Optimal Input Elimination

Abstract

This paper studies an optimal inputs elimination problem in large-scale network systems. We first solve an H2 optimization problem of the difference between the transfer functions of the original system and the system after the input variables elimination. It is shown that the problem can be rigorously solved by calculating the gradient and Hessian of this objective function. The solution means that, when the input variables to be eliminated were fixed, the H2 optimal inputs elimination is achieved by simply eliminating input variables without changing the driver nodes, which are state variables that are directly affected by an input signal. We next solve a finite combinatorial optimization problem to decide input variables to be eliminated. The objective function is defined by using the solution to the H2 optimization problem. It is shown that a greedy algorithm gives the global optimal solution to the finite combinatorial problem within a practical time. The algorithm can be understood that we eliminate input variables in ascending order of the average controllability centralities which assign relative importances to each node within a network. Finally, we demonstrate how to use the results in this paper by a simple example.

Keywords

• input elimination
• h2 optimization
• large-scale network systems