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This paper introduces methods of pseudo-linear algebra to unify the algebraic formalism of one-forms and the related polynomial approach for both continuous and discrete-time nonlinear control systems. Given approach covers also differene, q-shift and q-difference operators whereby this algebraic formalism is not only unified but also extended to wide class(More)
To achieve more accurate tracking control, a control strategy for servo pneumatic systems based on the feedback linearization theory is presented. The nonlinear pneumatic actuator system is transformed into a linear system description, with a linear input–output map by regular static state feedback and state coordinate transformation. A servo tracking(More)
This article is devoted to the training and application of neural networks based additive nonlinear autoregressive exogenous (NN-based ANARX) model. Training of NN-based ANARX model with MATLAB is discussed in detail and illustrated by examples. Dynamic state feedback linearization control algorithm is then applied for control of unknown nonlinear system
The paper addresses the problem of transforming the discrete-time single-input single-output nonlinear control system into the observer form using the state and output transformations. The necessary and sufficient solvability conditions are formulated in terms of differential one-forms, associated with the input-output equation of the control system. These(More)
and Applied Analysis 3 a splitting procedure of the box of reflection coefficients, new conditions for the Schur stability are given. The application of Theorem 1.2 for determining the stability of polynomials with multilinear coefficients yield conservative results. In 8, 9 sufficient conditions are given for ensuring that the image of a multilinear(More)
This paper discusses the problem of transforming the single-input single-output nonlinear control system into the nonlinear observer (input-output injection) form using the notion of adjoint polynomials. Such a polynomial approach to the sysnthesis of observers results in the transparent and elegant way for the computation of the one-forms needed to solve(More)
The paper describes an algebraic construction of the inversive difference field associated with a discrete-time rational nonlinear control system under the assumption that the system is submersive. We prove that a system is submersive iff its associated difference ideal is proper, prime and reflexive. Next, we show that Kähler differentials of the(More)
The algebraic approach of differential one-forms has been applied to study the realization problem of nonlinear input-output equations in the classical state space form, both in continuous- and discrete-time cases. Slightly different point of view in the studies of nonlinear control systems is provided by the polynomial approach in which the system is(More)