network DSC method is proposed for full state-constrained nonlinear systems. In Reference 8, the global tracking control with prespecified ultimate tracking accuracy is achieved for semi-strict feedback systems.…”

Section: Introductionmentioning

confidence: 99%

Adaptive dynamic surface asymptotic tracking control of uncertain strict‐feedback systems with guaranteed transient performance and accurate parameter estimation

Shi

Hou

Duan

et al. 2022

Intl J Robust & Nonlinear

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In this article, an adaptive dynamic surface control approach is proposed for uncertain strict-feedback systems (SFSs) to guarantee both the prescribed transient tracking performance and the asymptotic tracking while realizing the accurate parameter estimation. It is assumed that SFSs are subject to linearly parametric uncertainties in both the drift terms and the control coefficients. A new inequality on the arctangent function, which can be widely used in the robust or the adaptive control designs, is established. Owing to this inequality, nonlinear robust filters with arctangent functions are designed and embedded into the backstepping control algorithm to avoid the "differential explosion" problem. Moreover, an improved forgetting-factor-based parameter estimation error reconstruction mechanism is proposed. And the obtained parameter estimation errors are integrated into the adaptive laws to achieve the accurate parameter estimation. Furthermore, the projection operator is applied to avoid the singularity problem of the control law. Besides, an asymmetric error transformation is introduced to restrict the tracking error within the prescribed performance envelope. It is proved that the tracking error and the parameter estimation errors asymptotically converge to zero and the tracking error satisfies the prescribed transient performance. Finally, the effectiveness of the proposed control approach is validated in terms of the single-link manipulator actuated by a brush DC motor.

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Adaptive robust dynamic surface asymptotic tracking for uncertain strict-feedback nonlinear systems with unknown control direction

Cited by 17 publications

References 58 publications

Adaptive Dynamic Surface Control for a Class of Time Delay Nonlinear Systems with Extreme Learning Machine

Adaptive Dynamic Surface Control for a Class of Time Delay Nonlinear Systems with Extreme Learning Machine

Adaptive tracking control for a class of stochastic nonlinearly parameterized systems with time-varying input delay using fuzzy logic systems

Adaptive dynamic surface asymptotic tracking control of uncertain strict‐feedback systems with guaranteed transient performance and accurate parameter estimation

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