Asymptotic state prediction for continuous-time systems with delayed input and application to control

Besançon, Gildas; Duby, Georges; Benayache, Zohra

doi:10.23919/ecc.2007.7068540

Cited by 79 publications

(69 citation statements)

References 12 publications

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“…This may impose a limitation on some applications such as control over networks where the delay function ϕ(t) is generally discontinuous. A dynamic inversion procedure [23] may be an alternative approach for tackling this limitation.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…However, the computation of the prediction term could be challenging as it involves online integration of nonlinear functions. In [23], an asymptotic prediction approach based on an observed prediction computed by a dynamic system has been proposed for the control of linear time-invariant systems and also, as an extension, has been applied for the control of Lipschitz nonlinear systems with constant input delay. This dynamic observation prediction could avoid the inconvenience of the computation of the prediction.…”

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confidence: 99%

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Truncated Predictor Control of Lipschitz Nonlinear Systems With Time-Varying Input Delay

Zuo

Lin

Ding

2017

IEEE Trans. Automat. Contr.

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Abstract-This paper deals with control design for Lipschitz nonlinear systems with time-varying input delay. Based on a truncated prediction of the system state over the delay period, both a state and an output feedback control law are constructed. Within the framework of Lyapunov-Krasovskii functionals, a set of conditions are identified under which the closed-loop system under either the state feedback or the output feedback law is globally asymptotically stable at the origin. A numerical example is included to demonstrate the effectiveness of the proposed designs.

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Section: Problem Statement and Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

Truncated Predictor Control of Lipschitz Nonlinear Systems With Time-Varying Input Delay

Zuo

Lin

Ding

2017

IEEE Trans. Automat. Contr.

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“…The idea is similar to the one presented in [14] and [18]. However, it is extended to the time-varying delay case.…”

Section: Sub Observers-predictorsmentioning

confidence: 85%

“…This step has to be done very carefully since it can destabilize the system as pointed out in [13]. A prediction approach based on an approximated prediction computed thanks to a dynamic system has been proposed for the first time in [14] for the control of input delay systems. The advantage is that no discretization is required to compute the prediction.…”

Section: Introductionmentioning

confidence: 99%

Dynamic observation-prediction for LTI systems with a time-varying delay in the input

Léchappé

Moulay

Plestan

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-A predictive-based controller is proposed to control LTI systems in presence of time-varying delay in the input. The control method is based on the computation of an approximated (or asymptotic) prediction thanks to a dynamic system. Then, this prediction is "plugged" into any Lipschitz controller that stabilizes the delay-free system. Explicit conditions that guarantee the closed-loop stability are given thanks to a Lyapunov-Krasovskii analysis. A qualitative analysis of these conditions is performed and the results are illustrated in simulation.

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“…However, the predictor-based controllers involve integral terms of the control input, which result in difficulties in control implementation. To avoid the use of distributed terms, asymptotic prediction or dynamic prediction method is developed in [17] for system with constant input delay and the results are then extended to time-varying delay case in [18]. An other feasible solution is to ignore the troublesome integral part, and use the prediction based on the exponential of the system matrix, which is known as the Truncated Prediction Feedback (TPF) approach [19]- [24].…”

Section: Introductionmentioning

confidence: 99%

Control scheme for LTI systems with Lipschitz non‐linearity and unknown time‐varying input delay

Wang

Ding

2017

IET Control Theory & Applications

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Abstract:In this paper, we propose a control structure for a class of systems with Lipschitz nonlinearity and unknown time-varying input delay. This scheme considers the worst case scenario in control design with Truncated Prediction Feedback (TPF) approach, and takes into account the information of the lower bound of delay in the stability analysis. A finite-dimensional controller is constructed, requiring neither the nonlinear function nor the exact delay function. The truncated prediction deviation is minimized by employing the delay range, and then bounded by integral construction and related techniques. Within the framework of LyapunovKrasovskii functionals, sufficient delay-range-dependent conditions are derived for the closed-loop system to guarantee the global stability. Two numerical examples are given to validate the proposed control design. IntroductionIn Note that all the results above are built based on the assumption that the exact delay information is known, which may be irrealizable in many circumstances. The predictor-based feedback control methods suffer from a difficulty in practical implementation when the delay function is unknown. A Lyapunov-based adaptive control design is presented in [25] to deal with unknown constant delay for a class of linear systems. However, few results are available on stabilization for nonlinear systems with unknown time-varying input delay. The TPF control also encounters the same barrier since the prediction is based on the exact knowledge of the delay function [19]-[24].Inspired by the above observation and based on our previous results [26]-[30], in this paper, we propose a control scheme for a class of systems with unknown time-varying input delay and Lipschitz nonlinearity. The key contributions include: (i) in contrast to [13,16,[21][22][23], we propose a new control structure by merely using the delay upper bound, which greatly reduces the computation burden and improves the practical implementation; (ii) we extend the results on the truncated predictor feedback for linear systems to a class of Lipschitz nonlinear systems with unknown time-varying input delay and the derived conditions are less conservative with respect to the existing results [24]; (iii) the information of the lower bound of delay is taken into account in the stability analysis, which benefits the derived conditions. The remainder of this paper is organized as follows. Section 2 presents the problem formulation and a few preliminary results for the stability analysis. Section 3 presents the main results on the controller design and stability analysis. Simulation results are given in Section 4. Section 5 concludes the paper. Problem statement and preliminariesWe consider the systeṁwhere x(t) ∈ R n is the state, u(t) ∈ R p is the input, A ∈ R n×n and B ∈ R n×p are constant matrices with (A, B) being controllable, ζ(t) is a continuously differentiable function that incorporates the actuator delay, and ϕ : R n → R n , ϕ(0) = 0, is a Lipschitz nonlinear function with a Lipschitz constant γ. Fo...

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Asymptotic state prediction for continuous-time systems with delayed input and application to control

Cited by 79 publications

References 12 publications

Truncated Predictor Control of Lipschitz Nonlinear Systems With Time-Varying Input Delay

Truncated Predictor Control of Lipschitz Nonlinear Systems With Time-Varying Input Delay

Dynamic observation-prediction for LTI systems with a time-varying delay in the input

Control scheme for LTI systems with Lipschitz non‐linearity and unknown time‐varying input delay

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