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

Léchappé, Vincent; Moulay, Emmanuel; Plestan, Franck

doi:10.1109/cdc.2016.7798606

Cited by 18 publications

(11 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For an arbitrary large τ it may not be possible to find a suitable L, then delay-dependent stability conditions and gains L come to the focus. This problem can be avoided if the estimation is done by small steps as in [25] for constant delay, or as in [26] for time-varying ones, but the number of observers to be implemented may increase drastically. In order to use (2) for constant delay, one must know the length of the delay a priori and store past data from the observer.…”

Section: Motivation and Problem Statementmentioning

confidence: 99%

A Gramian-based observer with uniform convergence rate for delayed measurements

Rueda-Escobedo

Ushirobira²,

Efimov³

et al. 2018

2018 European Control Conference (ECC)

View full text Add to dashboard Cite

The problem of designing an observer for a linear time-invariant system with delayed measurements of the state is revisited in this paper. The delay is assumed to be time-varying with finite unknown lower and upper bounds. A Gramian-based observer is proposed with a fixed-time convergence rate to a ball. The efficiency of the obtained solution is illustrated by a numerical comparison with linear observers (one of which is tuned under the assumption that a nominal value of delay is available).

show abstract

Section: Motivation and Problem Statementmentioning

confidence: 99%

A Gramian-based observer with uniform convergence rate for delayed measurements

Rueda-Escobedo

Ushirobira²,

Efimov³

et al. 2018

2018 European Control Conference (ECC)

View full text Add to dashboard Cite

show abstract

“…This has been a matter of concern for some researchers,() as the discretization of the integral may lead to instability of the closed‐loop. In the work of Zhou et al, a first‐order truncated predictor that ignores the infinite‐dimensional part of the controller was proposed and extended later to include higher‐order terms in the work of Zhou et al An approach that avoids the use of distributed terms by introducing sequential predictors in observer form was introduced in the work of Besançon et al and further developed in the work of Najafi et al The advantage of avoiding distributed terms has been further exploited recently in the works of Léchappé et al, Cacace et al, Mazenc and Malisoff …”

Section: Introductionmentioning

confidence: 99%

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

Sanz

Garcia

Fridman

et al. 2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary The problem of output stabilization and disturbance rejection for input‐delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov‐Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed‐loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.

show abstract

“…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

View full text Add to dashboard Cite

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...

show abstract

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

Cited by 18 publications

References 23 publications

A Gramian-based observer with uniform convergence rate for delayed measurements

A Gramian-based observer with uniform convergence rate for delayed measurements

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

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

Contact Info

Product

Resources

About