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

Srinivasarengan K., Ragot J., Aubrun C., Maquin D.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 1

55--67

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.

Perfect nonlinear observers of descriptor discrete-time nonlinear systems

Kaczorek T.

Autobusy : technika, eksploatacja, systemy transportowe

2017

R. 18, nr 12

933--936, CD

Perfect nonlinear observers for descriptor discrete-time nonlinear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the perfect nonlinear observers is given and is demonstrated on a numerical example

Zaproponowano nową koncepcję doskonałych obserwatorów deskriptowych (singularnych) dyskretnych układów nieliniowych. Podano warunki konieczne i wystarczające istnienia tych obserwatorów dla dyskretnych układów nieliniowych. Podano również procedurę wyznaczania para-metrów tych obserwatorów i zlustrowano ją numerycznym przykładem.