International Journal of applied mathematics and computer science

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Paper details

Number 1 - March 2018
Volume 28 - 2018

An adaptive observer design approach for a class of discrete-time nonlinear systems

Krishnan Srinivasarengan, José Ragot, Christophe Aubrun, Didier Maquin

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 parameters. This results in less conservative conditions and a simplified design procedure. A basic waste water treatment plant simulation example is discussed to illustrate the design procedure.

adaptive observer, joint state and parameter estimation, Takagi–Sugeno model, time-varying parameter estimation, sector nonlinearity transformation, discrete-time nonlinear systems