This talk will address applications of optimal control theory to dispersive wave equations. We will discuss three technologically relevant experiments, each having its own unique challenge and physical setting including ultra-cold quantum fluids trapped by an external field, paraxial light propagation through a gradient index of refraction, and light propagation in periodic photonic crystals. In each of these settings, the physics can be modeled by dispersive wave equations, and the technological objective is to design the external trapping fields or propagation media such that a high fidelity or degree of coherence of the wave phenomena is achieved.
Finding an optimal control is numerically challenging since this amounts to solving a somewhat high-dimensional nonconvex optimization problem. To efficiently address the nonconvex nature of these problems, the program used is a global, nonconvex search based on a genetic algorithm which is then accelerated by a fast local method based on a projected gradient descent. This methodology is specifically tailored toward maintaining feasibility, via Tikhonov regularization, of implementing the computationally constructed control policies in technologically relevant settings.