Approximate optimal influence over an agent through an uncertain interaction dynamic

An approximate optimal indirect regulation problem is considered for two nonlinear uncertain agents. An influencing agent is tasked with optimally intercepting and directing a roaming agent to a goal location. The roaming agent is not directly controlled by the influencing agent, but instead moves based on some uncertain interaction dynamic. To overcome this challenge, a virtual controller is designed to yield a desired influence on the roaming agent. In addition, an approximate dynamic programming (ADP) strategy is used to develop an approximate optimal solution to the optimal control problem using a computationally efficient function approximation method. Because system uncertainties are considered in both agents, a data-based parameter identification method called integral concurrent learning (ICL) is used to identify uncertain dynamics. A Lyapunov-based stability analysis is performed which proves the closed-loop pursuing and roaming agent systems are uniformly ultimately bounded (UUB). Simulation and experimental results are provided to demonstrate the performance of the developed method.