Multiple Lyapunov Functions for Adaptive Neural Tracking Control of Switched Nonlinear Nonlower-Triangular Systems

Niu, Ben; Liu, Yanjun; Zhou, Wanlu; Li, Haitao; Duan, Peiyong; Li, Junqing

doi:10.1109/tcyb.2019.2906372

Cited by 142 publications

(63 citation statements)

References 46 publications

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“…Remark 4. As mentioned in this proof, conditions (8) imply inequality (22). Another necessary condition of (8) apart from 0 ∈ , is obtained from the definition of matrices Ψ i , which leads to inequality…”

Section: Resultsmentioning

confidence: 82%

“…Interestingly, the class of switched affine systems, which is considered in this article, has received less attention. Contributions dealing with the design of stabilizing control laws for switched affine systems expressed as a min-projection control strategy has been considered in the literature for instance in References 12-15 among many others, and even for systems with a general nonlinear form 16,17 and to various extended problems [18][19][20][21][22] . Therein, the proposed control laws may lead to arbitrarily fast switching control updates, also known as Zeno behavior.…”

Section: Introductionmentioning

confidence: 99%

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Robust switching control design for uncertain discrete‐time switched affine systems

Albea-Sánchez

Ventosa‐Cutillas

Seuret

et al. 2020

Intl J Robust & Nonlinear

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This article focuses on the design of a robust switching control law for uncertain switched affine systems in the discrete-time domain. More precisely, a novel control law is introduced whose parameters result from an optimization problem, aiming at reducing the volume of the attractive and invariant set, where the solutions to the closed-loop system converge to. The design is based on a quadratic Lyapunov function and guarantees global practical stabilization, that is, global stabilization in a neighborhood of a desired operating point and robustness with respect to model uncertainties. Our method and the associated relaxed control law are then compared with existing conditions from the literature and are validated through numerical examples.

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Section: Resultsmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Robust switching control design for uncertain discrete‐time switched affine systems

Albea-Sánchez

Ventosa‐Cutillas

Seuret

et al. 2020

Intl J Robust & Nonlinear

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show abstract

“…Now let us solve (9). The auxiliary function is defined aṡy(t) = −b 1 y(t) − ab 2 y (t), y(0) = y 0 , y(t) ≥ 0.…”

Section: System Description and Preliminariesmentioning

confidence: 99%

Almost fast finite‐time adaptive tracking control for a class of full‐state constrained pure‐feedback nonlinear systems

Liu

Niu

Zhao

et al. 2020

Intl J Robust & Nonlinear

Self Cite

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In this article, a novel almost fast finite-time adaptive tracking control scheme is proposed for a class of full-state constrained pure-feedback nonlinear systems based on barrier Lyapunov functions (BLFs). First, by employing the mean value theorem, the pure-feedback systems are converted to the strict-feedback structure with nonaffine terms. Then, by fusing adaptive backstepping technique and BLFs, the design difficulties caused by the nonaffine terms and full-state constraints are overcome. Furthermore, according to the predeveloped almost fast finite-time stability criterion, it is proved that the tracking error can converge to a small compact set and all signals of the closed-loop system can be bounded in an almost fast finite time. Finally, a simulation example of a single-link robot is presented to verify the effectiveness of the proposed control scheme. K E Y W O R D S almost fast finite time control, barrier Lyapunov functions, full-state constraints, pure-feedback nonlinear systems 1 INTRODUCTION In recent decades, due to the wide existence of nonlinear systems in practical engineering applications, nonlinear systems has been widely concerned by researchers in the field of control. However, compared with linear systems, the stability analysis and controller design of nonlinear systems are more difficult and complex. Fortunately, an effective analysis and design tool for nonlinear systems, the backstepping technique, was proposed in Reference 1 first. After this pioneering work, many excellent works have been achieved through the utilization of backstepping technology, such as References 2-7. As we all know, it is inevitable that uncertainties are contained in the practical plants. Nevertheless, the uncertainties in nonlinear systems were not considered in the above works. In order to deal with the uncertain parameters in the nonlinear system, the adaptive backstepping control algorithm was developed by properly designing the adaptive laws. Subsequently, the classical adaptive backstepping control algorithm has been employed to get many important results, for instance, References 8-23. Although these above works have made great contributions to the stability analysis and design of nonlinear systems, they have hardly utilized to the nonlinear pure-feedback systems. The material in this article was not presented at any IFAC meeting.

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“…The resilient controller design problem for regulation of cross movement of an intelligent vehicle was investigated by [6]. In further development, stochastic systems with Markovian jumping parameters and unknown system parameters have attracted much attention, and the tracking control problem of an indeterminate switched nonlinear system with non-lower triangular characteristics using the adaptive neural control algorithm was researched in [7]. The stochastic neural adaptive tracking control problem of an indeterminate switched nonlinear system with a non-strict feedback characteristic was investigated in [8], using the average dwell time approach.…”

Section: Introductionmentioning

confidence: 99%

Robust Adaptive Control for Stochastic Discrete-Time Nonlinear Systems and Application to Gas Engine as an Electric Vehicle Extender

Yang

Zhang

et al. 2020

IEEE Access

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In this paper, the problem of adaptive control with disturbance attenuation is investigated for stochastic discrete-time nonlinear systems with Markovian jumping parameters and unknown system parameters. Using the proposed control law and the sufficient conditions, the closed-loop system achieved ∞ performance. As a practical example of the considered problem, an air-fuel ratio controller for a gas engine intended as an electric vehicle extender is designed based on the proposed adaptive disturbance attenuation control algorithm. The air-fuel ratio controller is validated via a numerical simulation under three working conditions. The results of the numerical simulation show that the air-fuel ratio can be regulated into a range around its desired value by the proposed adaptive disturbance attenuation controller and that the adaptive law can be tuned to a steady value. The control performance indices of the proposed adaptive disturbance attenuation controller are smaller than those of the open-loop controller, which means that the proposed adaptive disturbance attenuation controller achieves a greater control effect.

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Multiple Lyapunov Functions for Adaptive Neural Tracking Control of Switched Nonlinear Nonlower-Triangular Systems

Cited by 142 publications

References 46 publications

Robust switching control design for uncertain discrete‐time switched affine systems

Robust switching control design for uncertain discrete‐time switched affine systems

Almost fast finite‐time adaptive tracking control for a class of full‐state constrained pure‐feedback nonlinear systems

Robust Adaptive Control for Stochastic Discrete-Time Nonlinear Systems and Application to Gas Engine as an Electric Vehicle Extender

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