  This paper presents a landing controller for a fixed-wing aircraft during the
landing phase, ensuring the aircraft reaches the touchdown point smoothly. The
landing problem is converted to a finite-time linear quadratic tracking (LQT)
problem in which an aircraft needs to track the desired landing path in the
longitudinal-vertical plane while satisfying performance requirements and
flight constraints. First, we design a smooth trajectory that meets flight
performance requirements and constraints. Then, an optimal controller is
designed to minimize the tracking error, while landing the aircraft within the
desired time frame. For this purpose, a linearized model of an aircraft
developed under the assumption of a small flight path angle and a constant
approach speed is used. The resulting Differential Riccati equation is solved
backward in time using the Dormand Prince algorithm. Simulation results show a
satisfactory tracking performance and the finite-time convergence of tracking
errors for different initial conditions of the flare-out phase of landing.
