An adaptive observer design approach for discrete-time nonlinear systems (original) (raw)
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An adaptive observer design approach for a class of discrete-time nonlinear systems
International Journal of Applied Mathematics and Computer Science, 2018
We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete-time systems. This class contains systems that could be transformed into a quasi-LPV (linear parameter varying) polytopic model in the Takagi-Sugeno (T-S) form. Such systems could have unmeasured premise variables, a case usually overlooked in the observer design literature. We assert that, for such systems in discrete-time, the current literature lacks design strategies for joint state and parameter estimation. To this end, we adapt the existing literature on continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear systems. A Lyapunov approach is used to illustrate stability, and bounds for the estimation error are obtained via the bounded real lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear systems with constant paramet...
An Adaptive Observer Design for Takagi-Sugeno type Nonlinear System
arXiv (Cornell University), 2017
Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provide an algorithmic procedure that would seamlessly connect the state estimation and parameter estimation parts of the observer design. Lyapunov approach is used for the stability analysis and the design procedure. The results are illustrated on a simulation example.
IFAC-PapersOnLine, 2017
Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provide an algorithmic procedure that would seamlessly connect the state estimation and parameter estimation parts of the observer design. Lyapunov approach is used for the stability analysis and the design procedure. The results are illustrated on a simulation example.
State and Parameter Estimation for Nonlinear Systems: a Takagi-Sugeno Approach
The main contribution of this paper is to propose a systematic approach to observer design for nonlinear Takagi-Sugeno (T-S) time-varying systems. The proposed procedure is based on the sector nonlinearity approach using the convex polytopic transformation. The exact writing of the time-varying nonlinear system as a T-S model allows to provide a state and parameter estimation.
IFAC-PapersOnLine
In this paper, we address the problem of nonlinear continuous-discrete adaptive observer design for a class of system with sampled data measurements subject to sensor nonlinearities. The main difficulty of the considered class of system is coming from the fact that the output equation contains unknown parameters which renders the design of a classical sampled data observer difficult. To overcome this difficulty, we propose a new online continuousdiscrete adaptive observer which ensures a simultaneous exponential convergence of both states and parameters. Comparing to other observer structures, our design is characterized by a simpler structure thanks to the introduction of a parametric adaptation law. To show the efficiency of our proposed approach, numerical simulations have been performed for different values of sampling time. In addition, the delayed-sampled measurements case is also illustrated.
State and parameter estimation for time-varying systems: A Takagi-Sugeno approach
IFAC Proceedings Volumes (IFAC-PapersOnline), 2013
The contribution of this paper is to propose a systematic approach to the observer design for linear time-varying systems. It is based on the exact rewriting of the original time-varying system into a polytopic linear model (PLM). This transformation uses the sector nonlinearity approach based on the convex polytopic transformation. Then a joint state and parameter observer can be designed for the PLM and the estimation errors convergence are proved.
Observer design for nonlinear systems represented by Takagi-Sugeno models
Wseas Transactions on Systems, 2010
In this paper, the problem of synthesis of a multiple observer for a class of uncertain nonlinear system represented by a Takagi-Sugeno multiple model is studied. The measure's uncertainties are considered as unknown outputs. To conceive the observer a mathematical transformation is considered to conceive an augmented system in which the unknown output appear as an unknown input. Convergence conditions are established in order to guarantee the convergence of the state estimation error. These conditions are expressed in Linear Matrix Inequality (LMI) formulation. An example of simulation is given to illustrate the proposed method.
Observer design for a class of nonlinear discrete time systems
2015
This paper demonstrates the observer design for large class of nonlinear discrete time systems. The use of the differential mean value theorem (DMVT) allows transforming the nonlinear error dynamics into a linear parameter varying (LPV) system. This has the advantage of introducing a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). For comparison, an observer based on the use of the one-sided Lipschitz condition is introduced. High performances are shown through real time implementation of the one-link flexible joint robot to ARDUINO MEGA 2560 device.
An adaptive observer design methodology for bounded nonlinear processes
Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
In this paper we address the problem of augmenting a linear observer with an adaptive element. The design of the adaptive element employs two nonlinearly parameterized neural networks, the input and output layer weights of which are adapted on line. The goal is to improve the performance of the linear observer when applied to a nonlinear system. The networks' teaching signal is generated using a second linear observer of the nominal system's error dynamics. Boundedness of signals is shown through Lyapunov's direct method. The approach is robust to unmodeled dynamics and disturbances. Simulations illustrate the theoretical results.