∓1-optimal feedback control strategy with application to longitudinal autopilots

The design of discrete-time optimal control to be implemented via the digital longitudinal autopilot for achieving a desired pitch attitude of aircraft is addressed in this paper. The performance index of the control system which needs to be minimized is defined as the upper bound on the absolute values of the difference between true and desired pitch attitudes in the presence of an arbitrary external unmeasured disturbance. The optimization is achieved by determining the two parameters of the digital PI-type control law needed to stabilize the pitch rate and also the one parameter of P-type control law required for the stabilization of the pitch attitude. To do this, the so-called ℓ₁-optimization approach extended in the modern control theory is utilized. An illustrative numerical example and simulation results are given to demonstrate the effectiveness of this approach.