arXiv subjects

Filippos Vokos

Publications and source records attributed to Filippos Vokos.

4 recordsLinked to original sources

arXiv2024

A Complete Inverse Optimality Study for a Tank-Liquid System

This paper presents a complete inverse optimality study for a linearized tank-liquid system where the liquid is described by the viscous Saint-Venant model with surface tension and possible wall friction. We define an appropriate weak solution notion for which we establish existence/uniqueness results with inputs that do not necessarily satisfy any compatibility condition as well as stabilization results with feedback laws that are constructed with the help of a Control Lyapunov Functional. We show that the proposed family of stabilizing feedback laws is optimal for a certain meaningful quadratic cost functional. Finally, we show that the optimal feedback law guarantees additional stronger stability estimates which are similar to those obtained in the case of classical solutions.

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arXiv2023

Feedback Stabilization of Tank-Liquid System with Robustness to Surface Tension

We construct a robust stabilizing feedback law for the viscous Saint-Venant system of Partial Differential Equations (PDEs) with surface tension and without wall friction. The Saint-Venant system describes the movement of a tank which contains a viscous liquid. We assume constant contact angles between the liquid and the walls of the tank and we achieve a spill-free exponential stabilization with robustness to surface tension by using a Control Lyapunov Functional (CLF). The proposed CLF provides a parameterized family of sets which approximate the state space from the interior. Based on the CLF, we construct a nonlinear stabilizing feedback law which ensures that the closed-loop system converges exponentially to the desired equilibrium point in the sense of an appropriate norm.

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arXiv2022

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

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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arXiv2022

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

We solve the output-feedback stabilization problem for a tank with a liquid modeled by the viscous Saint-Venant PDE system. The control input is the acceleration of the tank and a Control Lyapunov Functional methodology is used. The measurements are the tank position and the liquid level at the tank walls. The control scheme is a combination of a state feedback law with functional observers for the tank velocity and the liquid momentum. Four different types of output feedback stabilizers are proposed. A full-order observer and a reduced-order observer are used in order to estimate the tank velocity while the unmeasured liquid momentum is either estimated by using an appropriate scalar filter or is ignored. The reduced order observer differs from the full order observer because it omits the estimation of the measured tank position. Exponential convergence of the closed-loop system to the desired equilibrium point is achieved in each case. An algorithm is provided that guarantees that a robotic arm can move a glass of water to a pre-specified position no matter how full the glass is, without spilling water out of the glass, without residual end point sloshing and without measuring the water momentum and the glass velocity. Finally, the efficiency of the proposed output feedback laws is validated by numerical examples, obtained by using a simple finite-difference numerical scheme. The properties of the proposed, explicit, finite-difference scheme are determined.

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