A Feasibility Study to the Application of Interval Analysis to Re-Entry Trajectory Optimization
Weiwei Chu, Erwin Mooij, Erik-Jan Van Kampen, Ping Chu · 2008
*† ‡ § , Application of i nterval analysis is an innovative way of finding a guaranteed global optimu m. The main idea behind interval arithmetic is to use small intervals for the calculation instead of crisp numbers. As the interval algorithm has characteristics to check all numbers within the interval and contain s all feasible solutions, eventually a guaranteed global optimum can be found. This paper presents the results of a feasib ility study on how interval analysis can be applied to the non -linear re -entry -trajectory optimization problem of minim izing the heat load wh ile return ing to a desired landing point. To introduce the method two examples of static and dynamic optimization are presented first. Interval analysis applied to static optimization is very successful. Although the application to dynamic system s can su ccessfully give the global optimum, the method suffer s a lot from some intrinsic problems related to interval arithmetic, namely the so -called dependency problem, the wrapping effect and the huge number of feasible solutions returned from the algorithm . Th e re -entry trajectory optimization problem appeared to be very demanding for the applied algorithm .