基于状态反馈的导弹非线性H_2/H_∞鲁棒制导律

为了研究导弹导引规律的鲁棒性,将L_2增益理论与H_∞控制方法相结合,视导弹在追踪平面内的非线性运动学问题为有限时间内的混合H_2/H_∞问题.基于非线性二次型两人非零和微分对策理论,通过解李雅普诺夫稳定意义下的一对耦合哈密顿-雅可比偏微分不等式,得到了弹目相对运动的状态反馈纳什平衡点,由此得到了一种新型鲁棒制导律.仿真结果表明,与基于L_2增益理论的鲁棒制导律相比,该制导中具有更小的H_2性能指标,较H_∞制导律具有更强的鲁棒性.

Nonlinear H_2/H_∞ Robust Guidance Law of Missile Based on State Feedback

To study the robust property of the guidance law of missile, L_2 gain theory was integrated with H_∞ control method. The nonlinear kinematics problem of the missile in the pursuit plane was taken as a time-limited mixed H_2/H_∞ control problem. Based on the theory of nonlinear quadric two-person nonzero-sum differential game, the state feedback Nash balance point about the relative motion of target-missile was achieved through solving two coupled Hamilton-Jacobi partial differential inequations under the meaning of Lyapunov stabilization. A new robust guidance law was obtained. The simulation results indicate that compared with the robust guidance law based on L_2 gain theory, the designed guidance law possesses a less H_2 performance. Compared with H_∞ guidance law, the designed guidance law possesses a more robust property.