Estimating unbounded unknown inputs in nonlinear systems

Abstract Unknown inputs such as attacks on safety-critical systems is a major concern in the design of modern engineering systems. If the underlying system to be protected exhibits nonlinear dynamics, few observers/estimators in the current literature can handle unknown input estimation, particularly when the unknown inputs are unbounded. This paper proposes an extended state observer methodology for designing observers capable of reconstructing the state along with unknown inputs for a class of nonlinear systems that can be characterized via incremental quadratic constraints. Two classes of unknown inputs are considered: completely unknown inputs that have bounded derivatives, or (the generalization of the first) unknown inputs that are generated by nonlinear internal state-space models, where the model states are driven by completely unknown inputs; for instance, completely unknown inputs with bounded higher-order derivatives. The potential of the proposed design is demonstrated via numerical simulations.

[1]  Stefen Hui,et al.  Sliding-mode observers for systems with unknown inputs: A high-gain approach , 2010, Autom..

[2]  Hieu Minh Trinh,et al.  State and input simultaneous estimation for a class of nonlinear systems , 2004, Autom..

[3]  Marios M. Polycarpou,et al.  Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation , 2010, Autom..

[4]  Panagiotis Tsiotras,et al.  Low-bias control of AMB subject to voltage saturation: state-feedback and observer designs , 2005, IEEE Transactions on Control Systems Technology.

[5]  Florian Dörfler,et al.  Attack Detection and Identification in Cyber-Physical Systems -- Part II: Centralized and Distributed Monitor Design , 2012, ArXiv.

[6]  T. Floquet,et al.  On Sliding Mode Observers for Systems with Unknown Inputs , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..

[7]  C. D. Johnson,et al.  Accomodation of external disturbances in linear regulator and servomechanism problems , 1971 .

[8]  Andre Teixeira,et al.  Toward Cyber-Secure and Resilient Networked Control Systems , 2014 .

[9]  Vincent Cocquempot,et al.  Nonlinear unknown input observer design for diesel engines , 2013, 2013 American Control Conference.

[10]  L. Fridman,et al.  Higher‐order sliding‐mode observer for state estimation and input reconstruction in nonlinear systems , 2008 .

[11]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[12]  Shreyas Sundaram,et al.  Distributed Function Calculation via Linear Iterative Strategies in the Presence of Malicious Agents , 2011, IEEE Transactions on Automatic Control.

[13]  Yugeng Xi,et al.  Task-independent robotic uncalibrated hand-eye coordination based on the extended state observer , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[14]  A. Zemouche,et al.  Nonlinear-Observer-Based ${\cal H}_{\infty}$ Synchronization and Unknown Input Recovery , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Jun Yang,et al.  Generalized Extended State Observer Based Control for Systems With Mismatched Uncertainties , 2012, IEEE Transactions on Industrial Electronics.

[16]  Wen Chen,et al.  Observer-based strategies for actuator fault detection, isolation and estimation for certain class of uncertain nonlinear systems , 2007 .

[17]  Wilfrid Perruquetti,et al.  State reconstruction of nonlinear differential-algebraic systems with unknown inputs , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[18]  Yuanqing Xia,et al.  Attitude Tracking of Rigid Spacecraft With Bounded Disturbances , 2011, IEEE Transactions on Industrial Electronics.

[19]  Gregery T. Buzzard,et al.  State and Unknown Input Observers for Nonlinear Systems With Bounded Exogenous Inputs , 2017, IEEE Transactions on Automatic Control.

[20]  Shreyas Sundaram,et al.  State and unknown input observers for discrete-time nonlinear systems , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

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

[22]  Shihua Li,et al.  Speed Control for PMSM Servo System Using Predictive Functional Control and Extended State Observer , 2012, IEEE Transactions on Industrial Electronics.

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

[24]  Gregery T. Buzzard,et al.  Unknown Input Estimation for Nonlinear Systems Using Sliding Mode Observers and Smooth Window Functions , 2018, SIAM J. Control. Optim..

[25]  Shihua Li,et al.  Extended state observer-based sliding mode control for PWM-based DC–DC buck power converter systems with mismatched disturbances , 2015 .

[26]  Sanjay E. Talole,et al.  Performance Analysis of Generalized Extended State Observer in Tackling Sinusoidal Disturbances , 2013, IEEE Transactions on Control Systems Technology.

[27]  Jean-Pierre Barbot,et al.  An algebraic framework for the design of nonlinear observers with unknown inputs , 2007, 2007 46th IEEE Conference on Decision and Control.

[28]  Thomas Gustafsson,et al.  Nonlinear observer design for a class of Lipschitz time-delay systems with unknown inputs: LMI approach , 2011, 2011 XXIII International Symposium on Information, Communication and Automation Technologies.

[29]  Martin J. Corless,et al.  State and Input Estimation for a Class of Uncertain Systems , 1998, Autom..

[30]  H. Marquez,et al.  Design of unknown input observers for Lipschitz nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

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

[32]  Julien Clinton Sprott,et al.  Elementary chaotic flow , 1999 .

[33]  Shreyas Sundaram,et al.  Delayed unknown input observers for discrete-time linear systems with guaranteed performance , 2017, Syst. Control. Lett..

[34]  Behçet Açikmese,et al.  Observers for systems with nonlinearities satisfying incremental quadratic constraints , 2011, Autom..

[35]  M. Saif,et al.  Unknown input observer design for a class of nonlinear systems: an LMI approach , 2006, American Control Conference.

[36]  Emilia Fridman,et al.  State and unknown input observers for nonlinear systems with delayed measurements , 2018, Autom..

[37]  Nan Chen,et al.  Composite hierarchical anti‐disturbance control for nonlinear systems with DOBC and fuzzy control , 2014 .

[38]  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..