Abstract
This chapter proposes a hybrid control scheme for fully linearizable nonlinear systems, subject to uncertainty. Adopting a hybrid dynamic framework allows providing LMI-based tools for designing a sampled-data feedback controller whose internal state comprises the held value of the plant input. This controller state is discretely updated at exactly the classical linearizing control law, which is held constant during the continuous evolution of the closed loop. The updates happen at suitably triggered jumps, whose triggering rules stem from two different Lyapunov-based sets of inequalities, the first one ensuring robust in-the-small stability properties and the second one ensuring more desirable robustness in-the-large. Simulation results illustrate the effectiveness of the proposed hybrid control scheme.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aldhaheri, R.W., Khalil, H.K.: Effect of unmodeled actuator dynamics on output feedback stabilization of nonlinear systems. Automatica 32(9), 1323–1327 (1996)
Arcak, M., Seron, M., Braslavsky, J., Kokotovic, P.: Robustification of backstepping against input unmodeled dynamics. IEEE Trans. Autom. Control 45(7), 1358–1363 (2000)
Arcak, M., Teel, A., Kokotovic, P.: Robust nonlinear control of feedforward systems with unmodeled dynamics. Automatica 37, 265–272 (2001)
Biannic, J.-M., Burlion, L., Tarbouriech, S., Garcia, G.: On dynamic inversion with rate limitations. In: American Control Conference, Montreal, Canada, June 2012
Esfandiari, F., Khalil, H.K.: Output feedback stabilization of fully linearizable systems. Int. J. Control 56(5), 1007–1037 (1992)
Franco, A.L.D., Bourlès, H., De Pieri, E.R., Guillard, H.: Robust nonlinear control associating robust feedback linearization and \({\cal{H} }_\infty \) control. IEEE Trans. Autom. Control 51(7), 1200–1207 (2006)
Goebel, R., Sanfelice, R.G., Teel, A.R.: Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press (2012)
Goebel, R., Sanfelice, R.G., Teel, A.R.: Hybrid dynamical systems: robust stability and control for systems that combine continuous-time and discrete-time dynamics. IEEE Control. Syst. Mag. 29(2), 28–93 (2009)
Herrmann, G., Menon, P., Turner, M., Bates, D., Postlethwaite, I.: Anti-windup synthesis for nonlinear dynamic inversion control schemes. Int. J. Robust Nonlinear Control 20(13), 1465–1482 (2010)
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall (2002)
Lavergne, F., Villaume, F., Garcia, G., Tarbouriech, S., Jeanneau, M.: Nonlinear and robust flight control laws design for the longitudinal axis of an aircraft. In: 11th Australian International Aerospace Congress (AIAC’11), Melbourne (Australia), March 2005
Leite, V.J.S., Tarbouriech, S., Garcia, G.: Energy-peak evaluation of nonlinear control systems under neglected dynamics. In: 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS), Toulouse, France, September 2013
Löfberg, J.: YALMIP: a toolbox for modeling and optimization in MATLAB. In: In Proceedings of the CACSD Conference, Taipei, Taiwan (2004)
Menon, P.P., Herrmann, G., Turner, M.C., Lowenberg, M., Bates, D., Postlethwaite, I.: Nonlinear dynamic inversion based anti-windup—an aerospace application. In: World IFAC Congress, Seoul, Korea (2008)
Papageorgiou, C., Glover, K.: Robustness analysis of nonlinear flight controllers. AIAA J. Guid. Control. Dyn. 28(4), 639–648 (2005)
Prieur, C., Tarbouriech, S., Zaccarian, L.: Lyapunov-based hybrid loops for stability and performance of continuous-time control systems. Automatica 49(2), 577–584 (2013)
Reiner, J., Balas, G.J., Garrard, W.L.: Flight control design using robust dynamic inversion and time-scale separation. Automatica 32(11), 1491–1625 (1996)
Sanfelice, R.G., Copp, D., Nanez, P.: A toolbox for simulation of hybrid systems in Matlab/Simulink: hybrid equations (HyEQ) toolbox. In: Hybrid Systems: Computation and Control Conference (2013)
Topcu, U., Packard, A.: Local robust performance analysis for nonlinear dynamical systems. In: American Control Conference, St. Louis, USA, June 2009, pp. 784–789
Wang, Q., Stengel, R.F.: Robust nonlinear flight control of a high-performance aircraft. IEEE Trans. Control. Syst. Technol. 13(1), 15–26 (2005)
Wang, X., Van Kampen, E.J., Chu, Q., Lu, P.: Stability analysis for incremental nonlinear dynamic inversion control. J. Guid. Control. Dyn. 42(5), 1116–1129 (2019)
Yang, J., Chen, W.-H., Li, S.: Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties. IET Control. Theory & Appl. 5(18), 2053–2062 (2011)
Acknowledgements
This work was supported by the “Agence Nationale de la Recherche” (ANR) under Grant HANDY ANR-18-CE40-0010.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Tarbouriech, S., Prieur, C., Queinnec, I., Zaccarian, L., Garcia, G. (2024). Control of Uncertain Nonlinear Fully Linearizable Systems. In: Postoyan, R., Frasca, P., Panteley, E., Zaccarian, L. (eds) Hybrid and Networked Dynamical Systems. Lecture Notes in Control and Information Sciences, vol 493. Springer, Cham. https://doi.org/10.1007/978-3-031-49555-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-031-49555-7_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-49554-0
Online ISBN: 978-3-031-49555-7
eBook Packages: EngineeringEngineering (R0)