Exponential consensus of discrete-time non-linear multi-agent systems via relative state-dependent impulsive...

Area of Science:

• Control Theory
• Networked Systems
• Non-linear Dynamics

Background:

• Multi-agent systems (MAS) are crucial for distributed control and coordination.
• Achieving consensus (agreement) in MAS is a fundamental challenge, especially with complex dynamics.
• Impulsive control strategies offer efficient ways to influence system behavior at discrete time intervals.

Purpose of the Study:

• To investigate exponential consensus in discrete-time multi-agent systems with non-linear dynamics.
• To introduce and analyze novel relative state-dependent impulsive protocols.
• To establish sufficient conditions for achieving exponential consensus using these protocols.

Main Methods:

• Development of relative state-dependent impulsive protocols where trigger times depend on agent interactions.
• Transformation of the analysis of these protocols into an equivalent analysis of fixed-time impulsive protocols using a B-equivalence method.
• Derivation of sufficient conditions for exponential consensus based on the reduced fixed-time systems.

Main Results:

• Demonstration that exponential consensus can be achieved if the reduced fixed-time impulsive systems satisfy specific criteria.
• Validation of the theoretical findings through numerical simulations.
• The proposed protocols are applicable to general discrete-time multi-agent systems with non-linear dynamics.

Conclusions:

• Relative state-dependent impulsive protocols are effective for achieving exponential consensus in complex discrete-time multi-agent systems.
• The B-equivalence method provides a powerful tool for analyzing such impulsive protocols.
• The study offers a theoretical framework and practical validation for advanced consensus control strategies.