In this paper, an industrial grade adaptive control scheme is proposed for a micro-grid integrated dual active bridge driven battery management system (DIBMS). A benchmark industrial grade adaptive control scheme depends on two factors namely robustness and computational resource utilization when such controllers are implemented over processors. The mathematical model of DIBMS system is nonlinear, thus for desired response, non-linear controllers based on sliding mode variable structure control theory suits it well for the state regulation problem of DIBMS, however such controllers utilize high computational resources when practically implemented over processors. Keeping in view the above performance indices, this paper proposes an industrial grade computationally efficient and finite time adaptive robust convergent control for DIBMS system. A proportional integral (PI) scheme is used as central control unit and Hebbian algorithm with double integration of the state error is introduced for online tuning the gains of central control unit. The robustness and computational resource efficiency of the proposed control paradigm is validated using a laboratory scale test bench through TI Launchpad (TMS320F28379D). The superiority of the proposed AI based PI control paradigm is compared with classical PI, integer order sliding mode control (SMC), and fractional order SMC (FOSMC) in terms of computational resource utilization and robustness under all test conditions.