多饱和约束拦截弹参数时变系统控制器设计

针对拦截弹参数时变和执行机构饱和非线性影响控制系统性能，提出基于齐次多项式参数相关 Lyapunov 理论和非线性矩阵微分方程凸多面体转换算法相结合的鲁棒最优控制系统设计方案。 通过引入标准饱和约束算子，建立控制系统数学模型并给出控制系统结构；引入饱和归一化因子，把非线性参数时变微分方程转化成线性多胞型微分方程；基于齐次多项式参数相关Lyapunov理论和拓展Pólya’s定理，把参数时变多胞型微分方程转换成齐次多项式参数相关微分方程，并给出齐次多项式参数相关控制器结构；利用迭代算法把非线性矩阵不等式转换成线性矩阵不等式(LMIs)，进而基于LMI凸优化理论获得控制器解，设计出的控制器是关于齐次多项式阶次g和Pólya’s松弛度d的函数；通过定点和制导控制系统仿真校验了该算法，仿真结果表明随着齐次多项式阶次g和Pólya’s松弛度d的增加，设计出的控制器在确保系统稳定的前提下改善控制系统性能。

Gain Scheduled Controller Design for Interceptor Parameter Time Varying System with Multi Saturated Constraint

A method for designing a robust optimal controller based on homogeneous polynomial parameter dependent Lyapunov function theory (HPPDLF) combined with nonlinear matrix differential equations converted into convex polyhedron algorithm is proposed for parameter time varying system with actuator nonlinear multi saturated constraints in this paper. First, an actuator saturation constrained operator is established and the control system topologyis given. The nonlinear parameter time varying differential equations are converted into HPPD matrix differential equations by introducing saturation normalized factors. Based on HPPDLF theory and Pólya’s Theorem and the NLMIs are converted into LMIs by using iterative algorithm. And then the LMI controller solution is obtained based on LMI convex optimization theory, so the controllers are functions with respect to the degree of the homogeneous polynomial Lyapunov matrix g and level of Pólya’s relaxations d. Numerical simulations have demonstrated the effectiveness of the proposed approach.