Confronted with growing and fluctuating traffic demands, urban transportation system has been encountering mounting challenges in traffic congestion, especially at intersections. With enhanced traffic control precision enabled by the emerging Connected and Automated Vehicle (CAV) technologies, this study proposes a hybrid control strategy for connected and automated traffic at urban intersections, which enables the integration of diverse control schemes to harness their strengths and mitigate their weaknesses. With rolling horizon strategy, a nonlinear optimization model is developed to determine the optimal traffic control plans considering both current status and forthcoming vehicle arrivals. Vehicle delays are elaborately characterized without relying on any empirical assumptions. The original model is converted to a Mixed Integer Programming with Quadratic Constraints (MIP-QC) by employing appropriate linearization techniques, which could be solved by commercial solvers. For the acquisition of instant and reliable solutions, a multilayer feedforward network-based approximate algorithm is developed, referred as Value Approximation Control (VAC) algorithm. Theoretical derivation is provided to validate the capability of VAC algorithm in the precise approximations of the value function in the traffic plan optimization problem, and ultimately enabling to acquire global optimal solutions via specific network design and training techniques. Numerical experiments on both artificial and researcher-collected datasets demonstrate that our proposed VAC algorithm achieves performance nearly equivalent to the mathematical model. Significantly, it outperforms current state-of-art traffic control methods in terms of both intersection throughput and average vehicle delay. Moreover, sensitivity analysis reveals the robustness of the VAC algorithm against inaccuracy in vehicle arrival information, and the stable performance even in the presence of significant disturbances.