An output feedback control structure is proposed for processes in the presense of disturbance and incomplete state information. It combines moving horizon estimation (MHE) and model predictive control (MPC), where Carleman approximation is employed to reduce the nonlinear process plant model and then pair and streamline the computations between the two components. After Carleman approximation, the CMHE/CMPC pair reduces the dynamic optimization problem using analytical expressions for the cost functionals and constraints. CMHE provided state estimates become the initial conditions for CMHE to decide the optimal control signals. With these signals continuously updated in the process model used in CMHE, the state estimates accuracy increases. Analytical gradient vectors and Hessian matrices are supplied to the CMHE/CMPC pair to further reduce computation expenses. We present case studies on a nonlinear CSTR system to show the improvement in computational efficiency with the proposed CMHE/CMPC pair.