Single Agent Indirect Herding via Approximate Dynamic Programming

An approximately optimal herding problem is considered for a single herder and single target agent. The problem is called indirect herding because the target agent's movements are only indirectly controlled through interaction with the herding agent. To address this challenge, a virtual controller is used to yield a desired influence, inspired by backstepping methods. Approximate dynamic programming (ADP) is used to develop an approximate optimal solution. To facilitate the ADP development, integral concurrent learning is used along with a novel state following kernel for computational efficiency. A Lyapunov-based stability analysis is performed which proves the closed-loop herder and agent systems are uniformly ultimately bounded (UUB).