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针对模型不确定性和噪声非高斯容易导致Kalman滤波精度下降的问题,研究了一类组合导航系统的鲁棒H2/H∞多目标控制问题。将组合导航误差状态方程转化为不确定系统多胞型描述,基于线性矩阵不等式(LMI)将控制器存在条件转化为凸优化问题进行求解。系统的稳定性通过Lyapunov稳定性理论得到保证,通过H2和H∞控制达到抑制干扰的目的,通过保性能控制提高系统的快速性,而对于非零初始条件通过极点配置加速初始阶段的收敛。由仿真结果可以看出,该方法收敛快、鲁棒性强、精度较高。
Aiming at the problem that model uncertainty and non-Gaussian noise can easily lead to the degradation of Kalman filtering, a robust H2 / H∞ multi-objective control problem for a class of integrated navigation systems is studied. The integrated navigation error equation of state is transformed into an ambiguous system polytopic description. Based on the linear matrix inequality (LMI), the existing condition of the controller is transformed into a convex optimization problem. The stability of the system is guaranteed by Lyapunov stability theory. The control of H2 and H∞ achieves the suppression of interference. The system fastness is improved by guaranteed cost control, while the convergence of the initial stage is accelerated by the pole configuration for non-zero initial conditions. It can be seen from the simulation results that the proposed method converges fast, robust and accurate.