(57b) Boundary Predictive Control of Diffusion-Reaction Processes with State and Input Constraints

This work focuses on boundary predictive control of linear parabolic PDEs with input and state constraints. In contrast to our previous work [1] which has addressed predictive control subject to distributed actuation, the present work considers actuation entering at the boundary of the spatial domain. In particular, the evolution of a linear parabolic PDE is initially given by an abstract evolution equation in an appropriate Hilbert space. Modal decomposition techniques are used to decompose the infinite dimensional system into an interconnection of a finite-dimensional (slow) subsystem with an infinite-dimensional (fast) subsystem. The predictive controller synthesis is then formulated in a way that the construction of the cost functional accounts only for the weighted evolution of the slow (finite-dimensional) states, while in the state constraints a high-order (finite-dimensional) approximation of the fast states is utilized. An example of boundary control of a diffusion-reaction process, with spatially-uniform unstable steady state, subject to flux boundary conditions is considered. Simulation results demonstrate successful application of the proposed predictive control technique with infinite-dimensional closed-loop system stability and the state constraint being enforced at a point of the spatial domain that is far from the boundary where the control is implemented on the process.

S. Dubljevic, N. H. El-Farra, P. Mhaskar and Panagiotis D. Christofides, ``Predictive Control of Parabolic PDEs with State and Control Constraints'',IEEE Trans. Automat. Contr., (provisionaly accepted), 2004