Robust control of nonlinear systems with input unmodeled dynamics

In the rich repertoire of design methodologies for uncertain nonlinear systems, the problem of unmodeled dynamics has thus far received little attention. The authors initiate the investigation of nonlinear systems with input unmodeled dynamics. First the authors show that even in their simplest forms, they can result in dramatic shrinking of the region of attraction and in finite escape time. In this paper the authors introduce a dynamic nonlinear damping design which guarantees global boundedness in the presence of input unmodeled dynamics. With this design the authors achieve global asymptotic stability for strict-feedback systems and output-feedback systems.

[1]  M. Corless,et al.  A new class of stabilizing controllers for uncertain dynamical systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[2]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[3]  L. Praly,et al.  Preliminary results about robust lagrange stability in adaptive non-linear regulation , 1992 .

[4]  I. Kanellakopoulos,et al.  A toolkit for nonlinear feedback design , 1992 .

[5]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems. I. Linear parameterization , 1993, IEEE Trans. Autom. Control..

[6]  J. Slotine,et al.  Robust input-output feedback linearization , 1993 .

[7]  Z. Qu.  Model reference robust control of weakly non-minimum phase systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[8]  L. Praly,et al.  Stabilization by output feedback for systems with ISS inverse dynamics , 1993 .

[9]  Petar V. Kokotovic,et al.  Design of 'softer' robust nonlinear control laws , 1993, Autom..

[10]  Riccardo Marino,et al.  Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems, , 1993, Autom..

[11]  P. Kokotovic,et al.  Global robustness of nonlinear systems to state measurement disturbances , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  Z. Qu.  Model Reference Robust Control of SISO Systems with Significant Unmodelled Dyamics , 1993, 1993 American Control Conference.

[13]  Hassan K. Khalil,et al.  Robust Servomechanism Output Feedback Controllers for a Class of Feedback Linearizable Systems , 1993 .

[14]  Zhihua Qu,et al.  Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions , 1993, 1993 American Control Conference.

[15]  Andrew R. Teel,et al.  On output feedback stabilization for systems with ISS inverse dynamics and uncertainties , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[16]  M. Corless.  Control of Uncertain Nonlinear Systems , 1993 .

[17]  Miroslav Krstic,et al.  Control of feedback linearizable systems with input unmodeled dynamics , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[18]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[19]  L. Praly,et al.  Technical results for the study of robustness of Lagrange stability , 1994 .

[20]  B. Brogliato,et al.  Correction to "Adaptive control of robot manipulators with flexible joint" , 1996, IEEE Trans. Autom. Control..