Robust Second-Order Backstepping Design of Integrated Guidance and Control Based on a Fully Actuated System Approach

Abstract

This article investigates the angle constraint issue in the integrated guidance and control (IGC) design. By using the high-order fully actuated system (HOFAS) approach, a non-linear robust controller is presented under the framework of the second-order backstepping method. First, the IGC model is represented as a complete second-order non-linear system without any linearization assumption, where the modeling error, unmodeled non-linearity, and external disturbance are unknown uncertainties. Combined with the dynamic model, the non-linear system is transformed into a pseudo-feedback system. An IGC model with fully actuated features is established, consisting of the guidance, dynamics, and attitude subsystems. Then, under the framework of the backstepping method, the non-linear controller of each subsystem is designed based on the HOFAS approach and robust control law, and a tracking differentiator based on inverse hyperbolic sine function is used to obtain the precise differential signal of the virtual control command. The controller parameter matrix is solved according to the desired closed-loop poles, while the closed-loop system is transformed into a steady linear system with desired performance. The subsystem state convergence is proven by Lyapunov theory, and the stability of the whole system is analyzed. Finally, the simulation results of terminal angle constraint verify the effectiveness of the proposed robust IGC design.