Flight testing an optimal trajectory for the Saab J35 Draken

Introduction T HE desire to Ž nd the most efŽ cient  ight path has a long history.The developmentof the Ž rst high-performancejet aircraft made it crucial to  y a close to optimal path to perform a givenmission before the fuel ran out. The earliest methods for Ž nding optimal trajectorieswere based on calculusof variations.Discretization of the optimality conditions and solution using numerical methods made it possible to solve quite complicated problems; see Bryson and Desai for a discussion on early strategies. In recent years, the most common approach is to discretize the differential algebraic equations (DAEs) before stating optimality conditions and applying numericalmethods. This strategywas pioneeredbyHargravesandParis, who used theNPSOL optimization package.Recentdevelopmentsin discretizationofDAEs4 andsparse nonlinearoptimizationmethods i 8 represent the current state of the art in trajectory optimization. Althoughmany papers appear in the open literatureon the development of numerical methods for solving trajectory optimization problems, very few papers are available discussing the difŽ culties involved in trying to follow a numerically computed trajectory in a real  ight test. The purpose of the present paper is to report on a simple  ight test that was performed to demonstrate the difŽ culties that may appear in a  ight test. This paper describes the model and numerical implementation used to calculateoptimal trajectories.The presentationof numerical results then follows with the results obtained in the  ight test for a particular test case.