Ph.D Student | Sharf Miel |
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Subject | Network Optimization Methods in Passivity-Based Cooperative Control |

Department | Department of Aerospace Engineering |

Supervisor | Professor Daniel Zelazo |

Full Thesis text |

Cooperative control and multi-agent networks have been subject to extensive research over the last few years, exhibiting both a rich theoretical framework as well as a wide range of applications. In this venue, researchers have tried to establish a unified theory for networks of dynamical systems. Two recurring themes that appear in many theories include graph theory and energy-based control, i.e. the notion of passivity. Passivity was first applied to the world of multi-agent systems by Arcak, and since then many different variants of passivity were suggested to tackle cooperative control problems, including incremental passivity and equilibrium-independent passivity (EIP).

In 2014, Bürger, Zelazo and Allgöwer introduced the notion of maximally equilibrium-independent passive systems (MEIP), in which passivity with respect to all steady-state inputs is assumed, and the collection of all steady-state input-output pairs is a monotone relation. They showed that the steady-state limit of a diffusively-coupled multi-agent network, with MEIP agents and controllers, can be found by solving a pair of dual network optimization problems, known as the optimal potential and optimal flow problems, which have been studied in the field of network optimization for decades. Thus, a network optimization framework for analysis of multi-agent systems was established. However, it has a few main drawbacks. First, it requires the agents to be single-input-single-output systems, limiting the application to many real-world systems. Second, it requires that the agents are passive with respect to any steady-state they possess, excluding systems like generators and other passive-short systems. Lastly, the result they present is purely an analysis result, giving no method for synthesizing controllers.

The research presented in this thesis confronts all three problems. First, the notion of MEIP is extended to include multiple-input-multiple-output systems by applying the notion of cyclically monotone relations introduced by Rockafellar, and a generalized version of the network optimization framework is presented. Second, networks with passive-short agents are treated. In this case, the associated network optimization problems are non-convex, and it is shown that convexifying them results in a passivizing transformation for the agents, validating the augmented network optimization framework. Lastly, we apply the framework to solve various problems in cooperative control, including final-value synthesis, model-free synthesis, network identification, and fault detection and isolation.