Estimation of non-separable regressions containing parameter dependent exponential functions

This paper presents a method for generating a separable regression function from a nonseparable one, enabling theapplication of parameter estimation methods. In particular, we are interested in regressions containing parameter-dependent exponential functions - a scenario often encountered in physical systems. Our approach is based on algebraic techniques with the so-called annihilator theory, and utilizes an intermediate approximation of the nonlinear part by a polynomial function of the time. Two operators are proposed to define the annihilators: time delays and differential operators. The efficiency of the proposed approach is demonstrated in a nonlinearly parameterized fuel cell estimation problem.