An adaptive control scheme based on the multi-dimensional Taylor network(MTN) is proposed for multi-input multi-output(MIMO) non-linear uncertain time-varying systems with noise disturbances, and two MTNs are used to implement optimal control and nonlinear filtering respectively. Firstly, the MTN controller(MTNC) is proposed to realize real-time tracking control, and the closed-loop errors between the filtered outputs and expected values are taken as the inputs of the MTNC. According to the errors caused by the system uncertainties and based on the stable learning rate, the adaptive variable step size algorithm via linear reinforcement is designed to update the MTNC's weights rapidly. Then, the MTN filter(MTNF) is proposed to eliminate the measurement noises. Since the Lyapunov function of the errors between the measured values and MTNF outputs is defined, the adaptive MTN filtering system has the unique properties of both the MTN and Lyapunov-theory-based adaptive filtering(LAF) system. The MTNF outputs can be asymptotically convergent to the desired signals by selecting the appropriate weight law in the sense of Lyapunov. The convergence and stability of the MTNF are proved. Finally, the simulation results verify the effectiveness of the proposed scheme.