Optimal control of distributed actuator and sensor arrays

We consider optimal H-2 and H-infinity control design problems for distributed parameter systems with large arrays of sensors and actuators. We assume that the actuator and sensor array forms a regular lattice, and that the underlying dynamics have a property of spatial invariance with respect to shifts in the lattice. We show how Fourier transforms over the spatial domain reduces the optimization to a family of standard, finite-dimensional problems over spatial frequency. The solutions are then obtained by parameterized families of matrix algebraic Riccati equations. Such optimal controllers have a natural decentralized and separation structure which we analyze.