不确定离散系统最优保价静态输出反馈控制

目的研究在状态空间模型中的状态及控制矩阵中含有范数有界参数不确定线性离散系统的最优保价静态输出反馈控制问题. 方法给出了系统二次代价指标的一个上界,并利用拉格朗日乘子法优化了该界. 结果与结论给出了保证闭环系统二次稳定且使得二次代价指标界达到最小的静态输出反馈控制器存在的充分条件. 并提供了一个求解输出反馈增益的数值算法.

Optimal Guaranteed Cost Control via Static Output Feedback for Uncertain Discrete Time Systems

Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.