Output Tracking Control of PWA Systems

In this paper, an observer-based output-feedback control design solving the tracking problem for continuous piecewise affine (PWA) systems is proposed. The design of the dynamic controller is based on the idea of, on the one hand, rendering the system convergent by means of feedback (which makes all its solutions converge to each other) and, on the other hand, guaranteeing that the closed-loop system has a bounded solution corresponding to zero tracking error. This implies that all solutions of the closed-loop system converge to this bounded solution with zero tracking error. Using this synthesis approach, we solve the state tracking problem for general continuous PWA systems and the output tracking problem for a class of single-input-single-output PWA systems. The results are illustrated by application to mechanical systems with one-sided restoring characteristics and backlash

[1]  J. Willems,et al.  Stability theory of dynamical systems , 1970 .

[2]  Eduardo Sontag.  Nonlinear regulation: The piecewise linear approach , 1981 .

[3]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[4]  Eduardo D. Sontag,et al.  On the Input-to-State Stability Property , 1995, Eur. J. Control.

[5]  S. Monaco,et al.  Asymptotic properties of incrementally stable systems , 1996, IEEE Trans. Autom. Control..

[6]  Jean-Jacques E. Slotine,et al.  On Contraction Analysis for Non-linear Systems , 1998, Autom..

[7]  Henk Nijmeijer,et al.  System identification in communication with chaotic systems , 2000 .

[8]  Winfried Stefan Lohmiller,et al.  Contraction analysis of nonlinear systems , 1999 .

[9]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[10]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[11]  Petar V. Kokotovic,et al.  Observer-based control of systems with slope-restricted nonlinearities , 2001, IEEE Trans. Autom. Control..

[12]  David Angeli,et al.  A Lyapunov approach to incremental stability properties , 2002, IEEE Trans. Autom. Control..

[13]  Jozef Vörös,et al.  Modeling and parameter identification of systems with multisegment piecewise-linear characteristics , 2002, IEEE Trans. Autom. Control..

[14]  G. Feng.  Controller design and analysis of uncertain piecewise-linear systems , 2002 .

[15]  W. Heemels,et al.  On the dynamic analysis of piecewise-linear networks , 2002 .

[16]  J. How,et al.  Observer-based control of piecewise-affine systems , 2003 .

[17]  Mikael Johansson,et al.  Piecewise linear control systems - a computational approach , 2002, Lecture notes in control and information sciences.

[18]  Nathan van de Wouw,et al.  Convergent dynamics, a tribute to Boris Pavlovich Demidovich , 2004, Syst. Control. Lett..

[19]  M. Chen,et al.  Linear-matrix-inequality–based approach to H∞ controller synthesis of uncertain continuous-time piecewise linear systems , 2004 .

[20]  T. Sugie,et al.  Trajectory tracking control of bimodal piecewise affine systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[21]  H. Nijmeijer,et al.  Convergent piecewise affine systems: analysis and design Part II: discontinuous case , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[22]  N. Wouw,et al.  Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach , 2005 .

[23]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .