Human-in-the-loop systems with inner and outer feedback control loops: adaptation, stability conditions, and performance constraints

In this paper, we focus on human-in-the-loop physical systems with inner and outer feedback control loops. Specifically, our problem formulation considers that inner loop control laws use a model reference adaptive control approach to suppress the effect of system uncertainties such that the overall physical system operates close to its ideal behavior as desired in the presence of adverse conditions due to failures and/or modeling inaccuracies. Moreover, we consider that the outer loop control laws exist owing to employing either sequential loop closure and/or high-level guidance methods. As it is true in practice, in addition, humans are considered to inject commands directly to the outer loop dynamics in response to the changes in the physical system, where the outer loop commands affect inner loop dynamics in response to the commands received from the humans as well as in response to the changes in the physical system.