Gain scheduling the LPV way

Some nonlinear control problems in industry are successfully solved using gain-scheduling, a method primarily based on intuition from control design for linear systems. Linear parameter varying system (LPV) theory, introduced by Shamma et al. (1992), can be used to simplify some of the interpolation and realization problems associated with conventional gain-scheduling. However, many questions about the relevance of LPV theory to nonlinear control design remain. This paper illustrates, via examples, some of the issues.

[1]  P. Khargonekar,et al.  The H/sup infinity / control problem for linear time-varying systems , 1990, 29th IEEE Conference on Decision and Control.

[2]  Gilead Tadmor,et al.  Worst-case design in the time domain: The maximum principle and the standardH∞ problem , 1990, Math. Control. Signals Syst..

[3]  Wilson J. Rugh,et al.  Analytical Framework for Gain Scheduling , 1990, 1990 American Control Conference.

[4]  Michael Athans,et al.  Analysis of gain scheduled control for nonlinear plants , 1990 .

[5]  S. M. Shahruz,et al.  Design of controllers for linear parameter-varying systems by the gain scheduling technique , 1990, 29th IEEE Conference on Decision and Control.

[6]  Gain Scheduling: Potential Hazards and Possible Remedies , 1992, 1991 American Control Conference.

[7]  J. Doyle,et al.  H/sub infinity / control of LFT systems: an LMI approach , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[8]  S. Behtash,et al.  Design of controllers for linear parameter-varying systems by the gain scheduling technique , 1992 .

[9]  Stephen P. Boyd,et al.  Method of centers for minimizing generalized eigenvalues , 1993, Linear Algebra and its Applications.

[10]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

[11]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions for real parametric uncertainty , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  A. Packard.  Gain scheduling via linear fractional transformations , 1994 .

[13]  L. El Ghaoui,et al.  Performance control of rational systems using linear-fractional representations and LMIs , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  Etsujiro Shimemura,et al.  H∞ Control of Linear Systems with Scheduling Parameter , 1994 .

[15]  M. Overton,et al.  Optimizing eigenvalues of symmetric definite pencils , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[16]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[17]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[18]  Fen Wu,et al.  Induced L2‐norm control for LPV systems with bounded parameter variation rates , 1996 .

[19]  J. Doyle,et al.  𝓗∞ Control of Nonlinear Systems: a Convex Characterization , 1995, IEEE Trans. Autom. Control..

[20]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[21]  J. Tierno,et al.  Robustness analysis: nonlinear and growing , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[22]  Arkadi Nemirovski,et al.  The projective method for solving linear matrix inequalities , 1997, Math. Program..

[23]  Athanasios Sideris,et al.  H ∞ control with parametric Lyapunov functions , 1997 .

[24]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.