Solver-free optimal control for linear dynamical switched system by means of geometric algebra

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Solver-free optimal control for linear dynamical switched system by means of geometric algebra

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Solver-free optimal control for linear dynamical switched system by means of geometric algebra

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

MATHEMATICAL METHODS IN THE APPLIED SCIENCES

ISSN

0170-4214

e-ISSN

1099-1476

Svazek periodika

47

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

15

Strana od-do

1274-1288

Kód UT WoS článku

000859088900001

EID výsledku v databázi Scopus

2-s2.0-85138626335