Output Feedback Control of Parabolic PDE Systems with Input Constraints

This paper proposes a methodology for output feedback control of parabolic PDE systems with input constraints. Initially, Galerkin’s method is used for the derivation of a finite-dimensional ODE system that captures the dominant dynamics of the PDE system. This ODE system is then used as the basis for the synthesis, via Lyapunov techniques, of stabilizing bounded output feedback control laws that use only measurements of the outputs and provide, at the same time, an explicit characterization of the set of admissible control actuator locations that can be used to guarantee closed-loop stability for a given initial condition. Precise conditions that guarantee stability of the constrained closed-loop parabolic PDE system are provided. The proposed output feedback design is shown to recover, asymptotically, the set of stabilizing actuator locations obtained under state feedback, as the separation between the fast and slow eigenvalues of the spatial differential operator increases.