TY - GEN

T1 - State and parameter estimation using Chebyshev integral operator

AU - Živanović, Rastko

PY - 2011

Y1 - 2011

N2 - To formulate estimation problem for a observed nonlinear system, differential equations are required as a system model. We recast those equations as integral equations and apply integral operator, which is approximated by Chebyshev interpolating polynomial. Resulting equations of the nonlinear estimation problem are integral equations discretized on the grid of Chebyshev points. A sequence of linear least squares problems are solved iteratively. Grid resolution can be determined automatically to maximize computation accuracy. Numerical efficiency is achieved by applying iterative method that requires only matrix-vector multiplications, and via implementation of Discrete Cosine Transform when solving indefinite integrals. The estimation algorithm works with matrices having bounded low condition number compared to large and unbounded condition number for the formulation with differential operator. This achievement has important practical value when applying the algorithm with high-order models when the differential operator formulation is typically ill-conditioned. Application to a Duffing system having chaotic response, has been used to illustrate advantages of the proposed estimation algorithm based on Chebyshev integral operator.

AB - To formulate estimation problem for a observed nonlinear system, differential equations are required as a system model. We recast those equations as integral equations and apply integral operator, which is approximated by Chebyshev interpolating polynomial. Resulting equations of the nonlinear estimation problem are integral equations discretized on the grid of Chebyshev points. A sequence of linear least squares problems are solved iteratively. Grid resolution can be determined automatically to maximize computation accuracy. Numerical efficiency is achieved by applying iterative method that requires only matrix-vector multiplications, and via implementation of Discrete Cosine Transform when solving indefinite integrals. The estimation algorithm works with matrices having bounded low condition number compared to large and unbounded condition number for the formulation with differential operator. This achievement has important practical value when applying the algorithm with high-order models when the differential operator formulation is typically ill-conditioned. Application to a Duffing system having chaotic response, has been used to illustrate advantages of the proposed estimation algorithm based on Chebyshev integral operator.

UR - http://www.scopus.com/inward/record.url?scp=80052367859&partnerID=8YFLogxK

U2 - 10.1109/MED.2011.5983217

DO - 10.1109/MED.2011.5983217

M3 - Conference contribution

AN - SCOPUS:80052367859

SN - 9781457701252

T3 - 2011 19th Mediterranean Conference on Control and Automation, MED 2011

SP - 85

EP - 89

BT - 2011 19th Mediterranean Conference on Control and Automation, MED 2011

T2 - 2011 19th Mediterranean Conference on Control and Automation, MED 2011

Y2 - 20 June 2011 through 23 June 2011

ER -