By adjusting the parameter, the optimal reentry trajectory can be generated. Thus, the FSGP model for three fuzzy relations is designed. Their preemptive priorities are modelled into a relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree.
Secondly, all the objectives are fuzzified using membership functions. Then the dynamic optimal control problem is transformed into a static nonlinear multi-objective programming problem with preemptive priorities. Firstly, direct collocation method is adopted to discretize the dynamic model and constraints of hypersonic vehicles by selecting attack angle and bank angle at each node and collocation node as control variables. Accordingly, a fuzzy satisfactory goal programming (FSGP) method is proposed in this paper. It considers all the objectives with different attainment relations through minimizing the deviations from the expected values, which makes it easy to reformulate MOO model with priorities. For MOO, goal programming (GP), initially introduced by Charnes and Cooper, is also a promising methodology. For this requirement, different methods have been attempted, such as lexicographic optimization, varying-domain optimization, and two-step optimization. Preemptive priorities, as a special case of importance of objectives, require all the objectives to be solved in sequence. Nevertheless, selecting the preference function is still difficult, and the formulated programming model is strongly nonlinear. use the physical programming (PP) method to determine gliding reentry trajectory. apply NSGA-II algorithm to realize a two-objective optimization design of reentry trajectory, however, the computation burden of iterative optimization is heavy and the importance of different objectives cannot be reflected directly. But it is difficult to determine the weights. In early times, the method based on weighting factors is widely used to transform multi-objective problem into traditional single objective formulation. However, the expectations for reducing costs and enhancing performance are increasing gradually this brings about the development of multi-objective optimization (MOO) for reentry trajectory. Generally, the traditional design of reentry trajectory usually aims at a single objective, such as maximizing the range, maximizing the terminal velocity, etc. Bibeau adopt the collocation method to design the optimal reentry trajectory of a fixed-trim vehicle. Huntington and Rao design the gauss pseudospectral method for the optimal control of spacecraft. For example, Qu uses multiple shooting technique to calculate the reentry trajectory of American shuttle orbit. Thus, the direct approaches are applied frequently, such as direct shooting method, pseudospectral method, direct collocation method, etc. However, the radius of convergence is so small that acquiring this condition is very difficult. It is necessary for the indirect methods to derive the optimality condition called Hamiltonian boundary value. Most early investigators adopt the latter. The trajectory optimization methods are categorized into two major types, i.e., direct and indirect methods.
Therefore, a well-designed trajectory, particularly in reentry phase, is key to the stable flight of hypersonic vehicles. Obviously, hypersonic vehicles will play an increasingly important role in the future. The aircrafts which have the velocity of Mach 5 or more are defined as hypersonic vehicles.
The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired.
Then the fuzzy satisfactory goal programming model is proposed. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job.
0 kommentar(er)
