Abstract
A hybrid-impulsive second order/higher order sliding mode (2-SMC/HOSM) control is explored in order to reduce dramatically the convergence time practically to zero, achieving instantaneous (or short time) convergence and uniformity. For systems of relative degree 2, the impulsive portion of the control function drives the system’s output (the sliding variable) and it’s derivative to zero instantaneously (or in short time) achieving a uniform convergence. Then the discontinuous state or output feedback stabilizes system’s trajectory at the origin (or its close vicinity), while achieving the ideal or real second order sliding mode (2-SM). The Lyapunov analysis of the considered hybrid-impulsive-discontinuous systems is performed. Hybrid-impulsive continuous HOSM (CHOSM) control is studied in systems of arbitrary relative degree with impulsive action that achieves almost instantaneous convergence and uniformity. This approach allows reducing the CHOSM amplitude, since the task of compensating the initial conditions is addressed by the impulsive action. Two hybrid-impulsive 2-SMCs are studied in systems of arbitrary relative degree in a reduced information environment. Only “snap” knowledge of the all states is required to facilitate the impulsive action. The efficacy of studied hybrid-impulsive control algorithms is illustrated via simulations.
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References
Aldukali, F.M., Shtessel, Y.B.: Continuous higher order sliding mode control with impulsive action. In: 2015 IEEE 54th Annual Conference on Decision and Control (CDC), pp. 5420–5425. IEEE (2015)
Aldukali, F.M., Shtessel, Y.B., Glumineau, A., Plestan, F.: Impulsive-super-twisting control in reduced information environments. In: American Control Conference (ACC), pp. 7207–7212. IEEE (2016)
Angulo, M.T., Moreno, J.A., Fridman, L.: An exact and uniformly convergent arbitrary order differentiator. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 7629–7634. IEEE (2011)
Bhat, S.P., Bernstein, D.S.: Geometric homogeneity with applications to finite-time stability. Math. Control Signals Syst. (MCSS) 17(2), 101–127 (2005)
Butt, A., Popp, C., Pitts, H., Sharp, D.: NASA ares i launch vehicle roll and reaction control systems design status. In: 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, p. 5130 (2009)
Edwards, C., Shtessel, Y.: Adaptive continuous higher order sliding mode control. IFAC Proc. Vol. 47(3), 10826–10831 (2014)
Gelfand, I.M., Shilov, G.E.: Generalized Functions. Applications of Harmonic Analysis, vol. 4. Academic Press, New York (1964)
Glumineau, A., Shtessel, Y., Plestan, F.: Impulsive-sliding mode adaptive control of second order system. IFAC Proc. Vol. 44(1), 5389–5394 (2011)
Glumineau, A., Shtessel, Y., Plestan, F.: Lyapunov stability of a hybrid impulsive-sliding mode adaptive controller for second order system. In: 2012 IEEE 51st Annual Conference on Decision and Control (CDC), pp. 5477–5481. IEEE (2012)
Guan, Z.H., Hill, D.J., Shen, X.: On hybrid impulsive and switching systems and application to nonlinear control. IEEE Trans. Autom. Control 50(7), 1058–1062 (2005)
Honeywell: reaction control system (2010). http://www51.honeywell.com/aero/common/documents/myaerospacecatalog-documents/Missiles-Munitions/$Reaction_Control_Systems_(Tactical).pdf$
Karageorgos, A.D., Pantelous, A.A., Kalogeropoulos, G.I.: Transferring instantly the state of higher-order linear descriptor (regular) differential systems using impulsive inputs. J. Control Sci. Eng. 2009, 6 (2009)
Khalil, H.K.: Noninear Systems. Prentice-Hall, New Jersey (2002)
King, A.: Inertial navigation-forty years of evolution. GEC Rev. 13(3), 140–149 (1998)
Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58(6), 1247–1263 (1993)
Levant, A.: Higher-order sliding modes, differentiation and output-feedback control. Int. J. Control 76(9–10), 924–941 (2003)
Levant, A.: Principles of 2-sliding mode design. Automatica 43(4), 576–586 (2007)
Li, H.Y., Luo, Y.Z., Tang, G.J., et al.: Optimal multi-objective linearized impulsive rendezvous under uncertainty. Acta Astronaut. 66(3), 439–445 (2010)
Miller, B.M., Rubinovich, E.Y.: Impulsive Control in Continuous and Discrete-Continuous Systems. Springer Science & Business Media, New York (2012)
Moreno, J.A., Osorio, M.: Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans. Autom. Control 57(4), 1035–1040 (2012)
Orlov, Y.V.: Discontinuous Systems: Lyapunov Analysis and Robust Synthesis Under Uncertainty Conditions. Springer Science & Business Media, New York (2008)
Pisano, A., Usai, E.: Sliding mode control: a survey with applications in math. Math. Comput. Simul. 81(5), 954–979 (2011)
Plestan, F., Moulay, E., Glumineau, A., Cheviron, T.: Robust output feedback sampling control based on second-order sliding mode. Automatica 46(6), 1096–1100 (2010)
Rosello, A.D.: A vehicle health monitoring system for the space shuttle reaction control system during reentry. Ph.D. thesis, Draper Laboratory (1995)
Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Springer, Berlin (2014)
Shtessel, Y., Glumineau, A., Plestan, F., Aldukali, F.M.: Hybrid-impulsive second-order sliding mode control: Lyapunov approach. Int. J. Robust Nonlinear Control (2016)
Shtessel, Y., Glumineau, A., Plestan, F., Aldukali, F.M.: Hybrid-impulsive second-order sliding mode control: Lyapunov approach. Int. J. Robust Nonlinear Control 27(7), 1064–1093 (2017)
Shtessel, Y.B., Moreno, J.A., Fridman, L.M.: Twisting sliding mode control with adaptation: Lyapunov design, methodology and application. Automatica 75, 229–235 (2017)
Sobolev, S.L., Browder, F.E.: Applications of Functional Analysis in Mathematical Physics. American Mathematical Society, Dunod (1962)
Weiss, M., Shtessel, Y.: An impulsive input approach to short time convergent control for linear systems. Advances in Aerospace Guidance, Navigation and Control, pp. 99–119. Springer, Berlin (2013)
Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 44(10), 976–988 (1997)
Yang, X., Cao, J., Ho, D.W.: Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control. Cogn. Neurodynamics 9(2), 113–128 (2015)
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Shtessel, Y.B., Aldukali, F.M., Plestan, F. (2018). Hybrid-Impulsive Higher Order Sliding Mode Control. In: Clempner, J., Yu, W. (eds) New Perspectives and Applications of Modern Control Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-62464-8_17
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