Examples and motivation, connections and equivalences between finite and infinite dimensional systems, Carleman and Lie-Koopman linearizations. Abstract evolution equations, regularity, well posedness and semi-groups. Stability and spectral conditions. Controllability/Observability, optimal control, norms, and sensitivities of infinite dimensional systems. Approximation and numerical methods. Symmetries, arrays and spatial invariance, transform methods. Swarming, Flocking and large Multi-vehicle systems. Hydrodynamic stability and transition to turbulence.

Modelling, dynamics and control of spatially distributed systems such as those described by partial differential equations and dynamical systems on lattices. The emphasis will be on linear, constructive and algebraic techniques. The material in the course will be strongly motivated by physical examples. Prototype problems from spatially distributed arrays of dynamical systems and hydrodynamic stability will be used to illustrate the theory.