ESTONIAN ACADEMY
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eesti teaduste
akadeemia kirjastus
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proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
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Functions’ algebra in nonlinear control: computational aspects and software; pp. 89–107

Full article in PDF format | https://doi.org/10.3176/proc.2017.1.06

Authors
Juri Belikov, Arvo Kaldmäe, Vadim Kaparin, Ülle Kotta, Alexey Ye. Shumsky, Maris Tõnso, Alexey Zhirabok

Abstract

The paper describes the Mathematica-based software for studying nonlinear control systems. The software relies on an algebraic method, called functions’ algebra. The advantage of this approach, over well-known linear algebraic and differential geometric methods is that it is applicable to certain non-smooth systems. The drawback is that the computations are more complicated since the approach manipulates directly with the functions related to the system equations and not with the differential one-forms/vector fields that simplify (linearize) the computations. We have implemented the basic operations of functions’ algebra, i.e., partial order, equivalence, summation, and multiplication, but also finding the simplest epresentative of an equivalence class. The next group of functions is related to the control system and involves binary relation, operators m, M, and computation of certain sequences of invariant vector functions on the basis of system equations. Finally, we have developed Mathematica functions, allowing us to solve the following control problems in case of discrete-time systems: checking accessibility, static state feedback linearization, and disturbance decoupling.


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