<p>The article shows the use of nonlinear optimal control for the design of a missile’s longitudinal autopilot. This approach enables to stabilize the 2-DOF dynamic model of a tail-controlled missile that comprises as primary state variables the angle of attack and the pitch rotation rate of the projectile. It is proven that the dynamic model of the longitudinal dynamics of the missile is differentially flat. To apply the proposed nonlinear optimal control method the state-space model of the missile undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization takes place at each sampling instance around a temporary operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the missile an H-infinity (optimal) feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is solved repetitively at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The nonlinear optimal control scheme achieves fast and precise tracking of setpoints by the state variables of the longitudinal dynamics of the missile under moderate variations of the control inputs. To apply state estimation-based control of the missile the H-infinity Kalman Filter is used as a robust state observer. The proposed nonlinear optimal control method is compared against a multi-loop flatness-based control scheme which is also developed for the longitudinal missile dynamics.</p>