A New Prediction Scheme for Input Delay Compensation in Restricted-Feedback Linearizable Systems

Pasillas-Lépine, William; Lorı́a, Antonio; Hoang, Trong-Bien

doi:10.1109/tac.2016.2531042

Cited by 9 publications

(13 citation statements)

References 23 publications

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“…Since there exists a time delay in the input, the form of the actual control input at time t can be expressed as

ū false(t - h false) = F false(x false(t - h false) false)

, which is dependent on time‐delayed states. Inspired by the work of Pasillas‐Lépine et al, the input delay can be compensated by using the predicted values of the states at time t + h in order to obtain the control input at time t . The whole design procedure is demonstrated as the following steps.…”

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

“…The state prediction error is defined as

p_{1} false(t false) = x_{1}^{p} false(t - h, h false) - x_{1} false(t false) = e_{1}^{p} false(t - h, h false) - e_{1} false(t false),

and can be rewritten as

ė_{1} false(t false) = - α_{1} e_{1} false(t - h false) + e_{2} false(t false) + f_{1} false(x_{1} false(t false) false) - f_{1} false(x_{1} false(t false) + p_{1} false(t false) false) .

The most ideal situation is that the state predictor is able to exactly compute the future state value, ie, p ( t )=0, and accordingly, the term f 1 ( x 1 ( t ))− f 1 ( x 1 ( t )+ p ( t )) in can be viewed as a vanishing perturbation. Based on the dynamical equation , the prediction of e 1 is calculated through the integration of the ideal tracking error dynamics and the state prediction error obtained before the prediction instant, which is expressed as

e_{1}^{p} false(t, h false) = e_{1} false(t false) - α_{1} \int_{t}^{t + h} e_{1} false(τ - h false) normald τ - β_{1} \int_{- \infty}^{t + h} p_{1} false(τ - h false) normald τ + \int_{t}^{t + h} e_{2}^{p} false(τ - h, h false) normald τ,

where β 1 is a positive constant,

e_{2}^{p} false(t, h false)

denotes t...…”

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

“…The most ideal situation is that the state predictor is able to exactly compute the future state value, ie, p(t) = 0, and accordingly, the term (10) can be viewed as a vanishing perturbation. Based on the dynamical equation (10), the prediction of e 1 is calculated through the integration of the ideal tracking error dynamics and the state prediction error obtained before the prediction instant, 24 which is expressed as…”

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

“…where n is a positive constant. Then, the state prediction required in the control law can be computed through the tracking error prediction obtained by (24) and the virtual control law, that is,…”

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

“…Theorem 1. For the nominal system (1) in the strict-feedback form with input time delay, under Assumptions 1 to 3, the state predictors are given as (11), (18), and (24) and the nominal controller is designed as (21). Given the time-delay upper bound h * , if there exist positive constants i , i (1 ≤ i ≤ n), such that…”

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

See 4 more Smart Citations

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

Yan

Sun

Fei

2018

Intl J Robust & Nonlinear

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Summary In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.

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“…Since there exists a time delay in the input, the form of the actual control input at time t can be expressed as

ū false(t - h false) = F false(x false(t - h false) false)

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

“…The state prediction error is defined as

p_{1} false(t false) = x_{1}^{p} false(t - h, h false) - x_{1} false(t false) = e_{1}^{p} false(t - h, h false) - e_{1} false(t false),

and can be rewritten as

ė_{1} false(t false) = - α_{1} e_{1} false(t - h false) + e_{2} false(t false) + f_{1} false(x_{1} false(t false) false) - f_{1} false(x_{1} false(t false) + p_{1} false(t false) false) .

e_{1}^{p} false(t, h false) = e_{1} false(t false) - α_{1} \int_{t}^{t + h} e_{1} false(τ - h false) normald τ - β_{1} \int_{- \infty}^{t + h} p_{1} false(τ - h false) normald τ + \int_{t}^{t + h} e_{2}^{p} false(τ - h, h false) normald τ,

where β 1 is a positive constant,

e_{2}^{p} false(t, h false)

denotes t...…”

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

Section: Nominal Controller Design Using State Prediction Schemementioning

confidence: 99%

See 3 more Smart Citations

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

Yan

Sun

Fei

2018

Intl J Robust & Nonlinear

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show abstract

Adaptive fractional order predictive sliding mode control for congestion control of wireless access networks

Khoshnevisan

Liu

2022

Intl J Robust & Nonlinear

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This article studies congestion control of wireless access networks. In a wireless access network, it is necessary to design a robust active queue management (RAQM) technique to control congestion occurrence and to make the network robust simultaneously against some issues in the wireless link aspects, such as packet error rate (PER) and fading effects. On the other hand, a network is often described by a nonlinear model, in which the delayed packet drop probability is assumed as the input signal. So in this article, a RAQM technique is proposed based on an adaptive fractional order predictive sliding mode control (AFOPSMC) method, through which the following are achieved: (1) the stability of the nonlinear system with input delay is assured, (2) the congestion occurrence is prevented by controlling the queue measurement to the desired value, (3) the robustness against the external disturbances is achieved, and (4) the input signal obtained by the controller is limited between 0 and 1. In contrast to most recently published papers where input delay is ignored in the system description and input saturation is achieved through designing parameters, this article at first proposes a predictor to eliminate the input delay and then designs a compensated system to deal with the input signal constraint. Furthermore, the chattering phenomena, as a commonly caused issue in the sliding mode control, is eliminated based on the adaptive laws designed for the controller parameters. The theoretical results are validated and compared with some other related protocols through numerical simulations using Simulink and professional network simulator 2 (NS2).

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Theory on negative time‐delay looped system

Ravelo

2017

IET Circuits, Devices & Systems

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An innovative theory on the looped system generating negative time delay is presented. Both the direct and delayed feedback loop topologies of this system essentially consist of an independent-frequency gain and time-delay block. It is shown theoretically that for suitable parameters the system can generate a negative time delay by virtue of a negative group delay (NGD). Analytical expressions reveal that the system presents an unconditional low-pass NGD behaviour. The NGD properties as a function of the system parameters are derived. To demonstrate the feasibility of the developed NGD system concept, frequency-and time-domain analyses are performed with Matlab, resulting in a very good agreement between the simulations and theory. Furthermore, as illustrated by computational results, negative time-delay signal propagation (signal advance) is obtained. The proposed NGD system can potentially be useful for time-delay compensation in engineering systems.

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A New Prediction Scheme for Input Delay Compensation in Restricted-Feedback Linearizable Systems

Cited by 9 publications

References 23 publications

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

Adaptive fractional order predictive sliding mode control for congestion control of wireless access networks

Theory on negative time‐delay looped system

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