一类非线性状态观测器的设计

Design of a Class of Nonlinear State Observer

针对满足Lipschitz条件的非线性系统,构造了非线性状态观测器·对基于代数Riccati方程设计状态观测器增益阵的方法进行了仿真研究,针对求解代数Riccati方程需要不断调整参数而给求解问题带来的不便,采用线性矩阵不等式改进了状态观测器增益阵的选取方法,通过与两种不同构造形式的基于代数Riccati方程的观测器增益阵的求解方法的比较,仿真结果验证了基于线性矩阵不等式所构造的状态观测器增益矩阵的有效性,其比基于代数Riccati方程的方法具有更小的保守性,而且求解更加简便·最后讨论了Lipschitz常数对系统抗干扰能力的影响·

A nonlinear state observer was constructed for a class of nonlinear system satisfying Lipschitz condition by way of traditional design. Simulation studies were conducted on the design of observer gain matrix based on algebraic Riccati equation. Because the design was inconvenient to adjust some parameters to get a solution to the algebraic Riccati equation,the linear matrix inequality(LMI)optimization technique was utilized to pick another basis on which observer gain matrix was disigned. A comparison was thus made between the two designs. Discussing the comparison results,it was found that the design based on LIM was less conservative than that based on algebraic Riccati equation. The simulation results also demonstrated the effectiveness of the proposed LMI based design. At last,a useful discussion was made to the effect of Lipschitz constant on external disturbance rejection.