Continuously asymptotic tracking of disturbed interconnected systems with unknown control directions

Recently, the fruitful results on robust control for large-scale interconnected systems have been reported, but most of them are contingent upon “known control directions” and/or only acquire uniformly ultimately bounded performance in the presence of disturbances. Of particular interest in this paper is to develop a continuous and decentralized control algorithm for such systems, which can release the need to know the control directions, guarantee robustness against general system uncertainties (e.g., exogenous disturbances, unknown interactions), and achieve asymptotic output tracking. To this end, we apply a new Nussbaum function to the decentralized controller to identify the control directions despite global interactions. Then resorting to the robust-integral-of-sign-of-error (RISE) technique, we develop a closed-loop system that fully eliminates the effects of the system uncertainties while preserving the control variables’ continuity. Additionally, to synthesize the new Nussbaum function and the RISE method, a second-order filter designed for generating feasible feedback signals is constructed. Lyapunov-based stability analysis and numerical simulations are carried out to validate the robustness and the asymptotic convergence of the interconnected system under the proposed control scheme.