Abstract
A mesh adaptation method is proposed for solving optimal control problems with non-smooth control. The original optimal control problem (OCP) is transcribed into a nonlinear programming (NLP) problem by using the Runge-Kutta discretization method, in which the NLP can be solved by using standard nonlinear programming codes. The method employs collocations from the dyadic background points, which used for the second-generation wavelet (SGW) translation simultaneously. The SGW is used to approximate the control variables and get the wavelet coefficients once they are obtained. In regions contain discontinuities, the magnitude of the relevant wavelet coefficients is large than other regions. The corresponding dyadic background points are reserved as the collocation points. Furthermore, the approximation error of the control and/or state variables can be predicted by a given threshold. Thus, the accuracy and efficiency can be balanced in a simple way. Finally, the method is demonstrated by three numerical examples from the open literature.
Highlights
Numerical method of optimal control has wide spread application in aerospace field, such as flight trajectory optimization, missile guidance, orbit transfer, et al For these nonlinear optimal control problems, various control methods have been developed [1], [2], the direct transcription method is a general method
Based on the above idea, we propose a novel mesh adaptation method for numerically solving optimal control problems
The proposed mesh adaptation method for optimal control is based on the second-generation wavelet, which is mostly constructed on a set of uniform dyadic grids on the real line or interval
Summary
Numerical method of optimal control has wide spread application in aerospace field, such as flight trajectory optimization, missile guidance, orbit transfer, et al For these nonlinear optimal control problems, various control methods have been developed [1], [2], the direct transcription method is a general method. The proposed mesh adaptation method for optimal control is based on the second-generation wavelet, which is mostly constructed on a set of uniform dyadic grids on the real line or interval. SECOND-GENERATION WAVELET BASED MESH ADAPTATION ALGORITHM The mesh adaptation method is usually used to increase the accuracy of the solution for the optimal control problems. For the second-generation wavelet, every wavelet is uniquely associated with a grid point, and grid adaption is based on the analysis of wavelet coefficients; i.e., at any given iteration step of solving for optimal control problem, the used grid points consist of points corresponding to wavelets whose coefficients are greater than a given threshold ε, which is the parameter controls the accuracy of the solution
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