求解扩展Levine-Athans方程组的直接迭代算法

特定信息结构下大型线性系统无时限最优控制有解的必要条件是存在一组矩阵变量 { K,P,V} (P,V对称正定 )满足相应的扩展 L evine- Athans方程组 ,因而求解该方程组成为协调控制器设计中最为关键的一环。对此 ,论文提出了一种新的算法——直接迭代法 ,它在选择搜索方向、初始反馈增益矩阵和迭代缩放因子等方面具有独特之处。文中给出了算法的详细计算步骤并对其收敛性进行了严格的数学证明 ;一个典型 4机两区域电力系统分散与协调控制器的设计实例表明 ,新算法与传统的一阶梯度算法相比 ,具有收敛速度快 (快 3个数量级 )、精度高等优点

Direct iterative algorithm to solve the extended Levine-Athans equations

The necessary condition for existence of a solution to the optimal control problem of large scale linear systems with a given information structure is that a matrix group {K,P,V} (P,V is symmetric and positive) exists which satisfies the extended Levine Athans equations. Therefore, the key to designing coordinated controllers for large scale power systems is to solve the equations. This paper describes a new algorithm, the direct iterative method, to attack the problem. The proposed algorithm owns special advantages in selecting the search direction, the initial feedback matrix and the iterative factors. A rigorous mathematical proof is given for the convergence of the iteration procedure. The direct iterative algorithm is compared to the traditional first order gradient method using a control design problem for a typical two area four machine power system. The results show that the new method has superior speed and accuracy.