# A Complete Inverse Optimality Study for a Tank-Liquid System

arXiv: https://arxiv.org/abs/2405.16535 · HTML: https://mlsanity.com/paper/2405.16535/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2024.

## Built on by (most cited first, 1 of 1)

- [Families of Control-Cost-Parametrized Inverse-Optimal Universal Stabilizers](https://mlsanity.com/paper/2606.09047/) (2026)

## Abstract (arXiv)

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.