Estimation using L1 adaptive descriptor observer for multivariable systems with nonlinear uncertainties and measurement noises

Abstract In this paper, an L1 adaptive descriptor observer is designed for multivariable systems with nonlinear uncertainties and measurement noises. If the system is detectable, noises are bounded and some rank conditions are satisfied, an L1 adaptive descriptor observer is constructed to asymptotically estimate states, nonlinear uncertainties and measurement noises at the same time. The original system is augmented with all the system states and measurement noises, two design parameters provide additional degrees of freedom. The freedom of selecting these parameters allows us to choose the derivative gain to reduce the noise amplification, the proportional gain to ensure the stability of the estimated error dynamics. An adaptive law will update the adaptive parameters which represent the uncertainty estimates such that the estimation error between the predicted state and the real state is driven to zero at every integration time-step. Of course, neglection of the unknowns for solving the error dynamic equations will introduce an estimation error in the adaptive parameters. The magnitude of this error can be lessened by choosing the time step as small as possible, meanwhile, the picking up of time step should satisfy the hardware requirement. The two design parameters and adaptive law guarantee the performance bounds for the estimation errors, both states and nonlinear uncertainties. Numerical examples are given to illustrate the design procedures, and the simulation results demonstrate the satisfactory tracking performance.

[1]  C. Cao,et al.  Control of nonlinear systems using filtered high-gain observer , 2016, 2016 International Symposium on Flexible Automation (ISFA).

[2]  Tong Ma,et al.  L1 adaptive output‐feedback control of multivariable nonlinear systems subject to constraints using online optimization , 2019, International Journal of Robust and Nonlinear Control.

[3]  J. Gouzé,et al.  Interval observers for uncertain biological systems , 2000 .

[4]  Hassan K. Khalil,et al.  High-gain observers in the presence of measurement noise: A switched-gain approach , 2009, Autom..

[5]  Warren E. Dixon,et al.  Dynamic neural network-based robust observers for uncertain nonlinear systems , 2014, Neural Networks.

[6]  Yeng Chai Soh,et al.  High-Gain Observers With Sliding Mode for State and Unknown Input Estimations , 2009, IEEE Transactions on Industrial Electronics.

[7]  Ali Akbarzadeh Kalat,et al.  Observer-based robust composite adaptive fuzzy control by uncertainty estimation for a class of nonlinear systems , 2017, Neurocomputing.

[8]  Zhiwei Gao,et al.  Descriptor observer approaches for multivariable systems with measurement noises and application in fault detection and diagnosis , 2006, Syst. Control. Lett..

[9]  Yi Shen,et al.  Interval observer design for uncertain discrete-time linear systems , 2018, Syst. Control. Lett..

[10]  Rolf Isermann,et al.  Trends in the Application of Model Based Fault Detection and Diagnosis of Technical Processes , 1996 .

[11]  Ricardo G. Sanfelice,et al.  On the performance of high-gain observers with gain adaptation under measurement noise , 2011, Autom..

[12]  Chengyu Cao,et al.  Handling of nonlinear systems using filtered high‐gain output feedback controller , 2018 .

[13]  Olivier Bernard,et al.  Interval observers for linear time-invariant systems with disturbances , 2011, Autom..

[14]  Kalyana Chakravarthy Veluvolu,et al.  Sliding mode high-gain observers for a class of uncertain nonlinear systems , 2011, Appl. Math. Lett..

[15]  Tong Ma,et al.  L1 adaptive output‐feedback descriptor for multivariable nonlinear systems with measurement noises , 2019 .

[16]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[17]  Denis V. Efimov,et al.  Interval Observers for Time-Varying Discrete-Time Systems , 2013, IEEE Transactions on Automatic Control.

[18]  Rolf Isermann.  Model-based fault-detection and diagnosis - status and applications § , 2004 .

[19]  S. Żak,et al.  State observation of nonlinear uncertain dynamical systems , 1987 .

[20]  F. Mazenc,et al.  Interval observers for discrete‐time systems , 2014 .

[21]  Henk Nijmeijer,et al.  Adaptive observers and parameter estimation for a class of systems nonlinear in the parameters , 2009, Autom..

[22]  Janos Gertler,et al.  Fault Detection and Diagnosis , 2008, Encyclopedia of Systems and Control.

[23]  Zhiwei Gao,et al.  High-Gain Estimator and Fault-Tolerant Design With Application to a Gas Turbine Dynamic System , 2007, IEEE Transactions on Control Systems Technology.

[24]  Yan Wang,et al.  Interval observer design for LPV systems with parametric uncertainty , 2015, Autom..

[25]  Tong Ma,et al.  L1 adaptive control for general partial differential equation (PDE) systems , 2019, Int. J. Gen. Syst..

[26]  Alfredo Germani,et al.  A New Approach to Design Interval Observers for Linear Systems , 2015, IEEE Transactions on Automatic Control.

[27]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[28]  Nabil Derbel,et al.  Observer based adaptive neuro-sliding mode control for MIMO nonlinear systems , 2010 .

[29]  Fanglai Zhu,et al.  State estimation and simultaneous unknown input and measurement noise reconstruction based on adaptive H∞ observer , 2016 .

[30]  Pierre Apkarian,et al.  Overview of linear time-invariant interval observer design: towards a non-smooth optimisation-based approach , 2016 .