On Feedback Design for Systems with an Agent in the Loop

Systems with agents in the loop introduce new challenges in feedback design due to the dynamic and spatial constraints imposed by the agents’ movement and actuation capabilities. In this work, we develop a structured framework for designing feedback matrices in such systems while ensuring stability and optimal performance. We formalize the problem by incorporating controllability constraints arising from the agents’ limited ability to actuate at specific locations over time. Our approach leverages a periodic resampling of the system dynamics, allowing for the use of standard feedback design techniques while accounting for the time-varying nature of agent-actuated control. Furthermore, the computation of invariant sets that guarantee constraint satisfaction throughout the execution of the agents’ paths is also addressed. The developed methods are validated on a benchmark system where mobile agents actuate on interconnected subsystems.