This thesis investigates the application of alternating maximisation for active wake control in wind farms, focusing on both numerical static yaw optimisation and multi-agent deep reinforcement learning for dynamic yaw control. As the size and number of offshore wind farms continue to grow, effectively mitigating wake effects ---~where the airflow behind a turbine is disturbed, reducing the efficiency of downstream turbines~--- becomes increasingly important to maximise power output and ensure economic profitability.

Current numerical strategies are either sub-optimal, as they do not leverage the shape of the optimisation surface well, or expensive to optimise due to the computational demands of high-fidelity simulations. Similarly, current reinforcement learning approaches are too sample inefficient on contemporary wind farms of 40+ turbines to learn high-quality policies and likely suffer from credit assignment problems, other agents performing exploration, and relative over-generalisation. Alternating maximisation emerges as a promising candidate to address these challenges by providing an efficient and potentially more effective optimisation method.

In static yaw optimisation, the research analysed the effects of wind direction, wind speed, turbine layout, and yaw misalignment on the optimisation surface. Key findings indicate that Nash equilibria are transient and significantly influenced by these factors.

The sampling-based approach to alternating maximisation outperformed other methods, proving robust against variations in initial yaw configurations and optimisation orders. This approach required fewer samples and appears suitable for practical applications.

For dynamic yaw control, alternating maximisation with policy gradients demonstrated greater sample efficiency compared to distributed policy gradient methods. However, convergence to sub-optimal policies was common due to limited exploration capabilities. An oscillating exploration strategy enabled effective exploration of yaw angles, leading to high-quality policies.

The study primarily focused on farm power output, neglecting structural loading and leading-edge erosion. Future research should integrate these factors and explore dynamic yaw control under time-varying wind conditions.

Overall, alternating maximisation shows potential in enhancing wind farm performance through efficient optimisation strategies. Future work should refine these methods and address identified limitations to maximise practical applicability.