An adaptive observer design approach for discrete-time nonlinear systems

• Published in: International journal of applied mathematics and computer science 2018-03, Vol.28 (1), p.55-67
• Main Authors: Srinivasarengan, Krishnan, Ragot, José, Aubrun, Christophe, Maquin, Didier
• Format: Article
• Language: English
• Subjects: Automatic; Engineering Sciences
• ISSN: 1641-876X; 2083-8492
• DOI: 10.2478/amcs-2018-0004

We consider the problem of joint estimation of states and some constant parameters for a class of nonlinear discrete- time systems. This class contains those systems that could be transformed into a quasi-LPV (Linear Parameter Varying) polytopic model in 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 a joint state and parameter estimation. To this end, we adapt the existing literature for continuous-time linear systems for joint state and time-varying parameter estimation. We first develop the discrete-time version of this result for linear system. Lyapunov approach is used to illustrate stability and bounds for the estimation error are obtained through the Bounded Real Lemma. We use this result to achieve our objective for a design procedure for a class of nonlinear system with constant parameters. This results in less conservative conditions and a simplified design procedure. A simplified waste water treatment plant simulation example is given to illustrate the design procedure.