基于Riccati方程的导弹自适应姿态控制

针对存在参数不确定性的非线性弹体模型,提出基于状态相关Riccati方程的模型参考自适应状态控制方法。首先,针对弹体标称模型,建立特定形式下的Riccati方程,并求得其解析解,获得一种全局渐近稳定的次优控制律。然后,考虑到实际模型与标称模型之间存在的参数偏差会造成控制效果恶化,以标称模型下设计的闭环系统为参考模型,设计自适应控制律通过在线辨识参数使得实际模型趋向于参考模型,并保证跟踪误差和辨识误差有界。仿真结果表明,该控制律能够克服参数不确定性的影响,有效跟踪参考模型下的响应。

Missile adaptive attitude control based on Riccati equation

Aimed at the nonlinear missile model with parameter uncertainties, a model reference adaptive state control method based on the state-dependent Riccati equation is proposed. Firstly, based on the standard model, a Riccati equation with the special form is established and its analytic solution is obtained. The suboptimal control law which is globally asymptotically stable is acquired. Then, in view of the inferior result caused by the parameter deviation between the real model and the standard model, the closed-loop system designed under the standard model is regarded as a reference model. An adaptive control law is designed to urge the real model to approach to the standard model, and guarantees that the tracking error and the identification error are bounded. Simulation results show that the control law designed can overcome the effect caused by parameter uncertainties and track the response of the reference model well.