Predictor-Feedback Prescribed-Time Stabilization of LTI Systems With Input Delay

Espitia, Nicolás; Perruquetti, Wilfrid

doi:10.1109/tac.2021.3093527

Cited by 27 publications

(14 citation statements)

References 44 publications

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“…A periodic predictor-based control was involved in (Karafyllis, 2005) to stabilise a class of nonlinear triangular systems with time-delays. The fixed-time stabilisation problem of LTI TDSs with constant input delays was solved in (Zhou, Michiels, & Chen, 2021;Espitia & Perruquetti, 2021). In (Espitia & Perruquetti, 2021), a PDE-based predictor-based controller was designed for LTI systems in the canonical controllability form: the trajectories of the system are steered onto a fixed-time stable target system by virtue of a new Volterra backstepping transformation with time-varying kernel function and that is an upgraded version of (28).…”

Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

“…The fixed-time stabilisation problem of LTI TDSs with constant input delays was solved in (Zhou, Michiels, & Chen, 2021;Espitia & Perruquetti, 2021). In (Espitia & Perruquetti, 2021), a PDE-based predictor-based controller was designed for LTI systems in the canonical controllability form: the trajectories of the system are steered onto a fixed-time stable target system by virtue of a new Volterra backstepping transformation with time-varying kernel function and that is an upgraded version of (28). In (Zhou et al, 2021), an act-and-wait periodic predictor-based control, state-feedback and outputfeedback, of general LTI TDSs was proposed to guarantee the fixed-time stability; the control law is smooth and robust to slight model uncertainties.…”

Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

“…In (Zhou et al, 2021), an act-and-wait periodic predictor-based control, state-feedback and outputfeedback, of general LTI TDSs was proposed to guarantee the fixed-time stability; the control law is smooth and robust to slight model uncertainties. Moreover, the main advantage of (Zhou et al, 2021) over (Espitia & Perruquetti, 2021) is the avoidance of singularity, i.e. the control law of (Zhou et al, 2021) will not tend towards infinity when the prescribed convergence time approaches.…”

Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

“…Future research topics. In the future, the robust finite-time/fixed-time predictor-based controllers could be further investigated: the robustness of the control laws was not discussed in (Moulay et al, 2008;Karafyllis, 2005;Espitia & Perruquetti, 2021), and the fixed-time stability of (Zhou et al, 2021) is readily degraded to exponential stability under model uncertainties. Therefore, preserving the finite-time/fixed-time stability of TDSs despite model uncertainties and external disturbances will be a valuable topic for future researches.…”

Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

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Predictor-based control of time-delay systems: a survey

Deng

Léchappé

Moulay

et al. 2022

International Journal of Systems Science

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With the developments of wireless data communication and network technology, time-delays are widely found in nowadays' control systems, e.g. networked control systems, mobile robot systems, and multiagent systems. Predictor-based control is an effective method dealing with long time-delays because it can generally lead to a delay-free closed-loop system by introducing a prediction for future states. Recently, various predictor-based control methods have been developed for numerous control systems subject to different time-delays, which motivates this survey. This paper presents a comprehensive review of the up-to-date results on the predictor-based control of time-delay systems. Firstly, the ordinary differential equation-based approaches for designing and analysing predictor-based controllers are summarised. Secondly, one reports an alternative method of predictor-based control, in which the systems/controllers are understood in the sense of partial differential equations. Next, several integration-free predictor-based controllers are introduced: by abandoning the infinite-dimensional integral terms, the control laws become easier to realise in practice. Hereafter, the paper discusses the real-time implementations and the practical applications of predictor-based control methods to several particular control systems. Finally, this paper suggests some new trends of predictor-based control for future research.

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Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

Section: Finite-time and Fixed-time Predictor-based Controllersmentioning

confidence: 99%

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Predictor-based control of time-delay systems: a survey

Deng

Léchappé

Moulay

et al. 2022

International Journal of Systems Science

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“…The system with input delay should be linear. In 2021, N. Espitia modeled the input delay as a transport PDE, and the cascade PDE-ODE system was built [40]. A predictor-feedback prescribed-time controller was designed for a linear system with input delay.…”

Section: Introductionmentioning

confidence: 99%

A pattern‐based controller for a class of production processes with input delay

Wang

Pan

2022

Asian Journal of Control

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For the problem of stabilizing a non‐Newton mechanical system with input delay, a pattern‐based state‐feedback controller is proposed. At the beginning of the paper, pattern‐based dynamic description is introduced, and a discrete‐time state‐space model with input delay (DSMID) is obtained from the description method. Then based on the DSMID, an augmentation state‐space model without input delay is built by using the lifting technique. A stabilization method is put forward, and the relationship between stability and the feature of output‐class partition is given. At last, two simulations are carried out to demonstrate the effectiveness of the proposed method.

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Sliding mode control for disturbance rejection and estimation under measurement delay with PDE‐backstepping predictor

Pinto,

Oliveira,

Rodrigues

et al. 2023

Intl J Robust & Nonlinear

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In this article, we address the disturbance rejection problem for linear plants with delayed measured output. The output delay is allowed to be time‐varying and of arbitrary duration. The disturbances that may represent actuator faults are generated by an exogenous dynamic system and can be matched or unmatched. A predictor–based observer is designed via the PDE–backstepping (Partial Differential Equation–backstepping) method so that an estimate of the current state vector, as well as that of unmeasured disturbance, can be obtained. These estimates are used in to regulate the output and reject the disturbance by output feedback sliding mode control. In addition, a solution for finite‐time disturbance rejection (rather than exponential only) is also introduced when the sensor delay is constant. Numerical examples illustrate the performance and robustness of the both proposed predictor‐feedback control systems.

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Predictor-Feedback Prescribed-Time Stabilization of LTI Systems With Input Delay

Cited by 27 publications

References 44 publications

Predictor-based control of time-delay systems: a survey

Predictor-based control of time-delay systems: a survey

A pattern‐based controller for a class of production processes with input delay

Sliding mode control for disturbance rejection and estimation under measurement delay with PDE‐backstepping predictor

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