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Recent advancements in model-free deep reinforcement learning have enabledefficient agent training. However, challenges arise when determining the regionof attraction for these controllers, especially if the region does not fullycover the desired area. This paper addresses this issue by introducing afeedback motion control algorithm that utilizes data-driven techniques andneural networks. The algorithm constructs a graph of connectedreinforcement-learning based controllers, each with its own defined region ofattraction. This incremental approach effectively covers a bounded region ofinterest, creating a trajectory of interconnected nodes that guide the systemfrom an initial state to the goal. Two approaches are presented for connectingnodes within the algorithm. The first is a tree-structured method, facilitating"point-to-point" control by constructing a tree connecting the initial state tothe goal state. The second is a graph-structured method, enabling"space-to-space" control by building a graph within a bounded region. Thisapproach allows for control from arbitrary initial and goal states. Theproposed method's performance is evaluated on a first-order dynamic system,considering scenarios both with and without obstacles. The results demonstratethe effectiveness of the proposed algorithm in achieving the desired controlobjectives.

Deep Reinforcement Learning Graphs: Feedback Motion Planning via Neural Lyapunov Verification