基于观测器具有不确定性的鲁棒保性能控制

Observer Based Robust Guaranteed Cost Control of Systems with Uncertainties

在鲁棒性控制问题的研究中,针对系统状态不可测的具有范数有界不确定性和外界干扰的线性系统,其求解过程繁琐,某些参数选取不当。为了保证闭环系统的稳定性,提出一种基于观测器的鲁棒H∞保性能控制方法。根据李亚普诺夫原理和H∞理论,获得鲁棒H∞保性能控制器存在的一个充分性条件,用矩阵奇异值分解方法,将控制器和观测器存在条件转化为求解一个线性矩阵不等式的可行性。通过凸优化方法,获得最优的线性二次型性能指标和H∞性能指标。进行仿真的结果表明,上述方法求解简单,稳定性好,验证了所提方法的有效性。

In observer based guaranteed cost control,the gains of the designed observer and controller are often obtained by solving two linear matrix inequalities with the trial-and-error method.If some parameters are not chosen properly,the designed observer or controller may not exist.This paper presents an observer based robust H∞ guaranteed cost control for systems with norm bounded uncertainties and external disturbance.Based on Lyapunov and H∞ theories,a sufficient existence condition of the designed robust guaranteed cost controller is obtained.Using the method of singular value decomposition,the existence condition of the designed observer and controller is transformed into the feasibility problem of a linear matrix inequality,which can be easily solved.Using a convex optimization method,the quadratic and H∞ performance levels can be optimized.The proposed method can overcome the disadvantage of solving two linear matrix inequalities and choosing some parameters with the trial-and-error method.Simulation results have verified the effectiveness of the proposed method.