Abstract
In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau pseudospectral method with different collocation points in each mesh interval was used to solve the trajectory optimization model. Moreover, this method was compared with traditional h method. Simulation results show that this method can decrease the dimensionality of nonlinear programming (NLP) problem and therefore improve the efficiency of pseudospectral methods for solving trajectory optimization problems.
Highlights
Beyond visual range (BVR) combat is being the main form of future air combat [1,2,3]
Trajectory optimization of the air-to-air missile can be regarded as a complex nonlinear optimization problem
In allusion to the problems, such as too many collocation points in mesh optimization, high dimensionality of nonlinear programming (NLP) problem, and the low computational efficiency, a multiinterval mesh refinement method with unfixed collocation points was introduced in this paper
Summary
Beyond visual range (BVR) combat is being the main form of future air combat [1,2,3]. Pseudospectral methods have been a research hotspot in the domain of trajectory optimization [8, 9] In this method, the control and state are firstly discretized at certain collocation points in the time interval of interest, which are approximated by polynomial interpolation. Gong et al [15] designed a spectral algorithm for pseudospectral method which uses the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities In this method, the time interval was divided into smaller subintervals and the distribution of the nodes was controlled by knotting method. In allusion to the problems, such as too many collocation points in mesh optimization, high dimensionality of NLP problem, and the low computational efficiency, a multiinterval mesh refinement method with unfixed collocation points was introduced in this paper. The mesh needs to be further refined if the relative error is larger than the given value, and if nonsmooth point exists in the mesh, the number of mesh intervals will be increased; otherwise the number of collocation points will be increased
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