Multirate-Sampled Fuzzy Consensus Control for Nonlinear Markov-Switched MASs With Time-Varying Delays: An Ellipsoidal...

Area of Science:

• Control Theory
• Systems Engineering
• Robotics

Background:

• Investigates consensus problems in nonlinear Markov-switched multiagent systems (MASs).
• Addresses challenges posed by time-varying delays and uncertain semi-Markov transition (GUST) switched topologies.
• Highlights the need for flexible control strategies in complex networked systems.

Purpose of the Study:

• To design a novel multirate sampled-data consensus (MRSDC) control scheme for nonlinear Markov-switched MASs.
• To ensure mean-square reachable set (RS) consensus under general uncertain semi-Markov transition (GUST) switched topologies.
• To confine reachable states within ellipsoidal attracting-like regions.

Main Methods:

• Transformation of nonlinear Markov-switched MASs into quasilinear subsystems using Takagi-Sugeno (T-S) fuzzy modeling.
• Development of an aperiodic MRSDC control strategy with adaptive sampling rates.
• Introduction of a new free-weighting integral inequality and a looped-side Lyapunov functional.
• Derivation of sufficient consensus conditions using linear matrix inequalities (LMIs).

Main Results:

• Sufficient conditions derived in LMIs guarantee mean-square leaderless consensus for the MASs.
• The MRSDC scheme ensures reachable states remain confined within ellipsoidal attracting-like regions.
• Numerical validations using interconnected single-link robot arm systems (SLRASs) demonstrate the method's effectiveness.

Conclusions:

• The proposed MRSDC control strategy effectively achieves consensus in nonlinear Markov-switched MASs with time-varying delays.
• The adaptive sampling approach enhances flexibility and consensus performance.
• The developed method offers superior performance compared to existing approaches, as shown by comparative numerical examples.