We focus on the Lyapunov-based output feedback control problem for a class of distributed parameter systems with spatiotemporal dynamics described by input-affine linear and semilinear dissipative partial differential equations (DPDEs). The control problem is addressed via model order reduction. Galerkin projection is applied to discretize the DPDE and derive low-dimensional reduced order models (ROMs). The empirical basis functions needed for this discretization are recursively computed using adaptive proper orthogonal decomposition (APOD). To update the basis functions during process operation, APOD needs measurements of the system state's complete profile (called snapshots) at revision times. This paper's main objective is to minimize the demand for snapshots from the spatially distributed sensors by the control structure while maintaining closed-loop stability and performance. A control Lyapunov function is defined, and its value is monitored as the system evolves. Only when the value violates a closed-loop stability threshold, snapshots are requested for a brief period by APOD after which the ROM is updated, and the controller is reconfigured. The proposed approach is applied to stabilize the Kuramoto–Sivashinsky equation.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Modeling and Simulation
- Computer Science Applications
- Industrial and Manufacturing Engineering