Adaptive Control for a Class of Nonlinear Time-Delay System Based on the Fully Actuated System Approaches

Ning, Pengju; Chen, Hua; Ma, Rui

doi:10.1007/s11424-022-2019-2

Cited by 26 publications

(12 citation statements)

References 26 publications

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“…In this section, we propose an adaptive controller design based on the HOFA systems approach to stabilize the systems (9). Then, the system stability is established by the Lyapunov-Krasovskii function analysis.…”

Section: Controller Designmentioning

confidence: 99%

“…Theorem 1. Suppose that Assumptions 1-4 hold for systems (9), the adaptive controller can be designed in the following form:…”

Section: Controller Designmentioning

confidence: 99%

“…Proof. Firstly, substituting u d = −A 0∼n−1 z (0∼n−1) − u * into the time-delay nonlinear HOFA systems (9), one can easily obtain the closed-loop system as…”

Section: Controller Designmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive control of time‐delay nonlinear HOFA systems with unmodeled dynamics and unknown dead‐zone input

Zhang

Wang

Chen

2022

Intl J Robust & Nonlinear

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This paper focuses on the control problem of time-delay nonlinear high-order fully actuated (HOFA) systems with unmodeled dynamics and unknown dead-zone input. The primary objective of this paper is to design an adaptive controller by using the HOFA systems approach. To do so, we need to tackle some technical obstacles. Firstly, in order to deal with unmodeled dynamics in the HOFA systems, the technique of changing the supply rate is combined with the HOFA systems approach. Secondly, an adaptive dead-zone inverse is constructed to compensate for the influence of the unknown asymmetrical dead-zone input nonlinearity. Then, the controller is designed by the HOFA systems approach, and it is proved that all states of the systems converge to a bounded region based on the Lyapunov-Krasovskii functions. Finally, the simulation results demonstrate the effectiveness of the designed adaptive controller. K E Y W O R D Sadaptive controller designs, dead-zone input, fully actuated nonlinear systems, time-delay systems, unmodeled dynamics INTRODUCTIONIn recent years, the HOFA systems approach has received much attention, 1-7 which has been proven to be very effective and simple in dealing with the analysis and control problems of second-order or higher-order nonlinear systems such as Lagrangian systems, angular momentum, inverted pendulum systems, and so forth. A significant advantage of this approach is that a linear constant closed-loop system with an arbitrary assignable eigenstructure can be obtained, and all the design degrees of freedom existing in the closed-loop system are provided. Therefore, the feature helps to deal with many nonlinear system control problems, such as robust control, 3 adaptive control, 4 robust adaptive control, 5 disturbance attenuation 6 and disturbance decoupling. 7 On the basis of the study above, Liu 8 investigated the control problem of HOFA nonlinear systems with time-varying delays in the discrete-time domain. The problem of adaptive control for a class of time-delay systems was studied by the HOFA systems approach, 9 and a continuous adaptive controller was designed for the system. However, among the above results, it should be pointed out that there is still content for development based on the HOFA systems approach to deal with nonlinear problems such as nonlinear time-delay, unmodeled dynamics and dead-zone input, and so forth. It is well known that time-delay is widespread in the practical control systems, such as electrical power systems, communication systems, teleoperation systems, chemical reactor systems, and so forth. [10][11][12] Besides, as we all know, many systems cannot be accurately modeled due to certain factors when dealing with the control problems of practical physical systems, so we often encounter nonlinear systems with unmodeled dynamics. The existence of time-delay

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Section: Controller Designmentioning

confidence: 99%

“…Theorem 1. Suppose that Assumptions 1-4 hold for systems (9), the adaptive controller can be designed in the following form:…”

Section: Controller Designmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive control of time‐delay nonlinear HOFA systems with unmodeled dynamics and unknown dead‐zone input

Zhang

Wang

Chen

2022

Intl J Robust & Nonlinear

Self Cite

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“…As a very common physical phenomenon, time delay widely exists in various dynamic systems, such as islanded microgrid, maglev vehicles, mobile manipulator and so on [40][41][42]. For time delay, the future evolution usually depends on both the current state and explicitly the past values, which often causes unexpected transient response of the system and even causes instability [43]. It should be pointed out that in the process of stability analysis, the unknown term with time delay must be considered as a key factor [44].…”

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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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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“…At this point, the controller of HOFA time-delay system is given, so that the linear system with ideal characteristic structure is obtained [15]. Subsequently, for the strict feedback nonlinear time-delay system, an adaptive controller based on the HOFA system method is proposed to ensure the system asymptotically stable [16].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Asymptotic stabilization of Uncertain Nonstrict Feedback Nonlinear HOFA Systems with Time Delays

Zhao

Zhang

2022

Preprint

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We consider the adaptive control for the nonstrict-feedback uncertain nonlinear high-order fully actuated (HOFA) systems with either uncertain constant delay or time-varying delay. Different from the previous works, the most difficult point is that the uncertain nonlinear function in the HOFA systems contains nonstrict feedback form and time delay in system states. In order to overcome this difficulty, the arbitrary approximation property of the radial basis function neural network (RBF NN) is used to estimate the unknown nonlinear functions. What’s more, the nonstrict-feedback form is transformed into strict-feedback strcture by using the property of Gaussian function. In addition, the appropriate Lyapunov-Krasovskii functions and separation techniques are used to compensate the effect of the unknown constant time delay or time-varying delay. Based on the HOFA system approaches, two adaptive NN controllers are proposed to ensure the system with constant time-delay and time-varying delay to be stabilized asymptotically, respectively. Finally, the proposed control strategies are applied to the thermoacoustic instability systems to demonstrate the feasibility and effectiveness of the obtained results.

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Adaptive Control for a Class of Nonlinear Time-Delay System Based on the Fully Actuated System Approaches

Cited by 26 publications

References 26 publications

Adaptive control of time‐delay nonlinear HOFA systems with unmodeled dynamics and unknown dead‐zone input

Adaptive control of time‐delay nonlinear HOFA systems with unmodeled dynamics and unknown dead‐zone input

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

Adaptive Asymptotic stabilization of Uncertain Nonstrict Feedback Nonlinear HOFA Systems with Time Delays

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