Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis

Due to the difficulty of handling both hysteresis and interactions between subsystems, there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis, even though the problem is practical and important. In this paper, we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions. In the first scheme, no knowledge is assumed on the bounds of unknown system parameters. In case that the uncertain parameters are inside known compact sets, we propose an alternative scheme where a projection operation is employed in the adaptive laws. In both schemes, the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws. It is shown that the designed local adaptive controllers can ensure all the signals in the closed-loop system bounded. A root mean square type of bound is obtained for the system states as a function of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters. With Scheme II, the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available. In the absence of hysteresis, perfect stabilization is ensured and the L"2 norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied.

[1]  Lin Shi,et al.  Decentralized Adaptive Controller Design For Large-Scale Systems With Higher-Order Interconnections , 1992, 1992 American Control Conference.

[2]  Graham C. Goodwin,et al.  Stability analysis of decentralized robust adaptive control , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[3]  Ying Zhang,et al.  Robust decentralized adaptive stabilization of interconnected systems with guaranteed transient performance , 2000, Autom..

[4]  R. Simpson,et al.  Subharmonic ferroresonance in an LCR circuit with hysteresis , 1997 .

[5]  Y. Stepanenko,et al.  Intelligent control of piezoelectric actuators , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[6]  M. Brokate,et al.  Hysteresis and Phase Transitions , 1996 .

[7]  Yihui Jin,et al.  Stable adaptive control of backlash nonlinear system with bounded disturbances , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[8]  David J. Hill,et al.  Global boundedness of discrete-time adaptive control just using estimator projection , 1992, Autom..

[9]  Ying Zhang,et al.  Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis , 2004, IEEE Trans. Autom. Control..

[10]  Sun-Ki Hong,et al.  Torque calculation of hysteresis motor using vector hysteresis model , 2000 .

[11]  Gang Tao,et al.  Adaptive control of plants with unknown hystereses , 1995 .

[12]  Graham C. Goodwin,et al.  Guest editorial introduction to the special issue on dynamics and control of smart structures , 2001 .

[13]  M. L. Hodgdon,et al.  Mathematical theory and calculations of magnetic hysteresis curves , 1988 .

[14]  Petros A. Ioannou.  Decentralized adaptive control of interconnected systems , 1986 .

[15]  Amr A. Adly,et al.  Performance simulation of hysteresis motors using accurate rotor media models , 1995 .

[16]  Changyun Wen,et al.  Decentralized adaptive control using integrator backstepping , 1997, Autom..

[17]  Riccardo Marino,et al.  Nonlinear control design: geometric, adaptive and robust , 1995 .

[18]  Chia-Hsiang Menq,et al.  Hysteresis compensation in electromagnetic actuators through Preisach model inversion , 2000 .

[19]  M. Hodgdon.  Applications of a theory of ferromagnetic hysteresis , 1988 .

[20]  Petros A. Ioannou,et al.  Decentralized indirect adaptive control of interconnected systems , 1991 .

[21]  John S. Baras,et al.  Adaptive identification and control of hysteresis in smart materials , 2005, IEEE Transactions on Automatic Control.

[22]  Graham C. Goodwin,et al.  Stability analysis of decentralised robust adaptive control , 1988 .

[23]  B. D. Coleman,et al.  A constitutive relation for rate-independent hysteresis in ferromagnetically soft materials , 1986 .

[24]  D. D. Siljak,et al.  Decentralized Adaptive Control: Structural Conditions for Stability , 1988, 1988 American Control Conference.

[25]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis , 2000, IEEE Trans. Autom. Control..

[26]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[27]  Paolo Nistri,et al.  Mathematical Models for Hysteresis , 1993, SIAM Rev..

[28]  D. Siljak,et al.  Robustness of suboptimal control: Gain and phase margin , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[29]  Gang Tao,et al.  Adaptive Control of Systems with Actuator and Sensor Nonlinearities , 1996 .

[30]  Dragoslav D. Siljak,et al.  On decentralized stabilization and structure of linear large scale systems , 1981, Autom..

[31]  C. Wen.  Decentralized adaptive regulation , 1994, IEEE Trans. Autom. Control..

[32]  Petros A. Ioannou,et al.  Decentralized Adaptive Control , 1992 .

[33]  J. How,et al.  Robust stability and performance analysis of systems with hysteresis nonlinearities , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[34]  Farshad Khorrami,et al.  Adaptive control of systems with backlash hysteresis at the input , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).