基于BMI优化的航天器多目标可靠控制

Multi-objective Spacecraft Reliable Control Based on BMI Optimization

在考虑执行器故障的情况下,研究具有区域极点和方差约束的航天器拦截可靠控制问题。为降低设计的保守性,运用线性矩阵不等式(LMI)技术,提出了一种新的区域极点配置与方差约束的相容性条件。通过引入松弛变量,采用不同的Lyapunov矩阵分别满足方差约束和区域极点配置条件。以双线性矩阵不等式(BMI)的形式,给出了航天器拦截静态输出反馈可靠控制器存在的充分条件。通过适当的变量替换,将可靠控制器优化设计问题等价地转化为一个具有LMI和线性矩阵等式(LME)约束的参数优化问题,从而便于运用科学计算自由软件SCILAB进行求解。对某航天器拦截控制问题的仿真结果表明了所提方法的有效性。

The design problem of reliable controller against actuator failures with regional pole and variance constraints is researched for spacecraft interception.To reduce the design conservatism,a new consistency condition of regional pole assignment and variance constraints is proposed.More precisely,different Lyapunov matrices are employed to satisfy both variance constraints and regional pole assignment by introducing additional slack variables.Then,a sufficient condition for the existence of static output feedback reliable controller is presented in terms of bilinear matrix inequality (BMI).Furthermore,with proper variable changes,the design problem of optimal reliable controller is formulated as a parameter optimization problem with linear matrix inequality(LMI) and linear matrix equality(LME) constraints, which can be solved efficiently by using freeware SCILAB.Simulation results of spacecraft interception control show the effectiveness and advantages of the proposed approach.