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Optimal trajectory design accounting for the stabilization of linear time-varying error dynamics
طراحی مسیر راه اندازی بهینه برای تثبیت دینامیک خطای خطی متغیر خطی-2021 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.
keywords: LTV error dynamics | LTV stability | Optimal control-based LTV stabilization | Path-following error controller | Trajectory generation | Trajectory optimization |
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