Hybrid Finite-Frequency Attitude Control Motivated by Volterra Series

Abstract

An analytical solution of Euler’s equation is exhibited using the Volterra series theory in the frequency domain. Based on the Volterra series, the nonlinear output frequency response functions of Euler’s equation are formulated by a numerical algorithm to reveal an energy-transfer phenomenon. The output responses of Euler’s equation have some higher frequency parts than those of the inputs. It provides motivation to design a finite-frequency controller for Euler’s equation to accommodate the high-frequency parts of the outputs. A hybrid passive/finite gain control scheme fused with the generalized Kalman–Yakubovich–Popov lemma is used to generate a controller that is effective for stabilizing the angular velocities of Euler’s equation. Additionally, quaternions are considered in the proposed hybrid finite-frequency controller to stabilize the attitude of spacecraft. Simulation results are demonstrated to validate the effectiveness of the proposed control schemes.