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.
Linear Systems I