Robust adaptive control of nonlinear systems with unknown time delays

Ge, Shuzhi Sam; Fan, Hong; Lee, Tong Heng

doi:10.1109/isic.2004.1387649

Cited by 32 publications

(67 citation statements)

References 14 publications

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“…From a practical point of view, once the system reaches its origin, no control action should be taken for less power consumption. As is hard to detect owing to the existence of measurement noise, it is more practical to relax our control objective of convergence to a "ball" rather than the origin [24].…”

Section: Adaptive Control For First-order Systemmentioning

confidence: 99%

“…Theorem 1: Consider the closed-loop systems consisting of the first-order plant (8) and controller (21), (22), if gain with being a design constant, and is chosen as (24) with constant , and the NN weights are updated by (23), then for bounded initial conditions and , all signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the vector remains in a compact set defined by whose size, , can be adjusted by appropriately choosing the design parameters.…”

Section: Adaptive Control For First-order Systemmentioning

confidence: 99%

“…However, the uncertainties from unknown parameters or unknown nonlinear functions were not discussed. In [24], we studied a class of nonlinear time-delay systems, in which the virtual control coefficients are unknown constants with known sign and the system uncertainties are linearly parametrized with unknown constant parameters and known nonlinear functions. Practical stability was introduced to solve the singularity problem due to the appearance of or in the controller and the tracking error can be made to confine in a compact domain of attraction.…”

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confidence: 99%

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Adaptive Neural Control of Nonlinear Time-Delay Systems With Unknown Virtual Control Coefficients

Fan

Lee

2004

IEEE Trans. Syst., Man, Cybern. B

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Abstract-In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

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Section: Adaptive Control For First-order Systemmentioning

confidence: 99%

Section: Adaptive Control For First-order Systemmentioning

confidence: 99%

mentioning

confidence: 99%

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Adaptive Neural Control of Nonlinear Time-Delay Systems With Unknown Virtual Control Coefficients

Fan

Lee

2004

IEEE Trans. Syst., Man, Cybern. B

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619

180

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“…A notable contribution by Ge et al (2003Ge et al ( , 2005 is the construction of an integral Lyapunov function which is proved to be the key for the success of the approach. A function approximator has been used to describe the unknown nonlinear functions.…”

Section: Introductionmentioning

confidence: 99%

“…A function approximator has been used to describe the unknown nonlinear functions. Two types of artificial neural networks, the linearly parameterized neural networks (Ge et al, 2002(Ge et al, , 2003(Ge et al, , 2005 and the multilayer neural networks (Lewis, 1996), Huang, 2002, andZhang, et al, 1999), have been predominantly used for approximating a wide range of unknown nonlinear functions in control system design.…”

Section: Introductionmentioning

confidence: 99%

A generalized procedure in designing recurrent neural network identification and control of time-varying-delayed nonlinear dynamic systems

Zhang

Zhu

2010

Neurocomputing

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Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

Hashemi

2016

Adaptive Control & Signal

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In this paper, an adaptive dynamic surface control approach is developed for a class of multi-input multioutput nonlinear systems with unknown nonlinearities, bounded time-varying state delays, and in the presence of time-varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time-varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed-loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. of the traditional backstepping design method [32,33]. The problem of 'explosion of complexity' is the complexity of the controller that grows drastically as the order of the system increases. The 'explosion of complexity' is caused by repeated differentiation of certain nonlinear functions.One of the other serious problems that are frequently encountered in many practical control systems and brings uncertainties to the systems is time delays. Because of the effect of time delays, these systems may own instability and poor performance [34]. So far, considerable attention has been devoted to the stability analysis and control design for time delay systems [35][36][37][38][39][40][41][42][43][44]. The existence of time delays renders the actuator failure compensation problem much more complex and difficult. Many valuable research and practical results have been achieved in actuator failure compensation for linear time delay systems [45][46][47][48][49][50][51][52]. To the best of the author's knowledge, relatively, a few papers were published regarding actuator failure compensation for nonlinear time delay systems [53][54][55][56][57][58]. In [53], an adaptive actuator failure compensation scheme was developed for a class of multi-input nonlinear time delay systems with known parameters, nonlinearity, constant delay, constant control gains, and unknown actuator failure parameters. In [54], a robust state feedback controller was presented for time delay multi-input systems with known parameters, known constant control gains, unknown nonlinearity, and unknown constant delays. The proposed robust actuator failure compensator in [54] promised the boundedness of all the signals in the closed-loop system; however, the tracking problem was not considered. In [55][56][57], the adaptive actuator failure compensation schemes were presented for paramet...

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Robust adaptive control of nonlinear systems with unknown time delays

Cited by 32 publications

References 14 publications

Adaptive Neural Control of Nonlinear Time-Delay Systems With Unknown Virtual Control Coefficients

Adaptive Neural Control of Nonlinear Time-Delay Systems With Unknown Virtual Control Coefficients

A generalized procedure in designing recurrent neural network identification and control of time-varying-delayed nonlinear dynamic systems

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

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