Papers on Nonlinear Theory

1. Aaron D. Ames, Xiangru Xu, Jessy W. Grizzle, and Paulo Tabuada Control Barrier Function Based Quadratic Programs with Application to Automotive Safety Systems, Preprint IEEE Transactions on Automatic Control; Submitted June 2015; Revised and Resubmitted 20 April 2016.
2. Kevin Galloway, Koushil Sreenath, Aaron D. Ames, and J. W. Grizzle, Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs, Reprint IEEE Transactions on Robotics, Submitted Feb. 2013. Revised Feb. 2014 Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs, [Remark] While the result is illustrated here for a 2D robot, it applies to 3D compliant robots as well. Only depends on HZD. [Supplemental Material] Video on YouTube Other robotics video are here: Dynamic Leg Locomotion.
3. K. Akbari Hamed, B.G. Buss and J.W. Grizzle, Robust Stabilizing Continuous-Time Controllers for Periodic Orbits of Hybrid Systems: Application to Bipedal Robots, Submitted on 16 July 2014, IEEE Transaction of Robotics. [Animation 1],
4. K. Akbari Hamed, B. G. Buss, and J. W. Grizzle, Continuous-Time Controllers for Stabilizing Periodic Orbits of Hybrid Systems: Application to an Underactuated 3D Bipedal Robot 53rd IEEE Conference of Decision and Control (CDC 2014), December 2014. [Supplemental Material].
5. A. D. Ames, J.W. Grizzle and P. Tabuada, ``Control Barrier Function based Quadratic Programs with Application to Adaptive Cruise Control,'' 53rd IEEE Conference of Decision and Control (CDC 2014), December 2014.
6. Aaron D. Ames, Kevin Galloway, J.W. Grizzle, and Koushil Sreenath Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics, reprint 2 IEEE TAC, Vol. 59, NO. 4, pp 876-891. [Supplemental Material] Video on YouTube Other robotics video are here: Dynamic Leg Locomotion.
7. A.R. Teel, R. Goebel, B. Morris, A.D. Ames, J.W. Grizzle, A stabilization result with application to bipedal locomotion,, IEEE Conf. on Decision and Control, Florence, Italy, Dec., 2013.
8. Aaron D. Ames, Kevin Galloway, J.W. Grizzle, and Koushil Sreenath Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics, Submitted 26 Nov. 2012, IEEE TAC. [Supplemental Material] Video on YouTube Other robotics video are here: Dynamic Leg Locomotion.
9. Aaron D. Ames, Kevin Galloway, and J.W. Grizzle, Control Lyapunov Functions and Hybrid Zero Dynamics, Reprint 2012-CDC, Hawaii, USA, December, 2012. [Supplemental Material] The proofs could not be included in the final 6 page submission, so they are given here: Proofs for CLF and HZD.
10. Ioannis Poulakakis and J. W. Grizzle, The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper, Published IEEE Transaction on Automatic Control, Volume 54, Issue 8, Aug. 2009 Page(s):1779 - 1793.
11. B. Morris and J.W. Grizzle, Hybrid Invariant Manifolds in Systems with Impulse Effects with Application to Periodic Locomotion in Bipedal Robots, Published IEEE Transaction on Automatic Control, Volume 54, Issue 8, Aug. 2009 Page(s):1751 - 1764
12. Ioannis Poulakakis and J. W. Grizzle, Formal Embedding of the Spring Loaded Inverted Pendulum in an Asymmetric Hopper, Reprint European Control Conference (2007-ECC), Kos, Greece, July 2007.
13. B. Morris and J.W. Grizzle, A Restricted Poincare Map for Determining Exponentially Stable Periodic Orbits in Systems with Impulse Effects: Application to Bipedal Robots, Reprint 2005-CDC, Seville, Spain, December, 2005.
14. J.W. Grizzle, C.H. Moog, and C. Chevallereau, Nonlinear Control of Mechanical Systems with an Unactuated Cyclic Variable. Re-print, IEEE-TAC, Vol. 30, No. 5, May 2005, pp. 559-576. [Supplemental Material].
15. K. Peterson, J.W. Grizzle, and A.G. Stefanopoulou, Nonlinear Control for Magnetic Levitation of Automotive Engine Valves, Re-print, IEEE Tran. Control Systems Technology, Volume 14, Issue 2, March 2006. pp. 346 - 354
16. K. Peterson, J.W. Grizzle, and A.G. Stefanopoulou, Nonlinear Magnetic Levitation Of Automotive Engine Valves , 3rd IFAC Symposium on Mechatronic Systems, September 6-8, 2004, Sydney (Australia) [Kathy won a best paper presentation award!]
17. C. Chevallereau, J.W. Grizzle, and C.H. Moog, Nonlinear Control of Mechanical Systems with one Degree of Underactuation. Re-print, ICRA 2004, New Orleans, April 26 to May 1, 2004. [Supplemental Material].
18. E.R. Westervelt, J.W. Grizzle, and D.E. Koditschek, Hybrid Zero Dynamics of Planar Biped Walkers. Reprint, IEEE-TAC, Vol. 48, No. 1, January 2003, pp. 42-56. [Supplemental Material].
19. J.W. Grizzle and Jun-Mo Kang Discrete-time Control Design with Positive Semi-Definite Lyapunov Functions. , Systems and Control Letters, 43, 2001, pp. 287-292.
20. S. Diop, V. Fromion, and J.W. Grizzle A resettable Kalman filter, Reprint, Proceedings of the 2001 European Control Conference .
21. J.W. Grizzle, Gabriel Abba and Franck Plestan, Asymptotically Stable Walking for Biped Robots: Analysis via Systems with Impulse Effects. Reprint, IEEE T-AC, Volume 46, No. 1, January 2001, pp. 51-64. revised version. This paper received the 2002 George S. Axelby Award for the Best Paper in the IEEE Trans. Auto. Control during the years 2000 and 2001.
22. S. Diop, J.W. Grizzle and F. Chaplais On Numerical Differentiation Algorithms for Nonlinear Estimation, Reprint, Proceedings of the 2000 IEEE Conference on Decision and Control, Australia, December 2000.
23. Franck Plestan and J.W. Grizzle, Synthesis Of Nonlinear Observers Via Structural Analysis And Numerical Differentiation. Reprint, Proceedings of the September 1999 European Control Conference.

    A few older papers (See also IEEE Xplore)

24. Y.K. Song and J.W. Grizzle, The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems, Reprint, Journal of Mathematical Systems, Estimation and Control, Vol. 5, No. 1, 1995, pp. 59-78. (The journal in which this appeared seems to be hard for people to find) (submitted version)
25. P. Moraal and J.W. Grizzle Observer design for nonlinear systems with discrete-time measurements, Reprint, IEEE Transactions on Automatic Control, Vol. 40, No. 3, pp. 395--404, 1995.
26. P. Moraal and J.W. Grizzle Asymptotic observers for detectable and poorly observable systems, Reprint, Proceedings of the 1995 IEEE Conference on Decision and Control, New Orleans, December 1995.
27. J.W. Grizzle, A Linear Algebraic Framework for the Analysis of Discrete-Time Nonlinear Systems, Reprint, SIAM J. Control, Vol. 31, No. 4, July 1993, pp. 1026-1044.
28. S. Diop, J.W. Grizzle, P.E. Moraal, and A. Stefanopoulou, Interpolation and Numerical Differentiation for Observer Design, Reprint, 1994 American Control Conference, Baltimore, June 1994, pp. 1329-1333. Here is a longer version that appeared as an internal report [Control Group Reports, EECS Department, University of Michigan, September 1993]; it has more examples.
29. S. T. Chung and J.W. Grizzle Sampled-Data Observer Error Linearization, Reprint, Automatica, Vol. 26, No. 6, November, 1990, pp. 997-1007.
30. M.D. Di Benedetto and J.W. Grizzle An Intrinsic Notion of Regularity for Output Nulling, Inversion, and Dynamic Extension, Reprint, Control Theory and Advanced Technology, vol. 6, No. 3, September 1990. pp. 357-381.
31. M.D. Di Benedetto, J.W. Grizzle and C.H. Moog, Rank Invariants of Nonlinear Systems, Reprint, SIAM J. Control, Vol. 27, No. 3, May 1989, pp. 658-672.
32. J. W. Grizzle and A. Isidori, Block Noninteracting Control with Stability via Static State Feedback, Reprint, Mathematics of Control, Signals, and Systems, Vol. 2, 1989, pp. 315-341.
33. J. W. Grizzle, Local Input-Output Decoupling of Discrete Time Nonlinear Systems, Reprint, Int. J. of Control, Vol 43, No. 5, pp. 1517-1530, 1986.
34. J.W. Grizzle, Feedback Linearization of Discrete-Time Systems, Reprint, Lecture Notes in Control and Information Sciences, Vol. 83, Antibes, France, pp. 273-281, June 1986.
35. J. W. Grizzle, Distributions Invariantes Commandees pour les Systemes Non Lineaires en Temps Discret, Reprint, C. R. Acad. Sc. Paris, t. 300, Serie I, no. 13, pp. 447-450, 1985.
36. Jessy W. Grizzle, Steven I. Marcus and Kai Hsu, A decentralized control strategy for multiaccess broadcast networks, Reprint, Large Scale Systems, North-Holland Publishing Company, Vol. 3, 1982, pp. 75-78.
37. R. J. Mulholland and J. W. Grizzle, ``Modeling Perturbations of the Global Carbon Cycle," Reprint, Proc. of the International Conference on Cybernetics and Society, pp. 690-694, 1979.