基于动态补偿的受扰矩形广义系统最优跟踪控制

OPTIMAL TRACKING CONTROL BASED ON DYNAMIC COMPENSATION FOR RECTANGULAR DESCRIPTOR SYSTEMS WITH PERSISTENT DISTURBANCE

针对受外部干扰的矩形广义系统研究了基于动态补偿的最优跟踪控制问题.所给定的二次指标中包含有期望输出和实际输出的误差信号.联立原系统、干扰系统及期望输出系统,将问题转化为无干扰的标准线性二次优化问题.进而给出具有适当动态阶的补偿器,使得闭环系统是容许的,且相关的矩阵不等式和Lyapunov方程的解存在.此外,二次性能指标可写成一个与该解和系统初值相关的表达式.进一步求解具有双线性矩阵不等式约束的优化问题,并给出相应的路径跟踪算法以求得性能指标最小值以及补偿器参数.最后,通过数值算例说明本文方法的有效性和可行性.

The optimal tracking control for rectangular descriptor system with disturbance signal is considered based on the dynamic compensation. The given quadratic performance index contains the error signal of the real output and the reference output signal. In light of combining the original system with disturbance system and expected output system, this optimal tracking control problem is trans- formed into the standard linear-quadratic （LQ） optimal control problem without dis- turbance. Then a dynamic compensator with a proper dynamic order is given such that the closed-loop system is admissible and its associated matrix inequality and Lyapunov equation have a solution. Moreover, the quadratic performance index is derived to be a simple expression related to the solution and the initial value of the closed-loop system. Furthermore, the optimal problem is solved with the constraint of bilinear matrix inequality （BMI） and a corresponding path-following algorithm to minimize the quadratic performance index is proposed in which an optimal dynamic compensator is obtained. Finally, some numerical examples are provided to demon- strate the effectiveness and feasibility of the proposed results.