Direct iterative algorithm to solve the extended Levine-Athans equations
Cui Wenjin · Journal of Tsinghua University(Science and Technology) · 2001
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.