This paper proposes an approximation strategy for solving the Linear Quadratic Tracking problem that is both forward and local in time. The approach leverages the known form of the value function and a time reversal transformation to address boundary condition consistency. Experimental results are provided to demonstrate the performance of the proposed solution compared to the optimal solution. Additionally, it is shown that the proposed solution is a valid alternative to model predictive control strategies, significantly reducing computational burden. Finally, the presented results enable the possibility of using optimal control to formulate learning strategies for a class of recurrent neural networks.