State observer design for quadratic parameter varying (QPV) systems

This paper addresses the problem of state observation in quadratic parameter varying (QPV) systems. In particular, a state observer is designed in such a way that the estimation error converges to zero with a desired rate of convergence in a given polytopic region of the error space. Under some assumptions, it is shown that design conditions can be given in the form of a set of bilinear matrix inequalities (BMIs), which can be reduced to linear matrix inequalities (LMIs), which are computationally more tractable. The main characteristics of the proposed approach are illustrated by means of an example, which confirms the validity of the theoretical results.

[1]  Xiuzhen Zhang,et al.  Stability and stabilisation for time-varying polytopic quadratic systems , 2017, Int. J. Control.

[2]  C. Cosentino,et al.  State Estimation in Nonlinear Quadratic Systems , 2010 .

[3]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[4]  Christian Hoffmann,et al.  A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations , 2015, IEEE Transactions on Control Systems Technology.

[5]  P. Apkarian,et al.  LPV techniques for control of an inverted pendulum , 1999, IEEE Control Systems.

[6]  State observer for quadratic systems , 1983 .

[7]  Francesco Amato,et al.  Stability analysis of nonlinear quadratic systems via polyhedral Lyapunov functions , 2008, 2008 American Control Conference.

[8]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[9]  Thierry-Marie Guerra,et al.  Observer design for Takagi-Sugeno descriptor models: An LMI approach , 2015, Autom..

[10]  Junmin Wang,et al.  $\mathcal{H}_{\infty}$ Observer Design for LPV Systems With Uncertain Measurements on Scheduling Variables: Application to an Electric Ground Vehicle , 2016, IEEE/ASME Transactions on Mechatronics.

[11]  Tor Arne Johansen,et al.  Observers for interconnected nonlinear and linear systems , 2012, Autom..

[12]  Damiano Rotondo,et al.  Analysis and design of quadratic parameter varying (QPV) control systems with polytopic attractive region , 2018, J. Frankl. Inst..

[13]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[14]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[15]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[16]  Vijay Vittal,et al.  Application of the normal form of vector fields to predict interarea separation in power systems , 1997 .

[17]  Damiano Rotondo,et al.  State estimation and decoupling of unknown inputs in uncertain LPV systems using interval observers , 2018, Int. J. Control.

[18]  D. Luenberger.  An introduction to observers , 1971 .

[19]  S. Bittanti,et al.  Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty , 1996 .

[20]  Michael E. Fitzpatrick,et al.  Optimal design of a quadratic parameter varying vehicle suspension system using contrast-based Fruit Fly Optimisation , 2018, Appl. Soft Comput..

[21]  Damiano Rotondo,et al.  Robust unknown input observer for state and fault estimation in discrete-time Takagi–Sugeno systems , 2016, Int. J. Syst. Sci..

[22]  Saïd Mammar,et al.  On Unknown Input Observers for LPV Systems , 2015, IEEE Transactions on Industrial Electronics.

[23]  Keum-Shik Hong,et al.  Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays , 2015 .

[24]  Francesco Amato,et al.  An insight into tumor dormancy equilibrium via the analysis of its domain of attraction , 2008, Biomed. Signal Process. Control..

[25]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[26]  Shengyuan Xu,et al.  Observer design for uncertain nonlinear systems with unmodeled dynamics , 2015, Autom..

[27]  Bruno Siciliano,et al.  Modelling and Control of Robot Manipulators , 1997, Advanced Textbooks in Control and Signal Processing.

[28]  O. Rössler.  Chaotic Behavior in Simple Reaction Systems , 1976 .

[29]  Jeff S. Shamma,et al.  An Overview of LPV Systems , 2012 .

[30]  Robert Babuska,et al.  Fuzzy gain scheduling: controller and observer design based on Lyapunov method and convex optimization , 2003, IEEE Trans. Fuzzy Syst..

[31]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[32]  Damiano Rotondo.  Advances in Gain-Scheduling and Fault Tolerant Control Techniques , 2017 .

[33]  G. Balas,et al.  Development of linear-parameter-varying models for aircraft , 2004 .

[34]  Carlo Cosentino,et al.  On the region of attraction of nonlinear quadratic systems , 2007, Autom..