Nonlinear H∞ control scheme for a flying robot

Abstract In this paper, a nonlinear H∞ state feedback control is designed for both orientation and altitude of a flying robot system in the presence of external disturbance. An analytical solution is proposed for Hamilton-Jacobi-Isaac (HJI) equation. According to the quadrotor's orientation and altitude, a suitable storage function is considered and the appropriate robust control law is derived. The controller coefficients are tuned from Hamilton-Isaac-Jacobi inequality. The closed-loop nonlinear system with the proposed controller has L2-gain less than or equal to γ, and guarantee its asymptotic stability closed-loop nonlinear system with external disturbance. Simulations are provided with the model uncertainties and external disturbance to verify the robustness of the proposed controller. Simulation results confirm the effectiveness of the desired robust controller.

摘要：本文针对存在外部扰动的四旋翼飞行机器人系统的姿态与高度控制问题，设计了非线性H∞状态反馈控制器。针对哈密顿-雅可比-艾萨克（Hamilton-Jacobi-Isaac，HJI）方程，本文提出了一种解析求解方法。结合四旋翼飞行器的姿态与飞行高度特性，选取合适的存储函数并推导得到适配的鲁棒控制律，控制器参数可通过哈密顿-雅可比-艾萨克不等式进行整定。采用所提控制器的闭环非线性系统的L2增益不大于γ，且可保证存在外部扰动时该闭环非线性系统的渐近稳定性。本文通过设置带有模型不确定性与外部扰动的仿真实验，验证了所提控制器的鲁棒性，仿真结果证实了该目标鲁棒控制器的有效性。