$L_gV$ -Type Adaptive Controllers for Uncertain Non-Affine Systems and Application to a DC-Microgrid with PV and Battery

Adaptive control of general nonlinear systems with nonlinear parameterization is studied in this paper. Under the assumptions that the system has stable free dynamics and satisfies controllability-like conditions characterized by the Lie brackets of affine vector fields, it is proved that there exist $L_gV$ -type adaptive controllers that not only asymptotically regulate the state of the nonlinearly parameterized system but also guarantee global stability of the closed-loop system. The design of $L_gV$ -type adaptive controllers is also included. Applications of the proposed adaptive control scheme are presented, including an interesting case of a dc-microgrid with photovoltaic (PV) and battery system.