Functions’ algebra in nonlinear control: computational aspects and software

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 certa...

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Bibliographic Details
Published in:Proceedings of the Estonian Academy of Sciences 2017-01, Vol.66 (1), p.89-89
Main Authors: Belikov, Juri, Kaldmaee, Arvo, Kaparin, Vadim, Kotta, Uelle, Shumsky, Alexey Ye, Tonso, Maris, Zhirabok, Alexey
Format: Article
Language:English
Subjects:
Algebra
Computation
Computer programs
Control systems
Mathematical analysis
Mathematical models
Nonlinearity
Software
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Summary: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 representative 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.
ISSN:1736-6046
1736-7530
DOI:10.3176/proc.2017.1.06