Optimal trajectory design accounting for the stabilization of linear time-varying error dynamics  

作　　者：Patrick PIPREK Haichao HONG Florian HOLZAPFEL 

机构地区：[1]Institute of Flight System Dynamics,Technical University of Munich,Garching D-85748,Germany

出　　处：《Chinese Journal of Aeronautics》2022年第7期55-66,共12页中国航空学报（英文版）

基　　金：supported in part by the TUM University Foundation Fellowship;in part by the German Federal Ministry for Economic Affairs and Energy(BMWi)within the Federal Aeronautical Research Program LuFo V-3 through Project“HOTRUN”(No.20E1720A)。

摘　　要：This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization.Consequently,the trajectory is designed such that the Linear Time-Varying(LTV)dynamic system,describing the controller’s error dynamics,is stable,while additionally the desired optimality criterion is optimized and all enforced constraints on the trajectory are fulfilled.This is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent,quadratic Lyapunov function candidate.Special care is taken with regard to ensuring the correct definiteness of the ensuing matrices within the Lyapunov stability analysis,specifically considering a numerically stable formulation of these in the numerical optimization.The developed algorithm is applied to a trajectory design problem for which the LTV system is part of the path-following error dynamics,which is required to be stable.The main benefit of the proposed scheme in this context is that the designed trajectory trades-off the required stability and robustness properties of the LTV dynamics with the optimality of the trajectory already at the design phase and thus,does not produce unstable optimal trajectories the system must follow in the real application.

关 键 词：LTV error dynamics LTV stability Optimal control-based LTV stabilization Path-following error controller Trajectory generation Trajectory optimization 

分 类 号：V249.1[航空宇航科学与技术—飞行器设计] V448