Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: A Razumikhin functional method

Yu, Zhensheng; Du, Haibo

doi:10.1016/j.neucom.2010.12.030

Cited by 53 publications

(49 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the control literature, strict-feedback, pure-feedback, and stochastic nonlinear systems are frequently encountered [1][2][3][4][5]. In addition, there exist several real systems described by non-integer-order differential equations such as [6] regular variation in thermodynamics, viscoelastic systems, dielectric polarization, electrical circuits, biological and financial systems, electromagnetic waves, heat conduction in a semi-infinite slab, robotics, biophysics, and so on.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the existing controls in [2,8,10,11,40,62], the adaptive fuzzy control laws presented in [47][48][49] have solved the tracking problem for nonlinear uncertain discrete-time systems with unknown control direction and input nonlinearities (such as dead zone, backlash-like hysteresis, and backlash), by using the reinforcement learning algorithm. • Uncertainty: In most practical situations, the systems under control are unknown or partially unknown [4,7,12,13,17,19,22,31,42,56,57,61]. These facts require specific control tools to deal with the controller design process, being one of the most extended ones the adaptive control paradigm.…”

Section: Introductionmentioning

confidence: 99%

“…• Delays: Furthermore, in many practical control systems, delays are generally encountered [1, 3-5, 27-30, 39, 41, 53, 54, 63]. In fact, the existence of delays causes poor performance and even instability of the system under control [3][4][5]. The Lyapunov-Krasovskii method and the Lyapunov-Razumikhin method are usually employed to perform the stability analysis and controller design for time-delay systems [1,[3][4][5]27].…”

Section: Introductionmentioning

confidence: 99%

“…In fact, the existence of delays causes poor performance and even instability of the system under control [3][4][5]. The Lyapunov-Krasovskii method and the Lyapunov-Razumikhin method are usually employed to perform the stability analysis and controller design for time-delay systems [1,[3][4][5]27]. Compared with the Krasovskii technique, the Lyapunov-Razumikhin technique is applied to many timedelay systems such that the control design and the stability analysis can be relatively simple [1,[3][4][5] and without the usual assumption that the derivative of the delay terms must be less than unity.…”

Section: Introductionmentioning

confidence: 99%

“…The Lyapunov-Krasovskii method and the Lyapunov-Razumikhin method are usually employed to perform the stability analysis and controller design for time-delay systems [1,[3][4][5]27]. Compared with the Krasovskii technique, the Lyapunov-Razumikhin technique is applied to many timedelay systems such that the control design and the stability analysis can be relatively simple [1,[3][4][5] and without the usual assumption that the derivative of the delay terms must be less than unity. Moreover, the Lyapunov-Krasovskii functionals which are always composed by quadratic and integral functions have been extended for analyzing the nonlinear fractionalorder systems in [1,3,39,63].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Zouari

Boulkroune

Ibeas

et al. 2016

Neural Comput & Applic

View full text Add to dashboard Cite

This paper focuses on the adaptive neural output feedback control of a class of uncertain multi-input-multioutput nonlinear time-delay non-integer-order systems with unmeasured states, unknown control direction, and unknown asymmetric saturation actuator. Thus, the mean value theorem and a Gaussian error function-based continuous differentiable model are used in the paper to describe the unknown asymmetric saturation actuator and to get an affine model in which the control input appears in a linear fashion, respectively. The design of the controller follows a number of steps. Firstly, based on the semigroup property of fractional-order derivative, the system is transformed into a normalized fractional-order system by means of a state transformation in order to facilitate the control design. Then, a simple linear state observer is constructed to estimate the unmeasured states of the transformed system. A neural network is incorporated to approximate the unknown nonlinear functions while a Nussbaum function is used to deal with the unknown control direction. In addition, the strictly positive real condition, the Razumikhin Lemma, the frequency-distributed model, and the Lyapunov method are utilized to derive the parameter adaptive laws and to perform the stability proof. The main advantages of this work are that:(1) it can handle systems with constant, time-varying, and distributed time-varying delays, (2) the considered class of systems is relatively large, (3) the number of adjustable parameters is reduced, (4) the tracking errors converge asymptotically to zero and all signals of the closed-loop system are bounded. Finally, some simulation examples are provided to demonstrate the validity and effectiveness of the proposed scheme.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Zouari

Boulkroune

Ibeas

et al. 2016

Neural Comput & Applic

View full text Add to dashboard Cite

show abstract

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

Shahvali

Askari

2016

Adaptive Control & Signal

View full text Add to dashboard Cite

In this paper, an adaptive neural output-feedback control approach is considered for a class of uncertain multi-input and multi-output (MIMO) stochastic nonlinear systems with unknown control directions. Neural networks (NNs) are applied to approximate unknown nonlinearities, and K-filter observer is designed to estimate unavailable system's states. Due to utilization of Nussbaum gain function technique in the proposed approach, the singularity problem and requirement to prior knowledge about signs of high-frequency gains are removed, simultaneously. Razumikhin functional method is employed to deal with unknown state time-varying delays, so that the offered control approach is free of common assumptions on derivative of time-varying delays. Also, an adaptive neural dynamic surface control is developed; hence, explosion of complexity in conventional backstepping method is eliminated, effectively. The boundedness of all the resulting closed-loop signals is guaranteed in probability; meanwhile, convergence of the tracking errors to adjustable compact set in the sense of mean quartic value is also proved. Finally, simulation results are shown to verify and clarify efficiency of the offered approach.

show abstract

Finite‐time adaptive fuzzy tracking control for stochastic nonlinear systems with time‐delay via output‐feedback

Lei

Tao

et al. 2023

Adaptive Control & Signal

View full text Add to dashboard Cite

In this paper, the finite‐time adaptive fuzzy tracking control issue for stochastic nonlinear systems with time‐delay via output‐feedback is studied. Firstly, a state observer and fuzzy logic systems with infinite approximation capability are utilized to estimate the unmeasured states and identify unknown nonlinear characteristics, respectively. Then, a finite‐time adaptive fuzzy tracking controller is devised by the backstepping technology. It is shown that the presented control scheme can ensure the finite‐time square stability of the stochastic nonlinear systems with time‐delay, that is, the output tracking error converges to a sufficiently small neighborhood around the origin in finite‐time, and all signals of the closed‐loop system are bounded. Finally, the effectiveness of the presented control strategy is illustrated via two simulation examples.

show abstract

Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: A Razumikhin functional method

Cited by 53 publications

References 27 publications

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Observer-based adaptive neural network control for a class of MIMO uncertain nonlinear time-delay non-integer-order systems with asymmetric actuator saturation

Adaptive neural dynamic surface control of MIMO stochastic nonlinear systems with unknown control directions

Finite‐time adaptive fuzzy tracking control for stochastic nonlinear systems with time‐delay via output‐feedback

Contact Info

Product

Resources

About