Convergence Analysis using the Edge Laplacian: Robust Consensus of Nonlinear Multi-agent Systems via ISS Method

This study develops an original and innovative matrix representation with respect to the information flow for networked multi-agent system. To begin with, the general concepts of the edge Laplacian of digraph are proposed with its algebraic properties. Benefit from this novel graph-theoretic tool, we can build a bridge between the consensus problem and the edge agreement problem; we also show that the edge Laplacian sheds a new light on solving the leaderless consensus problem. Based on the edge agreement framework, the technical challenges caused by unknown but bounded disturbances and inherently nonlinear dynamics can be well handled. In particular, we design an integrated procedure for a new robust consensus protocol that is based on a blend of algebraic graph theory and the newly developed cyclic-small-gain theorem. Besides, to highlight the intricate relationship between the original graph and cyclic-small-gain theorem, the concept of edge-interconnection graph is introduced for the first time. Finally, simulation results are provided to verify the theoretical analysis.Comment: 22 pages, 10 figures; Submitted to International Journal of Robust and Nonlinear Contro

Cooperative Tasking for Deterministic Specification Automata

In our previous work [1], a divide-and-conquer approach was proposed for cooperative tasking among multi-agent systems. The basic idea is to decompose a requested global specification into subtasks for individual agents such that the fulfillment of these subtasks by each individual agent leads to the satisfaction of the global specification as a team. It was shown that not all tasks can be decomposed. Furthermore, a necessary and sufficient condition was proposed for the decomposability of a task automaton between two cooperative agents. The current paper continues the results in [1] and proposes necessary and sufficient conditions for task decomposability with respect to arbitrary finite number of agents. It is further shown that the fulfillment of local specifications can guarantee the satisfaction of the global specification. This work provides hints for the designers on how to rule out the indecomposable task automata and enforce the decomposability conditions. The result therefore may pave the way towards a new perspective for decentralized cooperative control of multi-agent systems.Comment: Preprint, Submitted for publicatio

Semistability-Based Robust and Optimal Control Design for Network Systems

In this report, we present a new Linear-Quadratic Semistabilizers (LQS) theory for linear network systems. This new semistable H2 control framework is developed to address the robust and optimal semistable control issues of network systems while preserving network topology subject to white noise. Two new notions of semistabilizability and semicontrollability are introduced as a means to connecting semistability with the Lyapunov equation based technique. With these new notions, we first develop a semistable H2 control theory for network systems by exploiting the properties of semistability. A new series of necessary and sufficient conditions for semistability of the closed-loop system have been derived in terms of the Lyapunov equation. Based on these results, we propose a constrained optimization technique to solve the semistable H2 network-topology-preserving control design for network systems over an admissible set. Then optimization analysis and the development of numerical algorithms for the obtained constrained optimization problem are conducted. We establish the existence of optimal solutions for the obtained nonconvex optimization problem over some admissible set. Next, we propose a heuristic swarm optimization based numerical algorithm towards efficiently solving this nonconvex, nonlinear optimization problem. Finally, several numerical examples will be provided.Comment: 31 page