Robust output regulation of uncertain chaotic systems with input magnitude and rate constraints

• Autorzy: Velosa C. M. N. , Bousson K.

Identyfikatory

DOI

10.1515/ama-2015-0040

• Języki publikacji: EN

Abstrakty

EN

The problem of output regulation deserves a special attention particularly when it comes to the regulation of nonlinear systems. It is well-known that the problem is not always solvable even for linear systems and the fact that some demanding applications require not only magnitude but also rate actuator constraints makes the problem even more challenging. In addition, real physical systems might have parameters whose values can be known only with a specified accuracy and these uncertainties must also be considered to ensure robustness and on the other hand because they can be crucial for the type of behaviour exhibited by the system as it happens with the celebrated chaotic systems. The present paper proposes a robust control method for output regulation of chaotic systems with parameter uncertainties and subjected to magnitude and rate actuator constraints. The method is an extension of a work recently addressed by the same authors and consists in decomposing the nonlinear system into a stabilizable linear part plus a nonlinear part and in finding a control law based on the small-gain principle. Numerical simulations are performed to validate the effectiveness and robustness of the method using an aeronautical application. The output regulation is successfully achieved without exceeding the input constraints and stability is assured when the parameters are within the specified intervals. Furthermore, the proposed method does not require much computational effort because all the control parameters are computed offline.

Słowa kluczowe

EN

output regulation; actuator constraints; parametric uncertainties; robust control; chaos; aeroelastic system

PL

regulacja mocy; chaos; niepewność parametryczna; układ aeroelastyczny

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2015
• Tom: Vol. 9, no. 4
• Strony: 252--258
• Opis fizyczny: Bibliogra. 19 poz., tab., wykr.

Twórcy

autor

Velosa C. M. N.

• LAETA-UBI/AeroG & Avionics and Control Laboratory, Department of Aerospace Sciences, University of Beira Interior, 6201-001 Covilhã, Portugal

autor

Bousson K.

• LAETA-UBI/AeroG & Avionics and Control Laboratory, Department of Aerospace Sciences, University of Beira Interior, 6201-001 Covilhã, Portugal

Bibliografia

• 1. Alstrom, B., Marzocca, P., Bollt, E., Ahmadi, G. (2010), Controlling Chaotic Motions of a Nonlinear Aeroelastic System Using Adaptive Control Augmented with Time Delay, AIAA Guidance, Navigation, and Control Conference, 1–14, Toronto, Ontario Canada.
• 2. Bernhard, P. (2002), Survey of Linear Quadratic Robust Control, Macroeconomic Dynamics, 6, 19–39.
• 3. Bousson, K., Velosa, C.M.N. (2014), Robust Control and Synchronization of Chaotic Systems with Actuator Constraints, P. Vasant (Ed.), Handbook of Research on Artificial Intelligence Techniques and Algorithms, 1–43, IGI Global.
• 4. Chen, C.L., Peng, C.C., Yau, H.T. (2012), High-order Sliding Mode Controller with Backstepping Design for Aeroelastic Systems, Communications in Nonlinear Science and Numerical Simulation, 17(4), 1813–1823.
• 5. Demenkov, M. (2008), Structural Instability Induced by Actuator Constraints in Controlled Aeroelastic System. In Proceedings of the 6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008). Saint Petersburg, Russia.
• 6. Deng, L., Xu, J. (2010), Control and Synchronization for Uncertain Chaotic Systems with LMI Approach, Chinese Control and Decision Conference (CCDC), 1695–1700.
• 7. Galeani, S., Teel, A.R., Zaccarian, L. (2007), Constructive Nonlinear Anti-windup Design for Exponentially Unstable Linear Plants, Systems & Control Letters, 56(5), 357–365.
• 8. Hippe, P. (2006), Windup In Control: Its Effects and Their Prevention, Springer.
• 9. Horowitz, I. (2001), Survey of Quantitative Feedback Theory (QFT), International Journal of Robust and Nonlinear Control, 11(10), 887– 921.
• 10. Huang, J. (2004), Nonlinear Output Regulation: Theory and Applications, Philadelphia: Siam.
• 11. Ott, E., Grebogi, C., Yorke, J.A. (1990), Controlling Chaos, Physical Review Letters, 64(11), 1196–1199.
• 12. Pecora, L.M., Carroll, T.L. (1990), Synchronization in Chaotic Systems, Physical Review Letters, 64(8), 821–824.
• 13. Saberi, A., Stoorvogel, A.A., Sannuti, P. (2011), Control of Linear Systems with Regulation and Input Constraints, Springer; Reprint of the original 1st ed.
• 14. Tanaka, K., Wang, H. O. (2001), Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (1st ed.), WileyInterscience.
• 15. Velosa, C.M.N., Bousson, K. (2014), Suppression of Chaotic Modes in Spacecraft with Asymmetric Actuator Constraints, Submitted to the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering.
• 16. Velosa, C. M. N., Bousson, K. (2015), Synchronization of Chaotic Systems with Bounded Controls, International Review of Automatic Control (IREACO), (To appear).
• 17. Vikhorev, K. S., Goman, M. G., Demenkov, M. N. (2008), Effect of Control Constraints on Active Stabilization of Flutter Instability, Proceedings of The Seventh International Conference on Mathematical Problems in Engineering Aerospace and Sciences (ICNPAA 2008), 1–8, Genoa, Italy.
• 18. Wang, C.-C., Chen, C.-L., Yau, H.-T. (2013), Bifurcation and Chaotic Analysis of Aeroelastic Systems, Journal of Computational and Nonlinear Dynamics, 9(2), 021004 (13 pages).
• 19. Zames, G. (1981), Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses, IEEE Transactions on Automatic Control, 26(2), 301–320.