Output regulation of general linear systems with saturating actuators

This paper studies the classical problem of output regulation for linear systems subject to actuator saturation. The asymptotically regulatable region, the set of all initial conditions of the plant and the exosystem for which output regulation is possible, is characterized in terms of the null controllable region of the anti-stable subsystem of the plant. Feedback laws are constructed that achieve regulation on the asymptotically regulatable region. These feedback laws are constructed from the stabilizing feedback laws in such a way that a stabilizing feedback law that achieves a larger domain of attraction leads to a feedback law that achieves output regulation on a larger subset of the asymptotically regulatable region and a stabilizing feedback law on the entire asymptotically null controllable region leads to a feedback law that achieves output regulation on the entire asymptotically regulatable region.

[1]  Eduardo Sontag.  An algebraic approach to bounded controllability of linear systems , 1984 .

[2]  Ali Saberi,et al.  Output regulation for linear systems subject to input saturation , 1996, Autom..

[3]  Eduardo Sontag,et al.  A general result on the stabilization of linear systems using bounded controls , 1994, IEEE Trans. Autom. Control..

[4]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[5]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[6]  Zongli Lin,et al.  Output regulation for linear systems subject to input saturation , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[7]  Zongli Lin,et al.  Low gain feedback , 1999 .

[8]  A. Teel.  A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

[9]  Tingshu Hu,et al.  Semi-global stabilization with guaranteed regional performance of linear systems subject to actuator saturation , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[10]  O. Hájek.  Control theory in the plane , 1991 .

[11]  Raffaella De Santis,et al.  Output regulation for linear systems with anti‐stable eigenvalues in the presence of input saturation , 2000 .

[12]  Tingshu Hu,et al.  Robust stabilization of exponentially unstable linear systems with saturating actuators , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[13]  Tingshu Hu,et al.  Stabilization of exponentially unstable linear systems with saturating actuators , 2001, IEEE Trans. Autom. Control..

[14]  A. Isidori,et al.  Output regulation of nonlinear systems , 1990 .