Distributed MPC based consensus for single-integrator multi-agent systems

Area of Science:

• Control Theory
• Robotics
• Networked Systems

Background:

• Achieving consensus in multi-agent systems (MASs) is crucial for coordinated behaviors.
• Discrete-time single-integrator dynamics and switching directed interaction graphs present significant control challenges.

Purpose of the Study:

• To develop model predictive control (MPC) schemes for achieving consensus in MASs.
• To investigate the impact of extended control horizons and graph switching on consensus.
• To establish sufficient conditions for guaranteed consensus.

Main Methods:

• Utilizing model predictive control (MPC) with an extended control horizon.
• Analyzing discrete-time single-integrator dynamics under switching directed graphs.
• Employing the properties of infinite products of stochastic matrices to derive conditions.

Main Results:

• Sufficient conditions derived for achieving consensus based on sampling period and interaction graph properties.
• Consensus is achievable asymptotically if the sampling period allows for a jointly directed spanning tree.
• Arbitrarily large sampling periods can guarantee consensus if the interaction graph consistently maintains a spanning tree.

Conclusions:

• The proposed MPC schemes effectively ensure consensus in MASs with switching interaction graphs.
• The extended control horizon provides additional flexibility for achieving robust consensus.
• Theoretical results are validated through simulations, demonstrating practical applicability.