Simultaneous Learning Optimization of Hamiltonian Systems and Trajectory Tracking Around an Asteroid

Abstract

This paper proposes a simultaneous learning optimization method of feedforward input and adjustable parameters using variational symmetry, which is a special property of Hamiltonian systems. First, a new input/output mapping of Hamiltonian representation is constructed, in which feedforward control input and a finite number of adjustable parameters are defined as the input to the system. Then, a modified variational symmetry for the present Hamiltonian system is derived by introducing two operators. Thanks to the modified variational symmetry, the present learning algorithm simultaneously calculates the gradient of a given cost function with respect to an arbitrary number of feedforward inputs and parameters included in the Hamiltonian with at most two gradient experiments without using the plant system model. Furthermore, the proposed method is applied to trajectory tracking control of a spacecraft near an asteroid. Here, the feedback gains of a local proportional derivative feedback controller to stabilize the system and feedforward control input to improve tracking performance are simultaneously optimized by learning. The present numerical simulations verify that the cost function decreases to a local minimum, the maximum tracking error significantly decreases, and the obtained optimal feedforward input behaves closely to the analytically calculated input for perfect tracking.