5. Indirect Approach to the Optimal Glide Trajectory Problem

Gliding problem of hypersonic aircrafts is a high-sensitivity two-point boundary value problem, it is difficult to solve with a single method. The initial value of the common state variable has no actual meaning, which is difficult to predict. Therefore, an optimization algorithm is proposed to solve two-point boundary value problem in this chapter, combining genetic algorithm, local optimization algorithm and neighboring extremum method. The key to solve optimal ballistic problem is to solve the two-point boundary value problem, that is, to find the initial value of a suitable set of common state variables to satisfy the terminal constraints. The initial value of the common state variable is very sensitive to results, and it is not necessarily continuous. Therefore, traditional search algorithms can only find local optimal solution, and are related to the selection of initial value. Solving the problem directly with a gradient algorithm sometimes gives no solution. Therefore, the selection of initial value of general optimization algorithm is a difficult problem. Genetic algorithm is an adaptive global optimization probability search algorithm, which simulates the genetic and evolutionary processes of living things in natural environment. It only needs to estimate the range of optimization variables, and it seeks global approximate optimal solution. However, genetic algorithm is computationally intensive, and often simply converge to a rough global optimal solution. Therefore, based on genetic algorithm, the global optimal solution is further obtained by algorithms with strong local search ability. That is to say, the global approximate optimal solution is obtained by genetic algorithm, and then the optimal solution is further obtained by other algorithms with strong local search ability. Then based on strict constraints, the neighboring extremum method is used to solve two-point boundary value problem, and the optimal solution satisfying all constraints is obtained. Feasibility of this method has been proved in practice.