Detail publikace
Solver-free optimal control for linear dynamical switched system by means of geometric algebra
DEREVIANKO, A. VAŠÍK, P.
Anglický název
Solver-free optimal control for linear dynamical switched system by means of geometric algebra
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
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.
Anglický abstrakt
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.
Klíčová slova anglicky
Clifford algebra; controllability; geometric algebra; switched system
Vydáno
01.02.2024
Nakladatel
WILEY
Místo
HOBOKEN
ISSN
0170-4214
Ročník
47
Číslo
3
Strany od–do
1274–1288
Počet stran
15
BIBTEX
@article{BUT179410,
author="Anna {Derevianko} and Petr {Vašík},
title="Solver-free optimal control for linear dynamical switched system by means of geometric algebra",
year="2024",
volume="47",
number="3",
month="February",
pages="1274--1288",
publisher="WILEY",
address="HOBOKEN",
issn="0170-4214"
}