This paper proposes a distributed finite-time coordination and tracking control framework for partially shaded photovoltaic (PV) arrays. The considered architecture combines a sampled-data outer coordination layer with a continuous-time inner tracking layer in order to improve global power extraction under nonuniform irradiance conditions. At the local level, each PV submodule is equipped with an artificial neural network (ANN) that provides a fast estimate of a baseline operating voltage from irradiance and temperature measurements. To move beyond purely local maximum power point tracking (MPPT) operation, a distributed finite-time observer is developed so that every agent reconstructs the sampled total array power using only neighbor-to-neighbor communication. Based on this shared information, a cooperative projected-ascent command-update law is introduced to refine the ANN initialization and generate improved voltage commands through a regularized sampled objective. In the inner loop, a reference filter and a robust sliding-mode controller are designed to guarantee accurate voltage tracking despite bounded modeling uncertainty and disturbances. Theoretical outputs determine the possibility of finite-time recovery of the sampled total power, the monotonicity and stationarity of the distributed command-update law, and the finite-time convergence to the sliding manifold and exponential tracking of the filtered command. Simulation studies carried out on a four-agent partially shaded PV array confirm the effectiveness of the proposed framework. Specifically, the distributed observer converges within the prescribed coordination interval, the cooperative outer layer monotonically improves the sampled cooperative objective, and the overall closed-loop architecture delivers an average power gain of $13.4079$ across the tested irradiance scenarios. These findings indicate that the proposed distributed architecture provides a flexible and reliable solution for cooperative MPPT in partially shaded PV systems.