Adaptive Robust Control of Non linear Systems: Effective Use of Information

Abstract This paper considers the adaptive robust control of nonlinear systems in the presence of parametric uncertainties and uncertain nonlinearities. The assumption on the allowable uncertain nonlinearities is relaxed to the extent that uncertain nonlinearities are required to be bounded by some known functions multiplied by unknown but bounded time-varying disturbances only. The approach uses robust feedback to attenuate the effect of uncertainties to achieve a prescribed transient performance and final tracking accuracy. The approach also uses parameter adaptation to reduce model uncertainties to achieve asymptotic tracking in the presence of parametric uncertainties without using switching or infinite-gain feedback. Different design methods are examined and compared.

[1]  M. Tomizuka,et al.  High performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[2]  Miroslav Krstic,et al.  Robustness of adaptive nonlinear control to bounded uncertainties , 1996 .

[3]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[4]  R.A. Freeman,et al.  Robust integral control for a class of uncertain nonlinear systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[5]  L. Praly,et al.  Adaptive nonlinear regulation: estimation from the Lyapunov equation , 1992 .

[6]  Graham C. Goodwin,et al.  A parameter estimation perspective of continuous time model reference adaptive control , 1987, Autom..

[7]  Salvatore Joseph Cusumano,et al.  Adaptive Robust Control , 1988 .

[8]  Masayoshi Tomizuka,et al.  Robust desired compensation adaptive control of robot manipulators with guaranteed transient performance , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[9]  Masayoshi Tomizuka,et al.  Zero Phase Error Tracking Algorithm for Digital Control , 1987 .

[10]  Masayoshi Tomizuka,et al.  Adaptive Robust Control of a Class of Multivariable Nonlinear Systems , 1996 .

[11]  Bin Yao,et al.  High performance adaptive robust control of nonlinear systems: a general framework and new schemes , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[12]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

[13]  Zhihua Qu,et al.  Exponentially stable trajectory following of robotic manipulators under a class of adaptive controls , 1992, Autom..

[14]  M. Tomizuka,et al.  Robust adaptive nonlinear control with guaranteed transient performance , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[15]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[16]  Masayoshi Tomizuka,et al.  Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form , 1997, Autom..

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

[18]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[19]  Petros A. Ioannou,et al.  Instability analysis and robust adaptive control of robotic manipulators , 1989, IEEE Trans. Robotics Autom..

[20]  Masayoshi Tomizuka,et al.  Comparative experiments of robust and adaptive control with new robust adaptive controllers for robot manipulators , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[21]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[22]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[23]  Masayoshi Tomizuka,et al.  High-performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments , 1997 .