Fault-tolerant control of fluid dynamic systems via coordinated feedback and switching

Abstract

This work addresses the problem of designing a fault-tolerant control system for fluid dynamic systems modeled by highly-dissipative partial differential equations (PDEs) with constrained control actuators. The proposed approach is predicated upon the idea of coordinating feedback controller synthesis and switching between multiple, spatially-distributed control actuator configurations. Using appropriate finite-dimensional approximations of the PDE system, a stabilizing feedback controller is designed for a given actuator configuration, and an explicit characterization of the constrained stability region is obtained. Switching laws are then derived, on the basis of these stability regions, to orchestrate the switching between the control actuator configurations, in a way that guarantees constraint satisfaction and preserves closed-loop stability of the infinite-dimensional system in the event of actuator failures. The results are demonstrated through an application of the proposed methodology to the suppression of wave formation in falling liquid films via the stabilization of the zero solution of the one-dimensional Kuramoto–Sivashinsky equation (KSE), with periodic boundary conditions, subject to actuator constraints and failures.