Observer-Based Distributed Consensus Control for Nonlinear Lipschitz and One-Side Lipschitz Fractional-Order Multi-Agent Systems

In this paper, an observer-based controller design for fractional-order multi-agent systems is discussed. By introducing a novel algorithm and leveraging appropriate lemmas and theoretical frameworks, we propose a stable observer and a distributed consensus protocol tailored for multi-agent systems within the Lipschitz and one-sided Lipschitz classes of nonlinear systems. Lipschitz systems have a bounded rate of change, ensuring proportional output to input differences, while one-sided Lipschitz systems relax this constraint, allowing differential growth in one direction for efficiency. The stability of the observer and the controller in achieving the consensus problem is demonstrated using the Lyapunov's second method. The proposed approach is rigorously developed, ensuring that the designed observer and controller meet the necessary stability criteria. Extensive simulation results validate the theoretical findings, showcasing the method's effectiveness and robustness in practical scenarios. Specifically, the simulations demonstrate that the proposed method achieves global Mittag-Leffler stability, with the estimated states converging to the actual states with minimal deviation. The method's advantages include its ability to handle a broader class of nonlinear systems, including those with large Lipschitz constants, and its robustness to uncertainties and nonlinearities. These simulations confirm the theoretical predictions and illustrate the practical applicability of our approach in real-world multi-agent systems, such as swarm robotics, power grids, and sensor networks.