Design of nonlinear observers with approximately linear error dynamics using multivariable Legendre polynomials

2006 ◽  
Vol 16 (15) ◽  
pp. 709-727 ◽  
Author(s):  
Joachim Deutscher ◽  
Markus Bäuml
Keyword(s):  
Legendre Polynomials ◽  
Nonlinear Observers ◽  
Error Dynamics

Nonlinear Observers with Linearizable Error Dynamics

1985 ◽  
Vol 23 (2) ◽  
pp. 197-216 ◽  
Author(s):  
Arthur J. Krener ◽  
Witold Respondek
Keyword(s):  
Nonlinear Observers ◽  
Error Dynamics

scholarly journals Optimal solution of the fractional order breast cancer competition model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Hassani ◽  
J. A. Tenreiro Machado ◽  
Z. Avazzadeh ◽  
E. Safari ◽  
S. Mehrabi
Keyword(s):  
Breast Cancer ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Numerical Experiments ◽  
Optimal Solution ◽  
Optimization Method ◽  
Competition Model ◽  
Basis Functions ◽  
Cell Populations ◽  
Operational Matrices

AbstractIn this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.

scholarly journals Experimental study of the $ \gamma p \rightarrow K^{0}\Sigma^{+}$, $ \gamma n \rightarrow K^{0} \Lambda$, and $ \gamma n \rightarrow K^{0} \Sigma^{0}$ reactions at the Mainz Microtron

2019 ◽  
Vol 55 (11) ◽  
Author(s):  
C. S. Akondi ◽  
K. Bantawa ◽  
D. M. Manley ◽  
S. Abt ◽  
P. Achenbach ◽  
...  
Keyword(s):  
Experimental Study ◽  
Cross Sections ◽  
Differential Cross ◽  
Legendre Polynomials ◽  
Neutral Kaon ◽  
Experimental Results ◽  
Differential Cross Sections ◽  
Theoretical Predictions ◽  
Photoproduction Reactions ◽  
Insight Into

Abstract.This work measured $ \mathrm{d}\sigma/\mathrm{d}\Omega$dσ/dΩ for neutral kaon photoproduction reactions from threshold up to a c.m. energy of 1855MeV, focussing specifically on the $ \gamma p\rightarrow K^0\Sigma^+$γp→K0Σ+, $ \gamma n\rightarrow K^0\Lambda$γn→K0Λ, and $ \gamma n\rightarrow K^0 \Sigma^0$γn→K0Σ0 reactions. Our results for $ \gamma n\rightarrow K^0 \Sigma^0$γn→K0Σ0 are the first-ever measurements for that reaction. These data will provide insight into the properties of $ N^{\ast}$N* resonances and, in particular, will lead to an improved knowledge about those states that couple only weakly to the $ \pi N$πN channel. Integrated cross sections were extracted by fitting the differential cross sections for each reaction as a series of Legendre polynomials and our results are compared with prior experimental results and theoretical predictions.

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