The brain is a nonlinear and highly Recurrent Neural Network (RNN). This RNN is surprisingly plastic and supports our astonishing ability to learn and execute complex tasks. However, learning is incredibly complicated due to the brain's nonlinear nature and the obscurity of mechanisms for determining the contribution of each synapse to the output error. This issue is known as the Credit Assignment Problem (CAP) and is a fundamental challenge in neuroscience and Artificial Intelligence (AI). Nevertheless, in the current understanding of cognitive neuroscience, it is widely accepted that a feedback loop systems play an essential role in synaptic plasticity. With this as inspiration, we propose a computational model by combining Neural Networks (NN) and nonlinear optimal control theory. The proposed framework involves a new NN-based actor-critic method which is used to simulate the error feedback loop systems and projections on the NN's synaptic plasticity so as to ensure that the output error is minimized.