Nonlinear H∞-control under unilateral constraints

References

• Aghabalaie, P., Hosseinzadeh, M., Talebi, H., & Shafiee, M. (2010). Nonlinear robust control of a biped robot. 2010 IEEE international symposium on Industrial Electronics (ISIE) (pp. 1907–1912). Bari, Italy: IEEE.
   Google Scholar
• Akhmet, M., & Turan, M. (2014). Bifurcation of discontinuous limit cycles of the Van der Pol equation. Mathematics and Computers in Simulation, 95, 39–54.
   Web of Science ®Google Scholar
• Ames, A., Galloway, K., & Grizzle, J. (2012). Control Lyapunov functions and hybrid zero dynamics. 2012 IEEE 51st annual conference on Decision and Control (CDC) (pp. 6837–6842). Maui, USA: IEEE.
   Google Scholar
• Aoustin, Y., & Formalsky, A. (2003). Control design for a biped: Reference trajectory based on driven angles as functions of the undriven angle. Journal of Computer and Systems Sciences International, 42(4), 645–662.
   Web of Science ®Google Scholar
• Baras, J., & James, M. (1993). Robust output feedback control for discrete-time nonlinear systems: The finite-time case. Proceedings of the 32nd IEEE conference on Decision and Control, 1993 (pp. 51–55). San Antonio, TX, USA: IEEE.
   Google Scholar
• Basar, T., & Bernhard, P. (1995). H∞-optimal control and related minimax design problems: A dynamic game approach. Berlin: Birkhauser.
   Google Scholar
• Bentsman, J., Miller, B.M., Rubinovich, E.Y., & Mazumder, S.K. (2012). Modeling and control of systems with active singularities under energy constraints: Single-and multi-impact sequences. IEEE Transactions on Automatic Control, 57(7), 1854–1859.
   Web of Science ®Google Scholar
• Biemond, J., van de Wouw, N., Heemels, W., & Nijmeijer, H. (2013). Tracking control for hybrid systems with state-triggered jumps. IEEE Transactions on Automatic Control, 58(4), 876–890.
   Web of Science ®Google Scholar
• Brogliato, B. (1999). Nonsmooth mechanics: Models, dynamics and control. London, UK: Springer-Verlag.
   Google Scholar
• Brogliato, B., Niculescu, S., & Orhant, P. (1997). On the control of finite-dimensional mechanical systems with unilateral constraints. IEEE Transactions on Automatic Control, 42(2), 200–215.
   Web of Science ®Google Scholar
• Chen, B., Lee, T., & Feng, J. (1994). A nonlinear H ∞ control design in robotic systems under parameter perturbation and external disturbance. International Journal of Control, 59(2), 439–461.
   Web of Science ®Google Scholar
• El-Farra, N.H., Mhaskar, P., & Christofides, P.D. (2005). Output feedback control of switched nonlinear systems using multiple Lyapunov functions. Systems & Control Letters, 54(12), 1163–1182.
   Web of Science ®Google Scholar
• Goebel, R., Sanfelice, R., & Teel, A. (2009). Hybrid dynamical systems. Control Systems, IEEE, 29(2), 28–93.
   Web of Science ®Google Scholar
• Goswami, A., Espiau, B., & Keramane, A. (1996). Limit cycles and their stability in a passive bipedal gait. Proceedings 1996 IEEE international conference on Robotics and Automation, 1996 ( Vol. 1, pp. 246–251). Minneapolis, MN, USA: IEEE.
   Google Scholar
• Grizzle, J., Plestan, F., & Abba, G. (1999). Poincare’s method for systems with impulse effects: Application to mechanical biped locomotion. Proceedings of the 38th IEEE conference on Decision and Control, 1999 ( Vol. 4, pp. 3869–3876). Phoenix, AZ, USA: IEEE.
   Google Scholar
• Haddad, W.M., Chellaboina, V., & Nersesov, S.G. (2006). Impulsive and hybrid dynamical systems: Stability, dissipativity, and contro. Princeton, NJ, USA: Princeton University Press.
   Google Scholar
• Haddad, W., Kablar, N., Chellaboina, V., & Nersesov, S. (2005). Optimal disturbance rejection control for nonlinear impulsive dynamical systems. Nonlinear Analysis: Theory, Methods & Applications, 62(8), 1466–1489.
   Web of Science ®Google Scholar
• Hamed, K., & Grizzle, J. (2013). Robust event-based stabilization of periodic orbits for hybrid systems: Application to an underactuated 3D bipedal robot. Proceedings of the 2013 American control conference. Washington, DC, USA.
   Google Scholar
• Hespanha, J.P., Liberzon, D., & Teel, A.R. (2008). Lyapunov conditions for input-to-state stability of impulsive systems. Automatica, 44(11), 2735–2744.
   Web of Science ®Google Scholar
• Hill, D., & Moylan, P. (1980). Connections between finite-gain and asymptotic stability. IEEE Transactions on Automatic Control, 25(5), 931–936.
   Web of Science ®Google Scholar
• Isidori, A., & Astolfi, A. (1992). Disturbance attenuation and H∞-control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control, 37(9), 1283–1293.
   Web of Science ®Google Scholar
• Li, Y., Li, T., & Jing, X. (2014). Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function. International Journal of Adaptive Control and Signal Processing, 28(2), 184–199.
   Web of Science ®Google Scholar
• Lin, W., & Byrnes, C. (1996). H∞-control of discrete-time nonlinear systems. IEEE Transactions on Automatic Control, 41(4), 494–510.
   Web of Science ®Google Scholar
• Mhaskar, P., El-Farra, N.H., & Christofides, P.D. (2006). Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control. Systems & Control Letters, 55(8), 650–659.
   Web of Science ®Google Scholar
• Montano, O., Orlov, Y., & Aoustin, Y. (2014). Nonlinear state feedback ${\mathcal{H}}_{\infty }$-control of mechanical systems under unilateral constraints. Proceedings of the 19th World Congress of the International Federation of Automatic Control (pp. 3833–3838). Cape Town, South Africa: IFAC.
   Google Scholar
• Montano, O., Orlov, Y., & Aoustin, Y. (2015). Nonlinear output feedback ${\mathcal{H}}_{\infty }$-control of mechanical systems under unilateral constraints. Proceedings of the 1st IFAC conference on Modelling, Identification and Control of Nonlinear Systems (pp. 284–289). Sain Petersburg, Russia: IFAC.
   Google Scholar
• Montano, O., Orlov, Y., Aoustin, Y., & Chevallereau, C. (2016). Orbital stabilization of an underactuated bipedal gait via nonlinear H∞-control using measurement feedback. Autonomous Robots, 1–19.
   Google Scholar
• Naldi, R., & Sanfelice, R.G. (2013). Passivity-based control for hybrid systems with applications to mechanical systems exhibiting impacts. Automatica, 49(5), 1104–1116.
   Web of Science ®Google Scholar
• Nešić, D., Teel, A.R., Valmorbida, G., & Zaccarian, L. (2013). Finite-gain stability for hybrid dynamical systems. Automatica, 49(8), 2384–2396.
   Web of Science ®Google Scholar
• Nešić, D., Zaccarian, L., & Teel, A. (2008). Stability properties of reset systems. Automatica, 44(8), 2019–2026.
   Web of Science ®Google Scholar
• Niu, B., & Zhao, J. (2013a). Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems. Systems & Control Letters, 62(10), 963–971.
   Web of Science ®Google Scholar
• Niu, B., & Zhao, J. (2013b). Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function. International Journal of Systems Science, 44(5), 978–985.
   Web of Science ®Google Scholar
• Orlov, Y. (2009). Discontinuous systems–Lyapunov analysis and robust synthesis under uncertainty conditions. London, UK: Springer.
   Google Scholar
• Orlov, Y., & Aguilar, L. (2014). Advanced ${\mathcal{H}}_{\infty }$ control–towards nonsmooth theory and applications. Berlin: Birkhauser.
   Google Scholar
• Orlov, Y., Montano, O., & Herrera, L. (2016). Hopf bifurcation of Van der Pol oscillators operating under unilateral constraints. American control conference. Boston, MA.
   Google Scholar
• Ortega, R., Perez, J.A., Nicklasson, P., & Sira-Ramirez, H. (2013). Passivity-based control of Euler–Lagrange systems: Mechanical, electrical and electromechanical applications. London, UK: Springer.
   Google Scholar
• Richter, H. (2011). A multi-regulator sliding mode control strategy for output-constrained systems. Automatica, 47(10), 2251–2259.
   Web of Science ®Google Scholar
• Rodrigues, L., & Boukas, E.K. (2006). Piecewise-linear H∞ controller synthesis with applications to inventory control of switched production systems. Automatica, 42(8), 1245–1254.
   Web of Science ®Google Scholar
• Su, Q., Wang, M., Dimirovski, G.M., Dong, X., & Zhao, J. (2012). Tracking of output-constrained switched nonlinear systems in strict-feedback form. 2012 31st Chinese control conference (CCC) (pp. 367–372). Hefei, China: IEEE.
   Google Scholar
• Van Der Schaft, A.J. (1991). On a state space approach to nonlinear H∞ control. Systems & Control Letters, 16, 1–8.
   Web of Science ®Google Scholar
• Westervelt, E., Grizzle, J., Chevallereau, C., Choi, J., & Morris, B. (2007). Feedback control of dynamic bipedal robot locomotion. Boca Raton, FL: CRC press.
   Google Scholar
• Willems, J. (1972). Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis, 45(5), 321–351.
   Web of Science ®Google Scholar
• Yuliar, S., James, M., & Helton, J. (1998). Dissipative control systems synthesis with full state feedback. Mathematics of Control, Signals and Systems, 11(4), 335–356.
   Web of Science ®Google Scholar
• Zhang, X., Zhao, J., & Dimirovski, G.M. (2012). L 2-gain analysis and control synthesis of uncertain switched linear systems subject to actuator saturation. International Journal of Systems Science, 43(4), 731–740.
   Web of Science ®Google Scholar