Trajectory Optimization And Guidance Of Hypersonic Vehicle Based On Improved Gauss Pseudospectral Method

In the past twenty years, near space is focused by some great countries. It is the idealspace to realize the hypersonic flying because of the thin air and the small resistance. Thehypersonic vehicle not only has the ability to entry the space but also can reentry the at-mosphere for attacking the ground targets fast. It has the big lift-to-drag ratio (LDR), wellmaneuverability, fast reaching the global world and great power, etc. It can be used in thefields of the global real-time scout, rapid deployment and remote precision attacking andimpacts the future war greatly. Therefore, much researches on the related technology andtheory of the hypersonic vehicle have won wide studies. It is the essential preconditionfor the mission to realize the trajectory optimization and high-precision guidance. Thisproblem is difcult to solve because of the nonlinear property of the motion equations,complexity of the environment and various nonlinear constraints. The thesis takes someresearches on this problem.1. The motion models and the aerodynamic model of the hypersonic vehicle arediscussed. The mathematical descriptions of the ascent trajectory optimization problem ofthe hypersonic vehicle are given for the engineering problems. The reentry motion modelis presented under the half velocity coordinate system. Considering the attacking angleand velocity variables, the bivariate aerodynamic coefcients model is built by analyzingthe characteristics of the data, The comparison shows that the proposed aerodynamiccoefcients model can well describe the regularity of the aerodynamic coefcients, whichprovides the basic model for the next trajectory optimization. The comparison resultsshow that the bivariate aerodynamic coefcients model has the high accuracy. On thebasis of the aerodynamic model, the characteristic of the LDR and the reentry trajectoryof the hypersonic vehicle with the diferent LDR are analyzed. The reentry trajectoryoptimization and the guidance problems of the hypersonic vehicle are described.2. The algorithm for solving the nonlinear optimal control problem with the pathconstraints is studied. The final state state integral constraints are nonlinear in the tradi-tional Gauss pseudospectral method (GPM). It isn’t in favour of the fast computation. Thecomputation of the costate doesn’t agree with those of the other pseudospectral methods.In order to increase the convergence rate, the nonlinear final state integral constraint istransformed into the linear one equivalently using the state diferential matrix and Gaussweights. Then, the number of the nonlinear constraints decreases. The improved Gauss pseudospectral method (IGPM) is proposed based on the linear final state integral con-straint. The new costate mapping theorem is proved to complete the GPM. The newcostate computation is the same with the other pseudospectral methods The simple com-putation of the initial costate is given to alleviate the complexity of the original method.Since the control doesn’t has the values at the boundaries time, the computations of theboundaries time are proposed based on the maximum principle considering the dynamicdiferential equations and path constraints.3. The multiphase trajectory trajectory optimization method of the standard Bolzamultiphase nonlinear optimal control problem is investigated. The dimension of the d-iferential matrix becomes too big when the number of the discrete points increases forthe nonlinear optimal control problem with the complex path constraints. And the com-putation efciency decreases. Therefore, The multiphase improved Gauss pseudospectralmethod (MIGPM) is proposed based on the IGPM by ideal of the multiple phases. Themultiphase costate mapping theorem is proved to compute the costate easily. The meth-ods of the costates and the controls at the break points are given. In order to increasethe accuracy of the solution, the multiphase trajectory optimization algorithm is proposedbased on MIGPM. It is used to solve the reentry trajectory optimization of the maximaldownrange problem of the hypersonic vehicle. The accuracy and the convergence of thesolution are better than those of the global trajectory optimization method.4. The dynamic trajectory optimization method with the ability of making the pathconstraints high accuracy and finding the discontinuous points is researched. The accura-cy of the path constraints isn’t good using the global trajectory optimization method forthe problem with the requirement of high precision and discontinuous control. The multi-phase trajectory optimization method hardly find the discontinuous points. The updatingmethods of the discrete points and the number of the phases are given by the compositiverelative error vector which is used as the judging conditions. Considering the satisfy-ing accuracy of the solution and the path constraints especially, the dynamic trajectoryoptimization method is proposed based on MIGPM. The examples illustrate that this al-gorithm has the ability of converging fast, finding the discontinuous points and dealingwith the path constraints.5. The minimal fuel ascent trajectory optimization problems of the hypersonic vehi-cle are studied in the vertical plane and the three-dimension space and reentry trajectorymaximal downrange and crossrange problems of the hypersonic vehicle are solved. Theascent optimal trajectory in the vertical plane and the ascent trajectory with the turning operation are solved by the iterative algorithm one based on the IGPM and the dynamictrajectory optimization algorithm. The results show that the minimal fuel trajectories areboth the velocity first and ascent type. In order to increase the convergence and preci-sion, two global trajectory optimization iterative algorithms are put forward. The simula-tion results show that two iterative algorithms can converge to the optimal solution well.The reentry trajectory optimization problems with maximal downrange and crossrangeare solved by the dynamic trajectory optimization algorithm and latest hp adaptive pseu-dospectral method. The dynamic trajectory optimization algorithm behaves better thanthose of the hp adaptive pseudospectral method in the field of the computation efciency,the converging radius and the ability of dealing with the path constraints. The propertyof the reentry optimal LDR is analyzed and the optimal LDR is almost the same with themaximal LDR during the reentry middle phase. It provides the reference for choosing theinitial value of the reentry trajectory optimization problem.6. The reentry on-line optimal feedback guidance problem of the hypersonic vehicleis researched. In order to suppress the model uncertainty and the disturbance, the methodof choosing the sample period is derived using the concept of the Caratheodory trajec-tory. The sampling period can guarantee that the tracking precision satisfies the errorrequirement under the condition of the computation delay. The on-line optimal feedbackguidance algorithm is put forward by the benefit of fast convergence of the pseudospec-tral method and the combination of the optimal control theory and the on-line optimalfeedback. The proposed trajectory optimization method and the on-line optimal feedbackguidance algorithm are combined to construct the framework of the reentry closed loopguidance system of the hypersonic vehicle, which meets the requirement of the on-linecomputation. It provides the solution for the reentry of the hypersonic vehicle with theautonomy, reliability and optimality. The on-line optimal feedback guidance method isapplied to the guidance problems，which are the maximal crossrange problem, the fixedpoints fixed direction attacking problem and the on-line autonomous obstacle-avoidancereentry guidance problem. The results show the proposed guidance framework can satisfythe requirement of the index.In conclusion, this thesis puts forward the trajectory optimization methods and theon-line optimal feedback guidance method for hypersonic vehicle, which lay the founda-tion for the on-line trajectory optimization and high-accuracy guidance.