Constraints driven optimal actuation policies for diffusion processes with collocated actuators and sensors

This work introduces modal model predictive control (MMPC) design methodology in the framework of optimal actuation policies which arise due to the presence of input and state constraints for a class of distributed parameter systems modeled by parabolic PDEs. The predictive control law accounts for input and state constraints and with respect to actuator/sensor position placement it generates an optimal actuation policy that switches applied control action among available pre-specified actuator locations. The proposed constrained predictive control law utilizes a low order modal representation in the optimization functional while higher modes are included only in the PDE state constraints. Accordingly, the proposed control law is formulated by the minimization algorithm whereby optimization is performed over all available preset collocated actuator/sensor positions. In this sense, the minimizing algorithm provides a control law that chooses among best collocated actuator/sensor positions available with respect to the lowest optimal cost among these positions. An example of a diffusion-reaction process, with spatially-uniform unstable steady state, subject to flux boundary conditions is considered.