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Distributed coordination of networked fractional-order systems.
1Department of Electrical and Computer Engineering, Utah State University, Logan, UT 84322 USA. yongcan.cao@aggiemail.usu.edu
Summary
This study explores distributed coordination in networked fractional-order systems. Fractional-order coordination algorithms can achieve faster convergence than integer-order ones, especially when fractional orders are time-varying.
Area of Science:
- Control Systems Engineering
- Networked Systems Theory
- Fractional Calculus Applications
Background:
- Distributed coordination is crucial for networked systems.
- Fractional-order systems offer enhanced dynamics compared to traditional integer-order systems.
- Understanding coordination in fractional-order networks is an emerging research area.
Purpose of the Study:
- To introduce a general fractional-order coordination model for networked systems.
- To establish conditions for achieving coordination in these systems.
- To analyze and compare the convergence properties of fractional-order versus integer-order coordination.
Main Methods:
- Development of a generalized fractional-order coordination model.
- Analysis of system dynamics under directed interaction graphs.
- Derivation of sufficient conditions for coordination based on graph properties and fractional order.
- Explicitly defining the coordination equilibrium.
- Comparative analysis of convergence rates.
Main Results:
- Sufficient conditions for achieving distributed coordination in fractional-order systems are presented.
- The coordination equilibrium for the general model is explicitly determined.
- A relationship between the number of agents, fractional order, and coordination is established.
- Fractional-order systems demonstrate potentially faster convergence than integer-order systems.
- Time-varying fractional orders can further enhance convergence speed.
Conclusions:
- The proposed general fractional-order coordination model effectively addresses distributed coordination in networked systems.
- Coordination is achievable under specific conditions related to the interaction graph and fractional order.
- Fractional-order coordination offers advantages in convergence speed, which can be optimized through dynamic order adjustment.
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