Autors: Das D., Taralova I., Loiseau J.J., Slavov, T. N.
Title: Fractional Mixed-integer Model Predictive Control of Fractional Rössler Oscillator
Keywords: Chaos, Fractional Mixed-Integer Model Predictive Control, Fractional-order Rössler system, Grünwald-Letnikov characterization, Gurobi, YALMIP

Abstract: V. 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.

References

  1. E.F. Camacho, and C. Bordons Model predictive control 2013 Springer Science & Business Media
  2. D. Das, I. Taralova, and J.J. Loiseau Time-delay feedback control of fractional chaotic rössler oscillator IFAC-PapersOnLine 58 5 2024 90 95
  3. D. Das, I. Taralova, J.J. Loiseau, and S. Filipova-Petrakieva Fractional model predictive control of fractional chaotic rössler oscillator IFAC-PapersOnLine 59 11 2025 156 161
  4. Gurobi Optimization, LLC (2025). Gurobi Optimizer Reference Manual. URL https://www.gurobi.com.
  5. Löfberg, J. (2004). Yalmip: A toolbox for modeling and optimization in MATLAB. In Proceedings of the 2004 IEEE International Conference on Robotics and Automation, 284-289. IEEE. IEEE Cat. No. 04CH37508.
  6. J.T. Machado, V. Kiryakova, and F. Mainardi Recent history of fractional calculus Communications in Nonlinear Science and Numerical Simulation 16 3 2011 1140 1153
  7. D.Q. Mayne, J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert Constrained model predictive control: Stability and optimality Automatica 36 6 2000 789 814
  8. R.D. McAllister, and J.B. Rawlings Advances in mixed-integer model predictive control. In 2022 American Control Conference (ACC) 2022 IEEE 364 369
  9. I. Petráš Fractional-order feedback control of a fractional-order system Journal of Electrical Engineering 59 6 2008 295 300
  10. I. Podlubny Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, volume 198 1998 Elsevier
  11. O.E. Rössler An equation for continuous chaos Physics Letters A 57 5 1976 397 398
  12. R. Scherer, S. Kalla, Y. Tang, and J. Huang The grünwald-letnikov method for fractional differential equations Computers & Mathematics with Applications 62 3 2011 902 917
  13. P. Sopasakis, and H. Sarimveis A tube-based mpc approach for discrete-time fractional-order systems subject to disturbances International Journal of Control 89 12 2016 2436 2445

Issue

IFAC-PapersOnLine, vol. 59, pp. 175-180, 2025, Albania, https://doi.org/10.1016/j.ifacol.2026.01.030

Вид: публикация в международен форум, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus