Distributed self-tuning consensus and synchronization

• New algorithm for distributed self-tuning synchronization of multi-agent systems.
• Error between velocity of an agent and the average of its neighbors is minimized
• Algorithm generates nonnegative and primitive inter-agent coupling matrix.
• The agent velocities converge toward same constant value.
• Velocities converge sufficiently fast so that distances between agents are bounded.

The problem of self-tuning of coupling parameters in multi-agent systems is considered. Agent dynamics are described by a discrete-time double integrator with unknown input gain. Each agent locally tunes the strength of interaction with neighboring agents by using a normalized gradient algorithm (NGA). The tuning algorithm minimizes the square of the error between an individual agent’s state (velocity) and the one step delayed average of its own state and the states of its neighbors. Assuming that the network graph is strongly connected, it is proved that the sequence of coupling parameters is convergent and all velocities converge toward the same constant value.