Energy management of hybrid photovoltaic (PV)-battery systems still serve as a challenging task owing to their complex and nonlinear characteristics, multicomponent structures, and the extensive range of environmental factors disturbing their nominal performance. The hybrid energy system developed in this study encompasses PV arrays, a battery component, one boost converter, and one bidirectional boost converter. In this paper, we propose a novel adaptive robust control framework for the optimal energy management of the PV-battery systems under many operating conditions and subject to unmodelled dynamics. An improved exponential-like adaptive integral sliding mode (EISM) control coupled to neural network approximator is introduced using a multi-rate convergence tweaking mechanism for the sliding surface to improve the transient performance of the closed-loop system. Furthermore, the entire dynamics of the hybrid energy system is considered unknown, unlike the previous studies that only assumed the parametric uncertainties. The global asymptotic stability of the system is guaranteed, and the effectiveness of this novel framework is compared to benchmark studies.