This paper presents a new idea of pseudo-inverse maps applied to the optimal pre-corrections of nonlinear systems. This notion is the result of search for optimal models and optimal past-correctors of nonlinear systems from the perspective of the Functional Theory of Nonlinear Systems discussed in this article. The systems considered are multidimensional, which means that they have any finite number of inputs and outputs. The signals on inputs and outputs are real or complex valued. Furthermore, the input and output signal sets are finally equipped with the structure of the Hilbert spaces. The maps considered are functions for the static systems, convolutions for the linear time-invariant systems and nonlinear operators for the nonlinear systems. It is worth noting that the nonlinear systems past- and pre-corrections presented in this paper are reduced to the modeling tasks of some systems which, in turn, can be reduced further to the generalized least mean square (LMS) approximations.
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The aim of this paper is to prove a generalization of abstract Gronwall lemma for a nonlinear operator. The applications to the differential-functional equations are given.
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We prove existence and uniqueness of strong global in tme solution for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals without the coercivity assumption for the free energy function. We approximate noncoercive models by a sequence of coercive problems and prove the convergence result.
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