Sub-optimal control of sparsely coupled systems

Abstract

In this paper we consider the sub-optimal control of sparsely coupled systems, characterized by linear differential equations with quadratic cost functional. The method proposed here converts the problem to a canonical form and identifies the variables from each sub-system which are strongly interacting. This is done by defining a threshold level matrix based on the eigenvalues of the sub-systems and their cost matrices. The elements of the coupling matrix in the canonical form is compared with the corresponding elements in the threshold level matrix to decide whether the coupling is significant or not. Sub-optimal controls are derived for each sub-system incorporating complete state of the sub-system and only those states from other sub-systems which are strongly interacting. A considerable saving in computation, as well as reduced hardware coat in terms of information transmission is achieved. The sub-optimal controller is derived for both constrained and unconstrained information structures. A few examples are given to illustrate the method.