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The article discusses the identification of a class of generalized Cobb-Douglas production functions with multiplicative errors in all variables. The article proposes a generalization of Cobb-Douglas production functions in the presence of memory for input and output variables. Parametrization of noise in the form of multiplicative noise in all observable variables is proposed. The logarithmic transformation of such production functions leads to the need to solve the problem of estimating the parameters of a linear difference equation in the presence of additive errors in all variables. To identify the parameters of production functions, a modification of the method of total least squares was used. Computational experiments have shown high accuracy of parameter estimation based on the proposed algorithm.

In the present work we propose the method for the solution inverse heat conduction problem that consists of the identification of unknown internal heat source function depending simultaneously on space and time variables. The source function can be represented as a separable variable. We consider an inverse problem of determining the heat source function based on temperature measurements.Inverse problem is formulated as an optimization problem, a variational formulation for solving the optimization problem is given. The estimation of internal heat source is investigated with the analytical method combined with the method for approximate modal definition of temperature state and source function. The temperature state and desired control input are represented in the form of finite expansion in terms of orthogonal system of eigenfunctions. The required eigencoefficients of temperature state can be determined using temperature measurements. Then eigencoefficients of heat source function can be defined sequentially.Some numerical examples are provided to show the efficiency of the proposed method.