Volume 28, 2022
|Number of page(s)||35|
|Published online||23 December 2022|
Feedback Stabilization of Tank-Liquid System with Robustness to Wall Friction
Department of Mathematics, National Technical University of Athens,
2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA
* Corresponding author: email@example.com
Accepted: 9 November 2022
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.
Mathematics Subject Classification: 35K10 / 93D20 / 93C20
Key words: Saint-Venant model / shallow water equations / feedback stabilization / Control Lyapunov Functional / PDEs
© The authors. Published by EDP Sciences, SMAI 2022
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