Boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction–diffusion systems

Espitia, Nicolás; Polyakov, Andrey; Efimov, Denis; Perruquetti, Wilfrid

doi:10.1016/j.automatica.2019.02.013

Cited by 86 publications

(54 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, the numerical method is introduced to solve them, which expands the choice range of system parameters and kernel PDEs (not limited to kernel PDEs with explicit solutions). (2) Robustness to a small perturbation in diffusion coefficients: The most striking feature in stability robustness analysis is that we prove the robustly Mittag-Leffler stability of the closed-loop system with the proposed output feedback controller, which is also nontrivial for integer-order PDE systems [20], [21].…”

Section: Contributionmentioning

confidence: 94%

Stabilization and Stability Robustness of Coupled Non-Constant Parameter Time Fractional PDEs

et al. 2019

View full text Add to dashboard Cite

This paper considers observer-based output feedback stabilization and stability robustness against small diffusivity perturbations of coupled time fractional partial differential equations (PDEs) with space-dependent (non-constant) parameters. Herein, the plant is equipped with the only available measurement at x = 0 and actuation at x = 1. By backstepping transformation, the well-posedness of the kernel matrix PDE and the observer gains are obtained. Then an output feedback controller is introduced and the Mittag-Leffler stability of the closed-loop system is proved by the fractional Lyapunov method. Robustness analysis of diffusion coefficients uncertainty (with a small perturbation in the diffusion coefficient) is also provided. The output feedback stabilization of the closed-loop system is tested by a numerical example. INDEX TERMS Coupled time fractional PDEs, output feedback boundary stabilization, uncertainty analysis, space-dependent coefficients.

show abstract

Section: Contributionmentioning

confidence: 94%

Stabilization and Stability Robustness of Coupled Non-Constant Parameter Time Fractional PDEs

et al. 2019

View full text Add to dashboard Cite

show abstract

“…For infinite dimensional systems, namely partial differential equations (PDEs), these non-asymptotic concepts have been of great interest and some contributions can be highlighted for 1D hyperbolic and parabolic PDEs: see e.g. [19], [5], [2], [5], [7], [6], [8], [22], [20]. For systems in both finite and infinite dimension, the need to meet some performance, time constraints and precision has highly motivated the stabilization and estimation in finite, fixed and prescribedtime.…”

Section: Introductionmentioning

confidence: 99%

Prescribed-time predictor control of LTI systems with input delay

Espitia

Perruquetti

2020

2020 59th IEEE Conference on Decision and Control (CDC)

Self Cite

View full text Add to dashboard Cite

This paper deals with the problem of prescribedtime stabilization of controllable linear systems with input delay. The problem is reformulated under a cascade PDE-ODE setting from which a prescribed-time predictor feedback is designed based on the backstepping approach, and whose transformation makes use of time-varying kernels. The bounded invertibility of the transformation is guaranteed. It is proved that the solution converges to the equilibrium in a prescribed-time. A simulation example is presented to illustrate the results.

show abstract

“…In the scope of parabolic distributed parameter systems, the finite-time control has become a hot research area [11][12][13][14]. In contrast to the lumped parameter systems, the problems of the fixed-time control and the fixed-time observer design of parabolic distributed parameter systems have not achieved a sufficient level of maturity [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the fixed-time concept of lumped parameter systems was extended to the distributed parameter systems which are modeled by partial differential equations. For example, in Espitia et al [16], the problem of the boundary state feedback for fixed-time stabilisation of a distributed parameter system with constants coefficient by backstepping methods is presented based on Song et al [7] and Coron and Nguyen [13]. On the basis of Smyshlyaev and Krstic [31], the explicit representation of solution of the kernel equations is carried out by employing the generalised Lagueree polynomials and the modified Bessel function.…”

Section: Introductionmentioning

confidence: 99%

Fixed‐time stabilisation of boundary controlled linear parabolic distributed parameter systems with space‐dependent reactivity

Bao

Cui

Lou

et al. 2020

IET Control Theory & Appl

View full text Add to dashboard Cite

The problems of state feedback and output feedback for fixed‐time stabilisation of a linear parabolic distributed parameter system with space‐dependent reactivity are considered by means of continuous backstepping approach and Lyapunov method. First, the invertible Volterra integral transformation with time dependent gain kernel is adopted to convert the original system into a fixed‐time stable target system with time‐dependent coefficient. The well‐posedness of the resulting kernel equations is proved by the method of successive approximation. Then a state feedback controller is designed to guarantee fixed‐time stabilisation of the closed‐loop system. Moreover, a fixed‐time observer is considered to estimate the state of the original system on the basis of the measurement signal at the boundary. Based on this observer, a observer‐based output feedback controller is established to fixed‐time stabilise the closed‐loop system in a prescribed time by using separation principle. Finally, a numerical simulation is provided to verify the feasibility of the proposed theoretical results by using the modified Ablowitz‐Kruskal‐Ladik scheme.

show abstract

Boundary time-varying feedbacks for fixed-time stabilization of constant-parameter reaction–diffusion systems

Cited by 86 publications

References 31 publications

Stabilization and Stability Robustness of Coupled Non-Constant Parameter Time Fractional PDEs

Stabilization and Stability Robustness of Coupled Non-Constant Parameter Time Fractional PDEs

Prescribed-time predictor control of LTI systems with input delay

Fixed‐time stabilisation of boundary controlled linear parabolic distributed parameter systems with space‐dependent reactivity

Contact Info

Product

Resources

About