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Modeling and Control of Spatially Distributed Systems
Course Number: ME245 Edit
Focus Area: Advanced Topics
Quarter (typical): Spring
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.