一类系统的关联反馈广义闭环协调控制

Extended closed-loop coordinated control of interconnection-regulation and feedback for a class of systems

为解决关联反馈广义闭环协调的能稳性问题,提出一种协调控制器的设计方法.给出关联反馈广义闭环协调控制模型的描述.针对系统矩阵A=AO+AU的直接可调部分AU具有特殊形式:所有行(列)元素全为0或者全不为0的协调能稳性问题,通过将其在数学形式上等价转化为线性时不变系统的能稳(能检测)问题,得到其可解的充要条件,并给出控制器的设计方法.结果表明:AU具该特殊形式的系统关联反馈广义闭环协调控制问题,可转化为相应的线性时不变系统的无约束控制问题;当AU不具该特殊形式,也即存在某行(列)既有零元又有非零元的情形时,该控制问题不能转化为线性时不变系统的无约束控制问题.对于一般情形下系统的关联协调控制问题,解决的关键是普通意义下的Cayley矩阵乘积与Hadamard矩阵乘积之间混合乘积的处理.

To solve the stabilizability problem of extended closed-loop coordinated control of interconnection-regulation and feedback,a kind of coordinated controller design method was proposed.The extended closed-loop coordinated control model was firstly described.The coordinated stabilization problem was investigated for a class of systems in which the regulated part AU of the system matrix A=AO＋AU had special form,i.e.all row（or column） elements were either zero or nonzero.This problem was converted equivalently to the stabilizability（detectability） problem of a linear time-invariance system to deduce the necessary and sufficient conditions of solvability and to propose the controller design method.The results show that when the regulated part AU has special form,the corresponding coordinated control problem can be converted to unconstrained stabilizability（detectability） problem of a linear time-invariance system,while the situation is the opposite for other forms of AU.The key of solving stabilizability problem of ge-neral coordinated control model is the mixture matrix product of Cayley product and Hadamard product.