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Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and costate estimation

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IEEE/CAA Journal of Automatica Sinica 2021年第8期8卷 1380-1388页

作者： Hossein Mirinejad Tamer Inanc Jacek M.Zurada College of Aeronautics and Engineering Kent State UniversityKentOH 44242 USA Department of Electrical and Computer Engineering University of LouisvilleLouisvilleKY 40292 USA Louisville LouisvilleKY 40292 USAand also with the Information Technology InstituteUniversity of Social Science90-113ŁódźPoland

This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control *** goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency *** proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of *** RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions *** efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control *** addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.

关键词： costate estimation direct trajectory optimization Galerkin projection numerical optimal control radial basis function interpolation

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costate estimation for dynamic systems of the second order

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中国科学:技术科学 2010年第3期 344-344页

作者： WEN Hao,JIN DongPing & HU HaiYan Institute of Vibration Engineering Research,MOE Key Lab of Structure Mechanics and Control for Aircraft,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state *** paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second *** a set of closure conditions,it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second ***,the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear *** proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conversion of the dynamic system from the second order to the first *** new approach is demonstrated via two classical benchmark problems.

关键词： costate estimation second order pseudo-spectral method

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