Constrained Design of Network Dynamics for Controllability Metrics
In this paper, we address the constrained design of continuous-time linear dynamics to improve system’s 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 to improve their control performance while considering the deployed actuation mechanisms. Specifically, we consider spectral properties of the ‘infinite’ controllability Gramian as control performance metrics, and perform constrained (i.e., bounded) changes in the system’s parameters while respecting its structure. In this paper, we show that three different (yet related) re-design problems for control enhancement can be cast as bilinear or linear matrix equality problems. We propose different strategies to obtain the solution of the problems, and assess their performance in the context of multi-agent networks, i.e., constrained network re-design to improve control performance in leader-follower setups.