Fractional Mixed-integer Model Predictive Control of Fractional Rössler Oscillator

This research presents a novel implementation of Fractional Mixed-Integer Model Predictive Control (FMIMPC) for the stabilization of the chaotic Rössler system, incorporating fractional-order dynamics via the Grünwald–Letnikov characterization. The system is represented using a discrete-time linear approximation around its equilibrium point, and the control strategy is based on a finite-horizon optimization that includes binary variables to allow switching between different cost levels adaptively. The Grünwald–Letnikov (GL) characterization is utilized to capture the system’s inherent memory effects, thereby enhancing the fidelity of the fractional-order modeling. The optimization problem is formulated in YALMIP and solved using the Gurobi solver, facilitating efficient handling of mixed-integer constraints. To assess the closed-loop stability under the proposed FMIMPC strategy, the largest Lyapunov exponent is estimated by monitoring the divergence of two initially adjacent trajectories governed by the same control policy. Numerical simulations demonstrate successful trajectory tracking and chaos suppression, as evidenced by convergence to the reference state and negative Lyapunov exponent trends. The results validate the potential of FMIMPC as a robust control strategy for fractional-order chaotic systems, where discrete switching logic, enabled by binary decision variables, allows adaptive transitions between multiple control modes based on system performance.