Finite Time Lyapunov Exponent Analysis of Model Predictive Control and Reinforcement Learning

Trajectory planning in an unsteady flow field is an important problem for intelligent mobile agents, with applications including environmental monitoring and data collection [1-6]. When planning trajectories, many applications aim at achieving certain objectives ranging from reaching a static goal location to maintaining certain connectivity of a multi-agent sensor network for part of or the entire the mission [7, 8]. Optimization and control are often employed in designing the decisionmaking algorithms on-board the mobile agents, enabling offline or real-time trajectory planning to achieve the desired objectives. Intelligent algorithms that leverage the background flow are necessary, since naively using full propulsion while aiming at a target can result in wasteful trajectories and the potential of the vehicle being swept away by large currents at a later time. However, even with on-board algorithms, it is still imperative to carefully choose the deployment locations since the agent's ability to reach certain regions is largely determined by its actuation limits and the background flow dynamics. For example, it might be impossible for two groups of agents that are dominated by close-by, but different flow structures, to rendezvous. Furthermore, tuning the hyperparameters of an on-board control strategy to obtain the best performance is a challenging task. The ability to summarize and visualize the dependence of the control performance on the control hyperparameters may aid in this process.