Guaranteed cost estimation and control for nonlinear system using LMI optimization

In the paper, a methodology for the guaranteed cost estimation and control for nonlinear system discrete-time systems is proposed. To solve such a challenging problem, the article starts with a general description of the system and assumptions regarding its nonlinearities. The subsequent part of the paper describes the design methodology of the robust observer and controller for the predefined cost function using linear matrix inequalities. The final part of the paper presents an illustrative example oriented towards a practical application to the multiple tank system, which illustrates the performance of the proposed approach.

[1]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[2]  W. Marsden.  I and J , 2012 .

[3]  Minyue Fu,et al.  A linear matrix inequality approach to robust H∞ filtering , 1997, IEEE Trans. Signal Process..

[4]  Ali Zemouche,et al.  Observer Design for Lipschitz Nonlinear Systems: The Discrete-Time Case , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Steven X. Ding,et al.  Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools , 2008 .

[6]  Masoud Abbaszadeh,et al.  LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems , 2009 .

[7]  A. Pertew,et al.  H ∞ synthesis of unknown input observers for non-linear Lipschitz systems , 2005 .

[8]  G. Sallet,et al.  Observers for Lipschitz non-linear systems , 2002 .

[9]  D. Siljak,et al.  Robust stability and stabilization of discrete-time non-linear systems: The LMI approach , 2001 .

[10]  Marcin Witczak,et al.  Robust ℌ∞ actuator fault diagnosis and fault-tolerant control for a multi-tank system , 2013, 2013 Conference on Control and Fault-Tolerant Systems (SysTol).

[11]  José Ragot,et al.  Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances , 2011, Int. J. Appl. Math. Comput. Sci..

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

[13]  Ali Zemouche,et al.  Observers for a class of Lipschitz systems with extension to Hinfinity performance analysis , 2008, Syst. Control. Lett..

[14]  Karolos M. Grigoriadis,et al.  Robust fault estimation of uncertain systems using an LMI‐based approach , 2008 .

[15]  Yi Shen,et al.  Actuator fault estimation observer design for discrete‐time linear parameter‐varying descriptor systems , 2015 .

[16]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[17]  Józef Korbicz,et al.  A robust fault-tolerant model predictive control for linear parameter-varying systems , 2014, 2014 19th International Conference on Methods and Models in Automation and Robotics (MMAR).

[18]  Neil Genzlinger.  A. and Q , 2006 .

[19]  Marcin Witczak,et al.  Predictive actuator fault-tolerant control under ellipsoidal bounding , 2016 .

[20]  Damiano Rotondo,et al.  An LMI approach to robust fault estimation for a class of nonlinear systems , 2016 .

[21]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[22]  Józef Korbicz,et al.  Design of unknown input observers for non-linear stochastic systems and their application to robust fault diagnosis , 2013 .

[23]  Marcin Witczak,et al.  Neural-network based robust predictive fault-tolerant control for multi-tank system , 2014, 2014 European Control Conference (ECC).

[24]  Anis Sellami,et al.  An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An , 2015, Int. J. Appl. Math. Comput. Sci..

[25]  M. Darouach,et al.  Two-stage Kalman estimator with unknown exogenous inputs , 1999, Autom..

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

[27]  R. Rajamani.  Observers for Lipschitz nonlinear systems , 1998, IEEE Trans. Autom. Control..