Output-Feedback Control of Viscous Liquid-Tank System and its Numerical Approximation

Karafyllis, Iasson; Vokos, Filippos; Krstić, Miroslav

doi:10.48550/arxiv.2201.13272

Cited by 1 publication

(6 citation statements)

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“…The problem studied in the present work is similar to the problem added in [22] and consequently there are some similarities between the present work and [22] (there are less similarities with [23] since [23] focuses on output feedback laws and numerical aspects). However, there are important differences between the present work and [22].…”

Section: Introductionmentioning

confidence: 89%

“…Another open issue is the construction of numerical schemes for the numerical approximation of the solutions of the closed-loop system. The issue was studied in [23], where we noticed the lack of numerical schemes that can be applied to the closed-loop system. Again, the stability estimates provided in the present work can help the analysis.…”

Section: Proofsmentioning

confidence: 99%

“…The feedback design is performed by employing either the backstepping methodology (see [13,14]) or the Control Lyapunov Functional (CLF) methodology (see [2-4, 9-12, 15, 18, 19, 29]). The only works that study the feedback stabilization problem for the viscous Saint-Venant model without linearization around an equilibrium point are [22,23]. More specifically, in [22,23] a feedback control law is constructed by employing the CLF methodology for the viscous Saint-Venant model without wall friction and surface tension (state feedback in [22] and output feedback in [23]).…”

Section: Introductionmentioning

confidence: 99%

“…The only works that study the feedback stabilization problem for the viscous Saint-Venant model without linearization around an equilibrium point are [22,23]. More specifically, in [22,23] a feedback control law is constructed by employing the CLF methodology for the viscous Saint-Venant model without wall friction and surface tension (state feedback in [22] and output feedback in [23]). In addition [22,23] are the only works that guarantee a spill-free movement of the fluid.…”

Section: Introductionmentioning

confidence: 99%

“…More specifically, in [22,23] a feedback control law is constructed by employing the CLF methodology for the viscous Saint-Venant model without wall friction and surface tension (state feedback in [22] and output feedback in [23]). In addition [22,23] are the only works that guarantee a spill-free movement of the fluid.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Feedback Stabilization of Tank-Liquid System with Robustness to Wall Friction

Karafyllis¹,

Vokos²,

Krstić³

2022

ESAIM: COCV

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We solve the feedback stabilization problem for a tank, with friction, containing a liquid modeled by the viscous Saint-Venant system of Partial Differential Equations. A spill-free exponential stabilization is achieved, with robustness to the wall friction forces. A Control Lyapunov Functional (CLF) methodology with two different Lyapunov functionals is employed. These functionals determine specific parameterized sets which approximate the state space. The feedback law is designed based only on one of the two functionals (which is the CLF) while the other functional is used for the derivation of estimates of the sup-norm of the velocity. The feedback law does not require the knowledge of the exact relation of the friction coefficient. Two main results are provided: the first deals with the special case of a velocity-independent friction coefficient, while the second deals with the general case. The obtained results are new even in the frictionless case.

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