Network design for controllability metrics

In this paper, we address the constrained design of continuous-time linear dynamics to improve system control performance, which can be measured as a function of the controllability Gramian. In contrast with the problem of deployment of actuation capabilities to achieve a specified control performance, we seek to change the dynamics of linear systems while considering the deployed actuation mechanisms. Specifically, we consider spectral properties of the `infinite' controllability Gramian as control performance metrics, and apply constrained (i.e., bounded) perturbations in the system's parameters while respecting its structure. We show that two different (yet related) re-design problems for control enhancement can be cast as bilinear or linear matrix equality problems. Lastly, we propose different strategies to obtain the solution of these problems, and assess their performance in the context of multi-agent networks in the leader-follower setup.