Adaptive Parameter Estimation

Abstract

AbstractThe problem of the parameter estimation indicates to obtain the values of parameters from the measurable input and output when the system contains unknown parameters or uncertainty. As we mentioned in Chap. 3, parameter estimation methods can be divided into two categories: on-line parameter estimation methods and offline parameter estimation methods. The offline parameter estimation methods refer to the optimization methods or the evolutionary methods, which has been discussed in Chap. 3. Those methods are used to identify the unknown parameters through an iterative optimization procedure, which requires the evolution of measured variables for a period of time. Latter a selected set of variables is optimized so that the simulated variables match the measured ones. Hence, this type of optimization methods usually takes fairly long time to achieve convergence, which depends on the experiment length, the number of variables and the concrete optimization algorithm. Consequently, relevant computational cost is required and it usually cannot be sampled in milliseconds or seconds. Regarding to the on-line parameter estimation method, adaptive parameter estimations are mainly considered to solve the estimation problem involving constant or slowly time-varying parameters. For the fuel cell system, there are many empirical parameters in the mathematical model, which are difficult to measure. Those empirical parameters in the mathematical model can be divided into two categories, which is the linearly parametric form and the nonlinearly parametric form. Especially for the unknown parameters in the nonlinearly parametric form, it introduces more challenging to design online parameter estimation method. Hence, it is necessary to propose the online parameter estimation methods for the linearly parametric form and the nonlinearly parametric form of the fuel cell system, respectively.