  The present work extends known finite-dimensional constrained optimal control
realizations to the realm of well-posed regular linear infinite-dimensional
systems modelled by partial differential equations. The structure-preserving
Cayley-Tustin transformation is utilized to approximate the continuous-time
system by a discrete-time model representation without using any spatial
discretization or model reduction. The discrete-time model is utilized in the
design of model predictive controller accounting for optimality, stabilization,
and input and output/state constraints in an explicit way. The proposed model
predictive controller is dual-mode in the sense that predictive controller
steers the state to a set where exponentially stabilizing unconstrained
feedback can be utilized without violating the constraints. The construction of
the model predictive controller leads to a finite-dimensional constrained
quadratic optimization problem easily solvable by standard numerical methods.
Two representative examples of partial differential equations are considered.
