Asymptotic Regulation of Time-Delay Nonlinear Systems With Unknown Control Directions

Summary The problem of global stabilization by nonsmooth state feedback is investigated for a family of time‐delay nonlinear systems with unknown control direction. Using the idea of the Nussbaum function from universal control, we present a delay‐free, nonsmooth dynamic state feedback strategy to achieve asymptotic state regulation with boundedness of the closed‐loop system. The proposed control scheme allows one to design a set of Lyapunov‐Krasovskii functionals and nonsmooth dynamic compensators simultaneously, by the technique of adding a power integrator. It is shown that while the effects of unknown control direction can be mitigated by the Nussbaum‐type gains, the strong nonlinearity with time delay can be effectively dealt with by nonsmooth state feedback controllers whose gains are updated dynamically.

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“…From Theorem , it is straightforward to deduce the following robust stabilization result obtained in the work of Pongvuthithum et al recently.…”

Section: Asymptotic State Regulation With Stabilitymentioning

confidence: 88%

Nonsmooth feedback stabilization of a class of nonlinear systems with unknown control direction and time delay

Rattanamongkhonkun

Pongvuthithum

Lin

2018

Intl J Robust & Nonlinear

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“…Time‐delay problems can occur in real applications and there have been many studies on global stabilization or regulation of the time‐delay systems, for example, see References 1‐4 and references therein. For example, in Reference 1, they have considered a stabilization problem for an input‐delayed chain of integrators with nonlinearity by state feedback controller where the delay is a constant and upper bound of the delay is known.…”

Section: Introductionmentioning

confidence: 99%

“…In Reference 2, authors have presented an adaptive control method for linear uncertain system with the constant delay for system regulation where the delay is a constant and upper and lower bounds of the delay are known. In Reference 3, they have studied a problem of global regulation for time‐delay nonlinear systems with unknown control direction and uncertain constant parameters. In Reference 4, authors have proposed a predictor‐based feedback controller for the stabilization of multi‐input linear time‐invariant systems with constant input delays where the delays are constants and its upper bounds are known.…”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, uncertain parameters are often encountered in many real systems 12‐16 and they can affect the stability/performance of the controlled systems. In this regard, various control methods for nonlinear systems with uncertain constant parameters have been studied 3,12,14 . For example, in Reference 12, they consider nonlinear systems with uncertain parameters where they assume that upper bounds of the uncertain parameters are known.…”

Section: Introductionmentioning

confidence: 99%

“…In Reference 14, a robust approximate feedback linearization control method for nonlinear systems with uncertain constant parameters associated with main diagonal states and input is proposed. In Reference 3, the problem of global state regulation for time‐delay nonlinear systems with bounded constant parameters is studied. However, uncertain parameters are often time‐varying in practice, for example, the flight aircraft system parameters are time‐varying, 13 the mass of electromagnetic levitation is time‐varying due to the movement of passengers, 15 and the sprung mass of vehicle suspension is slowly varying 16 .…”

Section: Introductionmentioning

confidence: 99%

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Choi

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Summary In this paper, we consider a global regulation problem for a class of feedforward nonlinear systems. The key features of our considered system are identified by the presence of uncertain time‐varying parameters associated with main diagonal states and input and an unknown time‐varying delay in the input. Moreover, the growth rates of nonlinearity and the input‐delay are only known to be finite. To solve our considered problem, we give a process to obtain a compact set that contains the allowed time‐varying parameters. Then, we propose an adaptive controller which handles both unknown growth rate of nonlinearity and input‐delay for system regulation. We carry out the rigorous system analysis and show the effectiveness of our proposed control scheme via an application example.

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Robust adaptive tracking control for nontriangular time‐delay nonlinear systems with input dead‐zone and multiple uncertainties

Xue

Liu

2020

Adaptive Control & Signal

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SummaryThis article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input‐delay. Different from the related studies, the considered systems involve input dead‐zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic‐gain‐based Lyapunov‐Krasovskii functional and by generalizing the tuning function method in the framework of time‐delay system theory. All the states of the closed‐loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.

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Asymptotic Regulation of Time-Delay Nonlinear Systems With Unknown Control Directions

Cited by 48 publications

References 18 publications

Nonsmooth feedback stabilization of a class of nonlinear systems with unknown control direction and time delay

Nonsmooth feedback stabilization of a class of nonlinear systems with unknown control direction and time delay

Adaptive control of feedforward nonlinear systems with uncertain time‐varying parameters and an unknown time‐varying delay in the input

Robust adaptive tracking control for nontriangular time‐delay nonlinear systems with input dead‐zone and multiple uncertainties

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