Truncated predictor feedback for linear systems with long time-varying input delays

Zhou, Bin; Lin, Zongli; Duan, Guang‐Ren

doi:10.1016/j.automatica.2012.06.032

Cited by 269 publications

(176 citation statements)

References 30 publications

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“…We first recall the truncated predictor feedback method [34], [35]. Consider an input-delayed systeṁ…”

Section: Preliminary Resultsmentioning

confidence: 99%

“…The resulting prediction is referred to as the truncated prediction [34]. The truncated prediction feedback method, which was originally developed for single linear systems [35]- [37], was later further developed for nonlinear systems [38], and for application in linear multi-agent systems [39], [40], where the open-loop dynamics of the agents is required to not exponentially unstable.…”

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confidence: 99%

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consensus control of multi‐agent systems with input delay and directed topology

Wang

Ding

2016

IET Control Theory & Applications

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In this study, the consensus problem for linear multi-agent systems with general directed graph in the presence of constant input delay and external disturbances is addressed. To deal with input delay, a truncated prediction of the agent state over the delay period is approximated by the finite dimensional term of the classical state predictor. The truncated predictor feedback method is used for the consensus protocol design. By exploring certain features of the Laplacian matrix, the H ∞ consensus analysis is put in the framework of Lyapunov analysis. The integral terms that remain in the transformed systems are carefully analyzed by using Krasovskii functional. Sufficient conditions are derived for the multi-agent systems to guarantee the H ∞ consensus in the time domain. The feedback gain is then designed by solving these conditions with an iterative LMI procedure. A simulation study is carried out to validate the proposed control design.

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“…We first recall the truncated predictor feedback method [34], [35]. Consider an input-delayed systeṁ…”

Section: Preliminary Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

consensus control of multi‐agent systems with input delay and directed topology

Wang

Ding

2016

IET Control Theory & Applications

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“…The works in [22][23][24] elaborate on the limitations of the finite spectrum assignment. Authors of [25] and [26] propose truncated output feedback controllers for linear systems and a class of Lipschitz nonlinear systems, respectively, to avoid implementation problems. Truncated output feedback controllers safely ignore the infinite dimensional term.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Prediction‐Based Control for Nonlinear Systems with Input Delay

Estrada-Sanchez

Velasco-Villa

Rodriguez-Cortes

2017

Mathematical Problems in Engineering

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This work has two primary objectives. First, it presents a state prediction strategy for a class of nonlinear Lipschitz systems subject to constant time delay in the input signal. As a result of a suitable change of variable, the state predictor asymptotically provides the value of the state units of time ahead. Second, it proposes a solution to the stabilization and trajectory tracking problems for the considered class of systems using predicted states. The predictor-controller convergence is proved by considering a complete Lyapunov functional. The proposed predictor-based controller strategy is evaluated using numerical simulations.

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“…The TPF approach originates from the low gain feedback technique [19]. In [21], it is shown that a TPF controller works for an arbitrarily large delay as long as the open loop linear system is not exponentially unstable. The result is then extended to general linear systems in [22], including exponentially unstable open loop poles.…”

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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Truncated predictor feedback for linear systems with long time-varying input delays

Cited by 269 publications

References 30 publications

consensus control of multi‐agent systems with input delay and directed topology

consensus control of multi‐agent systems with input delay and directed topology

Prediction‐Based Control for Nonlinear Systems with Input Delay

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

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