Output-feedback control of viscous liquid–tank system and its numerical approximation

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

“…• the functional W is a kind of mechanical energy of the liquid within the tank and has been used extensively in the literature of isentropic, compressible liquid flow (see [22,31,39,40]) as well as in [23][24][25].…”

“…As in [23][24][25] the state space will be appropriately defined in order to exclude states of the set S defined by ( 21) that violate the condition (17), i.e, the states that cause liquid spillage. We define the following…”

“…A robust with respect to wall friction stabilizing feedback law is constructed. Another study which deals with the nonlinear viscous Saint-Venant model is [24]. In [24] a stabilizing output-feedback control law for the viscous Saint-Venant PDE system without wall friction and without surface tension is constructed.…”

“…Another study which deals with the nonlinear viscous Saint-Venant model is [24]. In [24] a stabilizing output-feedback control law for the viscous Saint-Venant PDE system without wall friction and without surface tension is constructed. The output-feedback control law is utilized through a functional-observer methodology and a CLF methodology.…”

“…We achieve a spill-free exponential stabilization, with robustness to surface tension. As in [23][24][25] we follow a CLF methodology and we design the feedback law based on an appropriate functional, which is the CLF. The CLF determines a specific parameterized set which approximates the state space of the control problem from the interior.…”