Distributed Linear Quadratic Control and Filtering: a suboptimality approach

Design of distributed protocols for multi-agent systems has received extensive attention in the past two decades. A challenging problem in this context is to develop distributed synchronizing protocols that minimize given cost criteria. Recent years have also witnessed an increasing interest in problems of distributed state estimation for large-scale systems. Two challenging problems in this context are the problems of distributed H-2 and H-infinity optimal filtering.

In this dissertation, we study both distributed linear quadratic optimal control problems and distributed filtering problems.

In the framework of distributed linear quadratic control, both for leaderless and leader-follower multi-agent systems we provide design methods for computing state-feedback-based distributed suboptimal synchronizing protocols. In the framework of distributed H-2 suboptimal control, both for homogeneous and heterogeneous multi-agent systems we establish design methods for computing state-feedback-based and output-feedback-based distributed suboptimal synchronizing protocols.

The distributed H-2 and H-infinity optimal filtering problem are the problems of designing local filter gains such that the H-2 or H-infinity norm of the transfer matrix from the disturbance input to the output estimation error is minimized, while all local filters reconstruct the full system state asymptotically. Due to their non-convex nature, it is not clear whether optimal solutions exist. Instead of studying these optimal filtering problems, in this dissertation we therefore address suboptimality versions of these problems and provide conceptual algorithms for obtaining H-2 and H-infinity suboptimal distributed filters, respectively.