Observability and controllability analysis for sandwich systems with dead-zone

In this paper, an approach to analyze the observability and controllability of sandwich systems with dead-zone is proposed. In this method, a non-smooth state-space function is proposed to describe the sandwich systems with dead-zone which are also non-smooth nonlinear systems. Then, a linearization method based on non-smooth optimization is proposed to derive a linearized state-space function to approximate the non-smooth sandwich systems within a bounded region around the equilibrium points that we are interested in. Afterwards, both observability and controllability matrices are constructed and the methods to analyze the observability as well as controllability of sandwich system with dead-zone are derived. Finally, a numerical example is presented.

[1]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[2]  Ruoyu Li,et al.  Recursive Identification of Sandwich Systems With Dead Zone and Application , 2009, IEEE Transactions on Control Systems Technology.

[3]  Michael A. Arbib,et al.  Topics in Mathematical System Theory , 1969 .

[4]  A. Isidori.  Nonlinear Control Systems , 1985 .

[5]  L. Minchenko,et al.  Controllability of Nonsmooth Discrete Systems with Delay , 2002 .

[6]  Jozef Vörös,et al.  Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones , 2003, IEEE Trans. Autom. Control..

[7]  Gang Tao,et al.  Adaptive state feedback actuator nonlinearity compensation for multivariable systems , 2013 .

[8]  Héctor J. Sussmann,et al.  Single-input observability of continuous-time systems , 1978, Mathematical systems theory.

[9]  A. Schaft.  Observability and Controllability for Smooth Nonlinear Systems , 1982 .

[10]  Eduardo Sontag,et al.  Linear systems with sign-observations , 1993 .

[11]  Yu-Ning Wang,et al.  Model following variable structure control design in reciprocal state space framework with dead-zone nonlinearity and lumped uncertainty , 2012, 2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA).

[12]  Gerhard Jank.  CONTROLLABILITY, OBSERVABILITY AND OPTIMAL CONTROL OF CONTINUOUS-TIME 2-D SYSTEMS , 2002 .

[13]  Eduardo Sontag.  On the Observability of Polynomial Systems, I: Finite-Time Problems , 1979 .

[14]  Min Wu,et al.  Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone , 2014 .

[15]  Jerzy Klamka,et al.  Controllability of nonlinear discrete systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[16]  Joel W. Burdick,et al.  Nonsmooth controllability theory and an example , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[17]  Yonghong Tan,et al.  On-line identification algorithm and convergence analysis for sandwich systems with backlash , 2011 .

[18]  J. Klamka.  On the global controllability of perturbed nonlinear systems , 1975 .

[19]  Alexey N. Zhirabok,et al.  An approach to the analysis of observability and controllability in nonlinear systems via linear methods , 2012, Int. J. Appl. Math. Comput. Sci..

[20]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[21]  Steven Roman.  Advanced Linear Algebra , 1992 .

[22]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..