We investigate pulse shaping and optimization for a laser amplifier. Due to the complex character of the nonlinear PDE dynamics involved in the laser model, it is of interest to consider non-model based methods for pulse shaping. We determine input pulse shapes for an unknown laser dynamics model using iterative learning control (ILC) and high-dimensional extremum seeking (ES), which is a real-time optimization strategy. We utilize ILC to obtain the input pulse shape that generates a desired output pulse shape and ES to find the input pulse that maximizes the energy amplifier gain. Both single-pass and double-pass laser models are investigated. The effectiveness of these approaches is illustrated via numerical simulations.

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