Generation of stable oscillations in uncertain nonlinear systems with matched and unmatched uncertainties

References

• Adachi, M. , Ushio, T. , & Yamamoto, S. (2004). Synthesis of hybrid systems with limit cycles satisfying piecewise smooth constraint equations. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences , 87 (4), 837–842.
   Google Scholar
• Aguilar, L. T. , Boiko, I. , Fridman, L. , & Iriarte, R. (2009). Generating self-excited oscillations via two-relay controller. IEEE Transactions on Automatic Control , 54 (2), 416–420.
   Web of Science ®Google Scholar
• Aguilar-Ibánez, C. , Martinez, J. C. , de Jesus Rubio, J. , & Suarez-Castanon, M. S. (2015). Inducing sustained oscillations in feedback-linearizable single-input nonlinear systems. ISA Transactions , 54 , 117–124.
   PubMed Web of Science ®Google Scholar
• Albea, C., Gordillo, F., & Aracil, J. (2006). Control of the boost DC-AC converter by energy shaping. IEEE Industrial Electronics, IECON 2006-32nd Annual Conference on Nov 6-10, 2006 (pp. 754–759). Paris, France.
   Google Scholar
• Aracil, J. , Gordillo, F. , & Ponce, E. (2005). Stabilization of oscillations through backstepping in high-dimensional systems. IEEE Transactions on Automatic Control , 50 (5), 705–710.
   Web of Science ®Google Scholar
• Benmiloud, M. , & Benalia, A. (2016). Finite-time stabilization of the limit cycle of two-cell DC/DC converter: Hybrid approach. Nonlinear Dynamics , 83 (1–2), 319–332.
   Web of Science ®Google Scholar
• Biel, D. , Fossas, E. , Guinjoan, F. , Alarcón, E. , & Poveda, A. (2001). Application of sliding-mode control to the design of a buck-based sinusoidal generator. IEEE Transactions on Industrial Electronics , 48 (3), 563–571.
   Web of Science ®Google Scholar
• Binazadeh, T. (2016). Finite-time tracker design for uncertain nonlinear fractional-order systems. Journal of Computational and Nonlinear Dynamics , 11 (4), 041028
   Web of Science ®Google Scholar
• Binazadeh, T. , & Bahmani, M. (2017). Design of robust controller for a class of uncertain discrete‐time systems subject to actuator saturation. IEEE Transactions on Automatic Control , 62 (3), 1505–1510.
   Web of Science ®Google Scholar
• Binazadeh, T. , & Shafiei, M. H. (2013). Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach. Mechatronics , 23 , 888–892.
   Web of Science ®Google Scholar
• Cardenas-Maciel, S. L. , Castillo, O. , & Aguilar, L. T. (2011). Generation of walking periodic motions for a biped robot via genetic algorithms. Applied Soft Computing , 11 (8), 5306–5314.
   Web of Science ®Google Scholar
• Chemori, A. , & Alamir, M. (2005). Limit cycle generation for a class of non-linear systems with jumps using a low dimensional predictive control. International Journal of Control , 78 (15), 1206–1217.
   Web of Science ®Google Scholar
• Chenarani, H. , & Binazadeh, T. (2017). Flexible structure control of unmatched uncertain nonlinear systems via passivity-based sliding mode technique. Iranian Journal of Science & Technology, Transactions of Electrical Engineering , 41 (1), 1–11.
   Web of Science ®Google Scholar
• Favela-Contreras, A. , Carbajal, F. B. , Piñón, A. , & Raimondi, A. (2016). Limit cycle analysis in a class of hybrid systems. Mathematical Problems in Engineering , 2016 , 2981952.
   Google Scholar
• Golestani, M. , Mobayen, S. , & Tchier, F. (2016). Adaptive finite-time tracking control of uncertain non-linear n-order systems with unmatched uncertainties. IET Control Theory & Applications , 10 (14), 1675–1683.
   Web of Science ®Google Scholar
• Green, D. (1984). Synthesis of systems with periodic solutions satisfying V (x) = 0. IEEE Transactions on Circuits and Systems , 31 (4), 317–326.
   Google Scholar
• Guermouche, M. , Ali, S. A. , & Langlois, N. (2015). Super-twisting algorithm for DC motor position control via disturbance observer. IFAC-Papers On Line , 48 (30), 43–48.
   Google Scholar
• Haddad, W. M. , & Chellaboina, V. (2008). Nonlinear dynamical systems and control: A Lyapunov-based approach . Princeton, NJ: Princeton University Press.
   Google Scholar
• Hakimi, A. R. , & Binazadeh, T. (2015). Stable limit cycles generating in a class of uncertain nonlinear systems : Application in inertia pendulum. Modares Journal of Electrical Engineering , 12 (3), 1–6.
   Google Scholar
• Hakimi, A. R. , & Binazadeh, T. (2016). Inducing sustained oscillations in a class of nonlinear discrete time systems. Journal of Vibration and Control . doi:10/77546316659223
   Google Scholar
• Hakimi, A. R. , & Binazadeh, T. (2017). Robust generation of limit cycles in nonlinear systems: Application on two mechanical systems. Journal of Computational and Nonlinear Dynamics , 12 (4), 041013.
   Web of Science ®Google Scholar
• Hashimoto, S. , Naka, S. , Sosorhang, U. , & Honjo, N. (2012). Generation of optimal voltage reference for limit cycle oscillation in digital control-based switching power supply. Journal of Energy and Power Engineering, 6 (4), 623–628.
   Google Scholar
• Hobbelen, D. , de Boer, T. , & Wisse, M. (2008). System overview of bipedal robots flame and tulip: Tailor-made for limit cycle walking. In Intelligent Robots and Systems, IROS 2008, IEEE/RSJ International Conference on Sept, 22-26, 2008 , (pp. 2486–2491). IEEE.
   Google Scholar
• Kai, T. (2012). Limit-cycle-like control for planar space robot models with initial angular momenta. Acta Astronautica , 74 , 20–28.
   Web of Science ®Google Scholar
• Kai, T. (2013). Limit-cycle-like control for 2-dimensional discrete-time nonlinear control systems and its application to the Hénon map. Communications in Nonlinear Science and Numerical Simulation , 18 (1), 171–183.
   Web of Science ®Google Scholar
• Kai, T. , & Masuda, R. (2012). Limit cycle synthesis of multi-modal and 2-dimensional piecewise affine systems. Mathematical and Computer Modelling , 55 (3–4), 505–516.
   Google Scholar
• Khalil, H. K. (2014). Nonlinear control . Upper Saddle River, NJ: Prentice Hall.
   Google Scholar
• Ramirez-Rodriguez, H. , Parra-Vega, V. , Sanchez-Orta, A. , & Garcia-Salazar, O. (2014). Robust backstepping control based on integral sliding modes for tracking of quadrotors. Journal of Intelligent & Robotic Systems , 73 (1–4), 51–66.
   Web of Science ®Google Scholar
• Saublet, L. M. , Ghoachani, R. G. , Martin, J. P. , Mobarakeh, B. N. , & Pierfederici, S. (2016). Asymptotic stability analysis of the limit cycle of a cascaded DC–DC converter using sampled discrete-time modeling. IEEE Transactions on Industrial Electronics , 63 (4), 2477–2487.
   Web of Science ®Google Scholar
• Shiriaev, A. , Perram, J. W. , & Canudas-de-Wit, C. (2005). Constructive tool for orbital stabilization of underactuated nonlinear systems: Virtual constraints approach. IEEE Transactions on Automatic Control , 50 (8), 1164–1176.
   Web of Science ®Google Scholar
• Solomon, J. H. , Wisse, M. , & Hartmann, M. J. (2010). Fully interconnected, linear control for limit cycle walking. Adaptive Behavior, 18 (6), 492–506.
   Web of Science ®Google Scholar
• Teplinsky, A. , & Feely, O. (2008). Limit cycles in a MEMS oscillator. IEEE Transactions on Circuits and Systems II: Express Briefs, 55 (9), 882–886.
   Web of Science ®Google Scholar
• Yang, Y. , Feng, G. , & Ren, J. (2004). A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems. IEEE Transactions on Systems, Man, and Cybernetics – Part A: Systems and Humans, 34 (3), 406–420.
   Web of Science ®Google Scholar
• Zhang, A. , Ma, S. , Li, B. , Wang, M. , Guo, X. , & Wang, Y. (2016). Adaptive controller design for underwater snake robot with unmatched uncertainties. Science China Information Sciences ,59(5), 1–15.
   Web of Science ®Google Scholar