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Multimodal control parameter optimization for aircraft longitudinal automatic landing via the hybrid particle swarm-BFGS algorithm

The airborne automatic landing system needs to provide both accurate trajectory tracking and constant sink rate. In this article, a hybrid optimizer combining a modified particle swarm algorithm with the damped Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is presented to not only solve the parameter tuning problem for the automatic landing system design, but also explore the hidden properties of the multimodal optimization problem. In doing so, the quasi-random sequence-based particle initialization method is adopted to let the particles cover the problem domain more evenly. Then, the damped BFGS-based searching method is used to calculate the local minimum of each particle. A three-point searching method is adopted as a substitution method if the damped BFGS method fails. By using the modified niching method, each particle is updated and converges to an estimated local minimum point. Finally, a range of optimized solutions is analysed and presented to the engineer for the automatic landing system design. A series of simulations are carried out on a test bed based on a 6 degrees of freedom (DoF) non-linear model of the F/A-18. Comparative results verify the effectiveness of the proposed method.