Control of heterogeneous multi-agent systems and aerospace applications

This thesis work focuses on the control of multi-agent systems using graph theory, in particular deals with attitude coordinated control of spacecrafts. A multi-agent system is a dynamical system composed by a finite number of subsystems (agents), each of them is characterized by a set of equations describing its own dynamics. Each agent is also capable of sharing information about its states with the others, for instance displacement or angular velocity. This overall behaviour can be represented by a graph. The agents are considered to be governed by Newton‘s law for rotations, coupled with a flexible dynamics equation that models the possible presence of flexible parts attached to the rigid body of the spacecraft. The whole system is heterogeneous, meaning that each agent has different charachteristics. Starting from the work found in literature, mainly focused on undirected graph topologies, meaning that all the communications are biunivocal, it was extended to the directed topology cases, meaning that not all the agents need to both send and receive information from the others. In this context, consensus (that means the reach of the same state for all the agents) reachability is shown in different cases and new ways to tune the agents transient are proposed. For example non symmetric, weighted, generalized Laplacians, representing the communication graphs of attitude and angular velocity in a compact matrix form, are used as feedback gains, the eigenvalues and their relation with the modes of the whole system are studied. Generally the presence of a leader, which is an agent that acts as a reference for the attitude and angular velocity of the others, is considered, but also leaderless configurations are included. The system is then recomputed in discrete time in order to implement differentiators to overcome the possible absence of angular velocity transducers. Many simulations are performed with different parameters as inertia, flexible dynamics constants, graphs weigths, initial conditions and with different communication topologies. The presence of external disturbances is considered and the most relevant external torques are modeled. At last failure management is addressed, in particular the cases in which one or more of the agents interrupts the communications with the others for any reason. The topology is checked to be still capable of reaching consensus among the agents that still work. In this context some simulations with switching topologies are presented.