Adaptive control of unactuated dynamical systems through interconnections: Stability and performance guarantees

This article studies control and performance enforcement for a class of uncertain dynamical systems that consist of actuated and unactuated portions physically interconnected to each other. The proposed approach stabilizes the overall interconnected system in the presence of unknown physical interconnections as well as system uncertainties. Performance guarantees are enforced, individually, on the actuated as well as unactuated portions of the interconnected system via this approach. For enforcing these performance guarantees, a set-theoretic model reference adaptive control approach is used, in conjunction with linear matrix inequalities, to restrict the respective system error trajectories of the actuated and unactuated dynamics inside a priori, user-defined compact sets. The efficacy of the proposed approach is demonstrated using simulations.