Backstepping design for a class of coupled parabolic PDEs with spatially varying coefficient

Ghaderi, Najmeh; Keyanpour, Mohammad

doi:10.1002/asjc.2104

Cited by 12 publications

(10 citation statements)

References 28 publications

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“…Lemma 2 (Stability of the target system). Under Assumptions 1, 3, consider system ( 13)- (15), there exists a class  function 𝛽, such that…”

Section: Control Law Design and Stability Analysismentioning

confidence: 99%

“…Based on the predictor control method [11], many achievements have been made in compensating various input delays, such as time-varying input delays [12], state-dependent input delays [13], time-and state-dependent delays [14]. Using the backstepping technique, the original system is transferred to a target system, and a backstepping feedback controller is obtained in [15]. Finite-time convergence disturbance rejection for a flexible timoshenko manipulator is in [16].…”

Section: Introductionmentioning

confidence: 99%

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Predictor control for nonlinear systems actuated via transport PDEs with time/space varying propagation speeds

Cai

Yang

Liu

et al. 2021

Asian Journal of Control

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We consider predictor controls for two kinds of cascaded systems of nonlinear ordinary differential equations (ODEs) and transport partial differential equations (PDEs) with time/space varying propagation speeds. Since the propagation speeds depend on time/space variables, how to get the prediction states of PDEs is a key challenge. We solve this challenge in this paper. We construct two infinite backstepping transformations to transform the original systems into target systems and design predictor controls for these two kinds of cascaded systems, respectively. We prove stability of the closed‐loop systems using Lyapunov‐like arguments and derive alternative representations of cascaded systems as nonlinear systems with time/space varying input delays and also establish equivalent predictor feedbacks for the delay systems.

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“…Lemma 2 (Stability of the target system). Under Assumptions 1, 3, consider system ( 13)- (15), there exists a class  function 𝛽, such that…”

Section: Control Law Design and Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Predictor control for nonlinear systems actuated via transport PDEs with time/space varying propagation speeds

Cai

Yang

Liu

et al. 2021

Asian Journal of Control

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“…e results on radially varying reaction coefficients under revolution symmetry conditions on a sphere for unstable linear reaction diffusion equation using boundary control has been solved in [26]. Recently, Ghaderi and Keyanpour [27] studied the backstepping boundary control approach for multidimensional coupled parabolic PDEs.…”

Section: Introductionmentioning

confidence: 99%

Results on Boundary Control for Parabolic Systems Using Backstepping Method

Mathiyalagan

Renugadevi

Nidhi

2022

Mathematical Problems in Engineering

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This paper focuses on the stabilization problem for the linear parabolic system using the backstepping method. The exponentially stability results for considered parabolic system are derived in two cases with Dirichlet and Neumann local terms. Also, the boundary conditions for the problem is assumed to be mixed or Robin-type boundary conditions. The main aim is to achieve the stability of the considered system using the backstepping method with help of Volterra integral transformation. The explicit solutions of kernel functions in integral transformation is obtained by using Laplace transform and designed a boundary control law to the closed-loop system. Finally, the effectiveness and applicability of the derived results are validated through a single-species pattern generation model.

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“…During the last few decades, asymptotic or exponential stabilization of PDEs has been well investigated (see, e.g., Ghaderi and Keyanpour (2020a2020b, 2020c; Krstic and Smyshlyaev (2008) and references therein). FTS studies of the PDEs are still scarce in comparison with one of asymptotic or exponential PDE stabilization in literature.…”

Section: Introductionmentioning

confidence: 99%

Finite-time boundary stabilization of the reaction-diffusion system with switching time-delay input

Ghaderi

Keyanpour

Mojallali

2021

Transactions of the Institute of Measurement and Control

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The paper is devoted to the study of boundary finite-time control for a reaction-diffusion (RD) system with switching time-delayed input. The RD system with switching time-delay input is converted to a switching system of RD equation cascaded with a transport equation with non-delay boundary input. Next, a novel switching controller is designed for the cascaded RD-transport system based on the backstepping technique, and this causes the closed-loop system to be convergence in a finite-time. Simulation results are provided to exhibit the effectiveness of the proposed method.

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Backstepping design for a class of coupled parabolic PDEs with spatially varying coefficient

Cited by 12 publications

References 28 publications

Predictor control for nonlinear systems actuated via transport PDEs with time/space varying propagation speeds

Predictor control for nonlinear systems actuated via transport PDEs with time/space varying propagation speeds

Results on Boundary Control for Parabolic Systems Using Backstepping Method

Finite-time boundary stabilization of the reaction-diffusion system with switching time-delay input

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