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1. Realization of multivariable nonlinear systems via the approaches of differential forms and differential algebra

Creator:
Zhang, Jiangfeng, Moog, Claude H., and Xia, Xiaohua
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
realization, nonlinear system, differential ideal, and differential form
Language:
English
Description:
In this paper differential forms and differential algebra are applied to give a new definition of realization for multivariable nonlinear systems consistent with the linear realization theory. Criteria for the existence of realization and the definition of minimal realization are presented. The relations of minimal realization and accessibility and finally the computation of realizations are also discussed in this paper.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Realization of nonlinear input-output equations in controller canonical form

Creator:
Kaldmäe, Arvo and Kotta, Ülle
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
realization, nonlinear systems, and algebraic methods
Language:
English
Description:
In this paper necessary and sufficient conditions are given which guarantee that there exists a realization of a set of nonlinear higher order differential input-output equations in the controller canonical form. Two cases are studied, corresponding respectively to linear and nonlinear output functions. The conditions are formulated in terms of certain sequence of vector spaces of differential 1-forms. The proofs suggest how to construct the transformations, necessary to obtain the specific state space realizations. Multiple examples are added, which describe different scenarios.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra

Creator:
Belikov, Juri, Kotta, Ülle, and Tonsö, Maris
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
nonlinear control systems, input-output models, realization, and pseudo-linear algebra
Language:
English
Description:
In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows to simplify the existing step-by-step algorithm-based solution. The paper presents explicit formulas to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The method is straight-forward and better suited for implementation in different computer algebra packages such as \textit{Mathematica} or \textit{Maple}.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public