Design of pseudo-predictor feedback for neutral-type linear systems with both state and input delays

Zhou, Bin; Liu, Qingsong; Michiels, Wim

doi:10.1016/j.automatica.2019.108502

Cited by 12 publications

(13 citation statements)

References 36 publications

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“…where ψ, φ and µ are defined by (20), (12) and (25), respectively. As system (35) is a cascade of the usual transport equation and wave equation, it is well known that there exists a unique solution (ε(…”

Section: Controller Designmentioning

confidence: 99%

“…where ψ, φ and µ are defined by (20), (12) and (25), respectively. Now, it is easy to verify that such a defined (u(…”

Section: Controller Designmentioning

confidence: 99%

“…However, the problem of output tracking with input delay has little results. But the stabilization problem of input time-delay systems has been studied in [18]- [20]. Hence, motivated by [21,Ch.…”

Section: Introductionmentioning

confidence: 99%

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Performance Output Tracking for a One-Dimensional Wave Equation With Input Delay

Liu

2019

IEEE Access

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This paper is concerned with the performance output regulation problem for a wave equation with input delay and unmatched disturbance. Firstly, in the case of time delay, the input delay term is translated into a first-order hyperbolic equation and we obtain a cascade system. By applying the method of auxiliary trajectory, the unmatched disturbance is compensated and eliminated. Then, we design a state feedback controller. Meanwhile, with the measured error signal, we construct an observer for the cascade system. Based on the observer, an error feedback controller is developed by replacing the states with their estimations. By using Lyapunov functional method, we also prove the regulation error goes to zero exponentially. Thus, the problem of output tracking is solved for the wave equation in despite of input delay and unmatched disturbance. Finally, the numerical simulations are presented to validate the theoretical results. INDEX TERMS Wave equation, output regulation, time delay, unmatched disturbance.

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Section: Controller Designmentioning

confidence: 99%

“…where ψ, φ and µ are defined by (20), (12) and (25), respectively. Now, it is easy to verify that such a defined (u(…”

Section: Controller Designmentioning

confidence: 99%

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Performance Output Tracking for a One-Dimensional Wave Equation With Input Delay

Liu

2019

IEEE Access

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“…Intrinsically, the reduction or predictor controllers require some memory to store the past input values. Although there is the recent result that allows some unknown delay using the reduction controller in Reference 11, this result only considers linear systems.…”

Section: Introductionmentioning

confidence: 99%

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

Choi

2020

Adaptive Control & Signal

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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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“…Finite-dimensional controllers involving a closed-loop system matrix for a linear system with a single input delay also appeared in Cacace, Germani, & Manes (2014) for achieving partial spectrum assignment, and in Carravetta, Palumbo, & Pepe (2013) for solving the infinite horizon optimal control problem. Different from Cacace, Germani, & Manes (2014) and Carravetta, Palumbo, & Pepe (2013), the idea of PPF in Zhou (2014b) also allows to establish memory/infinite-dimensional controllers for linear systems with multiple pointwise and distributed input delays Zhou & Cong, 2016), and for neutral time-delay systems with both input and state delays (Zhou, Liu, & Michiels, 2019).…”

Section: Introductionmentioning

confidence: 99%

Pseudo predictor feedback stabilisation of linear systems with both state and input delays

Zhang

Zhou

Michiels

2020

International Journal of Control

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This paper is concerned with the stabilization of linear systems with both input and state delay by utilizing the predictor based delay compensation method. A pseudo predictor feedback control scheme is proposed, where the targeted closed-loop system is used for the prediction. This avoids the explicit dependence of the control input on past input data, and related instability problems in the implementation of the control law. It is proved that the stability of the closed-loop system is determined by the stability of the target closed-loop system, along with the stability of an associated integral delay system, which describes the additional dynamics induced by the pseudo predictor. In the considered case where the input delay is larger than the state delay the control law explicitly depends on the fundamental matrix of the system. It is shown that in case of commensurate delays, the control law can be directly expressed as a function of the original system matrices, while the stability of the integral delay system can be connected with the stability of an associated system with discrete delay, widening the applicability of analysis and design tools. For the synthesis of the feedback gains, a numerical procedure is presented to solve the simultaneous stabilization problem of the target system and the associated integral delay system. Numerical experiments are carried out to illustrate the effectiveness of the methodology.

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Design of pseudo-predictor feedback for neutral-type linear systems with both state and input delays

Cited by 12 publications

References 36 publications

Performance Output Tracking for a One-Dimensional Wave Equation With Input Delay

Performance Output Tracking for a One-Dimensional Wave Equation With Input Delay

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

Pseudo predictor feedback stabilisation of linear systems with both state and input delays

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