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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)
Five different state space realizability conditions for nonlinear single-input single-output high order input-output differential equation are compared and proved to be equivalent. Moreover, the explicit formulas are provided for calculation of the differentials of the state coordinates which can be integrated to obtain the state coordinates iff the(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)
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 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)
The paper studies the unmeasurable disturbance decoupling problem via the dynamic output feedback for discrete-time nonlinear control systems. To address the problem the novel algebraic approach, called the algebra of functions, is applied. The advantage of the latter over the differential geometric methods is that the system description may depend on(More)