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When analyzing electric devices, their parameters are assumed to be known. To analyze an electric circuit, its topology, element parameters, and characteristics of sources must be specified. Circuit currents and voltages, as well as other derived quantities such as real or reactive power, can then be determined. Similarly, the frequency-dependent or transient characteristics of the circuit can be determined.

Any design electric device should satisfy several criteria, and each individual criteria is associated with an objective functional (). Therefore in most practical cases when simultaneous fulfilment of conditions is desirable, solving of multicriterion (multiobjective) inverse problems may be required []. Hence various criteria may have inconsistent character; individual objective functionals () cannot simultaneously take on their minimal values at the same vector

In this chapter the so-called stiff inverse problems and methods obtaining their solution will be discussed. We will begin with several examples of stiff problems which will be considered in order to become familiar with their basic properties, and subsequently give definitions of problems of such a type. Further, in Sections 3.2 and 3.3, two basic principles will be introduced which provide a basis for solving stiff problems. Specifically, the principle of quasi-stationarity of derivatives, and the principle of repeated measurements. In Section 3.4, problems of diagnostics of sinusoidal current circuits that are typical inverse problems in circuit theory will be discussed. Conditions, at which these problems should be considered as stiff will be discussed as well. In Section 3.5, a new effective method of diagnostics stiff problems solution will be introduced and illustrated by results of numerical solution of some problems. In Section 3.6, the problem of localization of one or several perturbation sources in an electric circuit by results of measurement of voltages in circuit nodes located remotely with respect to the perturbation sources will be discussed.

In this chapter we shall consider an effective method for solving inverse electromagnetic problems by applying Lagrange multipliers. In this chapter we shall also explore the properties and features of this method for practical use. In Section 4.1, we shall examine the application of Lagrange multipliers as continuous functions for electromagnetic optimization problems. When derived, the equations for field potentials and auxiliary adjoining functions can be used to show how to construct the boundary conditions for these functions and the algorithm for the numerical solution of optimization problems. Furthermore, in Section 4.2 we illustrate, through a number of examples, the procedure of finding field sources of the adjoining function, including the appropriate equations. The search for optimum distribution of a substance in a space can be carried out in various classes of media such as homogeneous, non-uniform, isotropic, nonlinear, etc. In Section 4.3, we shall also consider an algorithm for variations of the medium properties, allowing one to achieve local minima of the objective functional. Specific features of the method and its numerical realization will be considered by means of practical examples and application of benchmark problems in Section 4.4. Section 4.5 deals with the problems of computing values. In Section 4.6 some issues of the Lagrange method application for solution of optimization problems in non-stationary electromagnetic fields will be discussed.

In this section we shall consider problems of synthesis of equivalent circuits of transmission lines. As it was already noted repeatedly, synthesis of an equivalent circuit is a typical inverse problem of circuit theory.