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

Chinese Journal of Aeronautics 2022年第7期35卷 55-66页

作者： Patrick PIPREK Haichao HONG Florian HOLZAPFEL Institute of Flight System Dynamics Technical University of MunichGarching D-85748Germany

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 ***,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 *** is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent,quadratic Lyapunov function *** 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 *** 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 *** 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

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