Figure 2
From: Enabling Controlling Complex Networks with Local Topological Information
The contribution of this work in demonstrating a “link” (red solid arrows) from “structural controllability” to “optimal cost control”. In (a), the question mark means that currently there is no existing work considering such a problem. Our work is based on two facts: (i) To ensure “structural controllability”, we propose LM which is proven to steadily approximate the global optimal solution found by MM with linear time complexity (SI, Section 2.2); (ii) To achieve “optimal cost control”, we introduce ILQR in (b) to design an optimal controller for uncertain LTI systems when the input matrix B becomes selectable, by employing “OPGM” (SI, Section 3.2). We uncover that nodes which should be connected to external inputs tend to divide elementary topologies (stem, circle and dilation) averagely for achieving a lower cost since the control cost is mainly dependent on the length of the longest control path, which inspires (red dashed arrows) the design of the MCLP algorithm without using global topology. By combining LM and MLCP together (red solid arrows), we are able to obtain an optimal control of large scale complex networks by only using local topological information.
