A solution to a multi‐object decision problem for distributed‐parameter control system
Kiyotaka Shimizu, Ryu Katayama · Electronics and Communications in Japan (Part I Communications) · 1982
Abstract This paper discusses the static multi‐object control problem for a distributed system in which more than one geographically distributed decision‐maker (control station) performs control based on their own object functions. The object function of the control station is given in an integral form, with the range of integration being limited to an interval which is of interest to the control station. Then the multi‐object control problem is formulated as an optimization problem for a vector functional, leading to the optimality condition. The paper further discusses the multi‐object decision problem to determine the unique optimal control input from the set of non‐inferior solutions of the multi‐object control problem. The problem is called the central decision problem, where there exists an upper‐level decision maker and his preferable solution is determined based on the global viewpoint and the central object function. The problem is called a set decision problem when such an upper‐level decision maker does not exist, and the solution preferable to the set members is selected for the benefit of the whole set. A method of solution with two steps is proposed using the restricted simplex method and internal point penalty method. The gradient method is used for numerical computation to optimize the system of partial differential equations.