Seaweed biomass offers significant potential for climate mitigation, but large-scale, autonomous open-ocean farms are required to fully exploit it. Such farms typically have low propulsion and are heavily influenced by ocean currents. We want to design a controller that maximizes seaweed growth over months by taking advantage of the non-linear time-varying ocean currents for reaching high-growth regions. The complex dynamics and underactuation make this challenging even when the currents are known. This is even harder when only short-term imperfect forecasts with increasing uncertainty are available. We propose a dynamic programming-based method to efficiently solve for the optimal growth value function when true currents are known. We additionally present three extensions when as in reality only forecasts are known: (1) our methods resulting value function can be used as feedback policy to obtain the growth-optimal control for all states and times, allowing closed-loop control equivalent to re-planning at every time step hence mitigating forecast errors, (2) a feedback policy for long-term optimal growth beyond forecast horizons using seasonal average current data as terminal reward, and (3) a discounted finite-time Dynamic Programming (DP) formulation to account for increasing ocean current estimate uncertainty. We evaluate our approach through 30-day simulations of floating seaweed farms in realistic Pacific Ocean current scenarios. Our method demonstrates an achievement of 95.8% of the best possible growth using only 5-day forecasts. This confirms the feasibility of using low-power propulsion and optimal control for enhanced seaweed growth on floating farms under real-world conditions.

翻译：海藻生物质在气候缓解方面具有重要潜力，但需要大规模自主开放式海洋农场才能充分利用这一潜力。此类农场通常推进力较弱且受洋流影响显著。我们旨在设计一种控制器，通过利用非线性时变洋流抵达高生长区域，在数月内最大化海藻生长。即使已知洋流信息，复杂动力学特性与欠驱动性仍使该问题极具挑战性。当仅有短期不完美预测且不确定性随时间递增时，问题难度进一步加剧。我们提出基于动态规划的方法，在真实洋流已知时高效求解最优生长价值函数。此外，针对现实场景中仅掌握预测信息的情况，我们提出三项扩展：（1）将所提方法的价值函数作为反馈策略，获取所有状态与时间下的生长最优控制，实现等效于每时间步重新规划的闭环控制，从而缓解预测误差；（2）利用季节性平均洋流数据作为终端奖励，构建超越预测时域的长周期最优生长反馈策略；（3）提出折扣有限时域动态规划模型，以处理递增的洋流估计不确定性。通过为期30天的太平洋真实洋流场景浮式海藻农场仿真评估，我们的方法在仅使用5日预测数据时实现了最优可能生长的95.8%。这证实了在现实条件下，利用低功率推进与最优控制增强浮式农场海藻生长的可行性。