Solver-free optimal control for linear dynamical switched system by means of geometric algebra
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F24%3APU145765" target="_blank" >RIV/00216305:26210/24:PU145765 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.8752" target="_blank" >https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.8752</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.8752" target="_blank" >10.1002/mma.8752</a>
Alternative languages
Result language
angličtina
Original language name
Solver-free optimal control for linear dynamical switched system by means of geometric algebra
Original language description
An algorithm for finding a control of a linear switched system by means of Geometric Algebra is designed. More precisely, we develop a switching path searching algorithm for a two-dimensional linear dynamical switched system with a non-singular matrix whose integral curves are formed by two sets of centralized ellipses. It is natural to represent them as elements of Geometric Algebra for Conics and construct the switching path by calculating switching points, i.e., intersections and contact points. For this, we use symbolic algebra operations or, more precisely, the wedge and inner products that are realizable by sums of products in the coordinate form. Therefore, no numerical solver to the system of equations is needed. Indeed, the only operation that may bring in an inaccuracy is vector normalization, i.e., square root calculation. The resulting switching path is formed by pieces of ellipses that are chosen, respectively, from the two sets of integral curves. The switching points are either intersections in the first or final step of our algorithm, or contact points. This choice guarantees the optimality of the switching path with respect to the number of switches. Two examples are provided to demonstrate the search for the intersections of the conics and, consequently, a description is presented of the construction of a switching path in both cases.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN
0170-4214
e-ISSN
1099-1476
Volume of the periodical
47
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
15
Pages from-to
1274-1288
UT code for WoS article
000859088900001
EID of the result in the Scopus database
2-s2.0-85138626335