<p>This paper investigates the optimal gradient tracking problem for a bilinear vibrating plate system governed by a fourth-order partial differential equation, where the control acts on the velocity term and is assumed to be distributed and bounded in both space and time. To align with practical engineering scenarios, the spatial domain is assumed to be at most three-dimensional. We formulate and analyze an optimal control problem aimed at minimizing a cost functional composed of the deviation between the desired gradient state and the solution of the controlled system, in addition to a regularization term representing the energy expenditure of the control. Using variational analysis and standard convexity arguments, we establish the existence of an optimal control and derive the corresponding first-order optimality system, which characterizes the optimal control. Additionally, we consider and compare two different configurations of admissible control sets: space-dependent and time-dependent distributed control strategies. Numerical simulations are provided to validate the theoretical results and demonstrate the effectiveness of the proposed control approach in achieving accurate gradient tracking.</p>