Nonlinear joint state and parameter estimation: Application to a wastewater treatment plant

•Joint state and parameter estimation for nonlinear time-varying systems.•A systematic procedure of representation with no loss of information.•First contribution based on the polytopic approach.•Application to a wastewater treatment plant.•Data issued from the European Program Benchmark Cost 624.

A systematic approach to joint state and time-varying parameter estimation for nonlinear systems is proposed in this paper. Applying the sector nonlinearity transformation to both the system nonlinearities and the time-varying parameters, the original system is equivalently rewritten as a Takagi–Sugeno system with unmeasurable premise variables. A joint state and parameter observer whose parameters are designed by solving an LMI optimization problem is then proposed. The target application is a realistic model of an activated sludge wastewater treatment plant, being an uncertain nonlinear system affected by a time-varying parameter.