Nonlinear H-Infinity Control

This research concerns the development of nonlinear extensions of the H-infinity approach to robust controller design for linear systems. Many new and important issues arise in the nonlinear context, including the dynamical behavior of the infinite dimensional information state system.

Here is a glimpse of the interesting behavior of singular information state dynamics:

• 2-D hyperbolic I
• 2-D purely singular

My recent work with J. W. Helton builds on earlier work with J.S. Baras, R.J. Elliott, W.H. Fleming, C. Teolis and S. Yuliar, and appears in the book

J.W. Helton and M.R. James, Extending H-Infinity Control to Nonlinear Systems : Control of Nonlinear Systems to Achieve Performance Objectives, SIAM, 1999, ISBN 0-89871-440-0. (More details.)

Work on applying nonlinear H-Infinity control and on developing related methods has been carried out with I.R. Petersen, E. Gallestey, W.M. McEneaney, D.J.N. Limebeer and B.D.O. Anderson.

Selected Papers:

• E. Gallestey, M.R. James and W.M. McEneaney , Max-Plus Approximation Methods in Partially Observed H-Infinity Control (PS.GZ)
• 1997 CDC Workshop on Nonlinear H-Infinity Control (HTML) (PPT)
• M.R. James, J.S. Baras and R.J. Elliott, Risk-Sensitive Control and Dynamic Games for Partially Observed Discrete-Time Nonlinear Systems, IEEE Trans. Aut. Control, 39(4) (1994) 780-792.
• M.R. James, Recent Developments in Nonlinear H-Infinity Control, IFAC NOLCOS, Lake Tahoe, June 1995. (PS) (PDF)
• M.R. James and J.S. Baras, Partially Observed Differential Games, Infinite Dimensional HJI Equations, and Nonlinear H-Infinity Control, SIAM J. Control and Optimization, 34(4), 1996, 1342-1364.
• M.R. James and J.S. Baras, Robust H-Infinity Output Feedback Control for Nonlinear Systems, IEEE Trans. Aut. Control, 40(6) (1995) 1007-1017.
• B.D.O. Anderson, M.R. James and D.J.N. Limebeer, Robust Stabilization of Nonlinear Systems via Normalized Coprime Factor Representations, Automatica, 34(12) 1998, 1593-1599.
• Nonlinear H-Infinity Control: A Stochastic Perspective (PDF)
• Receding horizon H-infinity control (PDF)