Study On The Optimal Control Method For The Whole Trajectory Of Advanced Vehicles

With the vigorous development of advanced vehicles based on TSIEN H.S.-trajectory,trajectory optimization to maximize flight range has become an essential part of the vehicles’research.The whole trajectory calculation method has important physical significance and practical value for the global trajectory prediction in the overall design of advanced vehicles,such as the global physical space optimization ability,the trajectory whole range optimization,the engine mode switching state optimization,etc.Unique to the current phase-by-phase trajectory study,this paper focuses on the new characteristics of large velocity scope,broad airspace,strong maneuver and discontinuous aerodynamics of the whole trajectory,and explores the optimal control method for the whole trajectory calculation.A review of the relevant methods of trajectory calculation shows that the pseudospectral method has a good advantage in the aspects of optimality,convergence,and applicability.Therefore,this paper develops the mesh refinement method based on pseudospectral theory for the characteristics of the whole trajectory.And the typical models of advanced vehicles are established to explore the optimal control method for the specific scenarios of the whole trajectory calculation.The details are listed as follows:1.Study on the theory and applicability of pseudospectral method.Through theoretical analyses and demonstrations of numerical cases,the applicable rules of pseudospectral method are established based on the continuity of system variables,which form the theoretical basis for the method research in this paper.2.An improved pk mesh refinement pseudospectral method is proposed.Focusing on the complexity of multi-peak and difficult expression of variable curves in the velocity scope,broad airspace,and strong maneuvering trajectory,a pk pseudospectral method was proposed based on the theory of reducing the distribution points to achieve the same differential approximation by optimizing the piecewise locations.The comparison experiments with hp and ph pseudospectral demonstrated the advantages of pk pseudospectral in terms of the number of collocation points,the number of intervals,convergence,and computational efficiency.3.Two models with typical aerodynamic configurations are constructed.Aim at the data requirements of whole trajectory calculation,two typical models of the axisymmetric body with the power-law revolution nose and lifting body with the Waverider configuration,which are similar to Kinzhal and x-51a respectively,are constructed by referring to the public literature of Russia and America,and they are used as the research subjects for the whole trajectory calculation.4.The study of the whole trajectory problem in the discontinuous aerodynamics linking case of unknown-states and known-time.Based on the Kinzhal similarity model,the whole trajectory calculation scenario of the unknown-states and known-time linking discontinuous system dynamics is constructed.A mesh refinement knotting pseudospectral method based on constraints extending is developed for the discontinuous system dynamics.The feasibility,convergence,local and global optimization ability of the method for whole trajectory calculation are demonstrated by comparison experiments.At the same time,the good solving efficiency of pk pseudospectral method is proved.5.Study on the discontinuous aerodynamics trajectories of with the unknown linked time whether the linked states is known or unknown.Based on the X-51A similarity model,two new scenarios for calculating the whole trajectory are constructed.Through numerical simulation,the universality of pk pseudospectral is ulteriorly demonstrated for solving the whole trajectory problems of two scenarios of unknown-time linking discontinuous dynamics.To sum up,this paper solves the complexity of trajectory expression and system dynamic discontinuity in trajectory whole-path calculation.And conclusions are as follows:(1)compared with phase-by-phase trajectory solving,whole-path trajectory solving has the advantages of global optimization,the self-solving ability of phase-linking variables,same solution accuracy,and local optimization ability;(2)for the optimal control problem with a wide range of time or a wide range of trajectory’s variables,the pk pseudospectral method can effectively refine the collocation points of mesh to save the time of optimization progress;(3)for the whole trajectory calculation problem of dynamic discontinuous,the pk pseudospectral method can be widely applied to the problems of linkage between discontinuous dynamic systems under any combination of uncertain state and time.