Optimal Trajectory Design Accounting for Robust Stability of Path-Following Controller

Abstract

This study presents an optimal control framework that designs an optimal trajectory while additionally accounting for the stability of a path-deviation error controller that is dependent on the states provided by the optimal trajectory. Thus, instead of designing the controller independent of the trajectory, the stability is enforced as part of the optimization constraints in connection with the optimal trajectory it should follow. This allows to trade off controller and trajectory optimally and thus permits an improved exploitation of the system capabilities. To achieve this goal, the classic trajectory optimization problem formulation is augmented by stability constraints and feedback gains, with the latter being used as optimization parameters. These stabilize the path-following error dynamics by means of gain scheduling and enforce desired response characteristics. Here, the response is shaped, for once, by enforcing limits on the position of the real and imaginary parts of the eigenvalues as well as by limiting their sensitivity. Especially the latter is a way of robustifying the feedback controller in the time domain. The applicability of the proposed method is shown in an aviation-related scenario by solving a missile guidance problem.