Inverse problem of the Lorenz system parametric identification is considered in the case of incomplete information about solutions of the system. In the present paper, it is assumed that only two solutions of the system from three are known in different combinations. The problem of the parameter identification of the system is solved by means of elimination of unknown functions from the original system. The obtained system of equations has the same order as the original one, but contains the unknown original parameters in new combinations. Sometimes, the number of new unknown parameters is higher than number of the original unknowns. In this case, the method of the constrained least squares minimization is used in the special formulation, developed by the authors. This novel formulation exploits linearity of the system with respect to the new unknown parameters, by means of which the number of nonlinear equations becomes equal to the number of the constraints between the new parameters. Two methods of the constraint minimization are considered: the classical method of Lagrange’s multipliers and a novel method of the auxiliary parameters. Numerical simulations demonstrate effectiveness of the algorithms.

In the present paper, which is the continuation of the previous one, the problem of parameter identification of the Lorenz system is solved in assumption that only one of three functions is known at discrete time instants on finite time initial time interval. Two other functions are assumed to be unknown. The regular methods of guess values determination of the unknown parameters are developed. They are based on the Lagrange multiplier and auxiliary parameters approaches. A novel method of initial value problem solution is proposed in which the abovementioned guess values are used for more accurate estimation of the system parameters. It is demonstrated that the proposed IVP method simultaneously solves three different tasks: the problem of function interpolation from its discrete values on the initial time interval; the problem of unknown functions reconstruction on the same time interval, and the problem of extrapolation of all functions on limited time interval. It is also shown that the proposed method reconstructs the Lorenz attractor from limited data volume and data including random components.