Tau Method for Linear Quadratic Regulator Problems

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Authors

  • A. Gavina Instituto Superior de Engenharia do Porto and Laboratório de Engenharia Matemática Author
  • J. Matos Instituto Superior de Engenharia do Porto and Centro de Matemática da Universidade do Porto Author
  • P.B. Vasconcelos Faculdade de Economia da Universidade do Porto and Centro de Matemática da Universidade do Porto Author

DOI:

https://doi.org/10.5890/JAND.2014.06.004

Abstract

We are interested in investigating the applicability of the Operational Tau method to solve optimal control problems. The present work focuses on quadratic regulator problems defined on infinite time. For the numerical approximation of the solution, domain transformation technique is studied as well as a special treatment of orthogonal polynomial basis. Numerical resultsobtained via a MATLAB implementation of the proposed approach are shown, illustrating its effectiveness.

References

[1] Ortiz, E.L. And Samara, H.,(1981), An operational approach to the Tau method for the numerical solution of non-linear differential equations, Computing, 27, 15-25,

[2] Athans, M. and Falb, P.L., (2007), Optimal Control: An Introduction to the Theory and its Applications, Dover Publications, Inc, (2007).

[3] Lanczos, C.,(1938), Interpolation of empirical and analytical functions, Journal of Mathematical Physics, 17, 123-199.

[4] Ortiz, E.L., (1969), The Tau method, SIAM Journal on Numerical Analysis, 6, 480-492 .

[5] Fahroo, F. and Ross, I.M.,(2008), Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems, Journal of Guidance, Control, and Dynamics, 31(4) 927-936.

[6] Rodrigues, Maria João and Matos, José(2012), A tau method for nonlinear dynamical systems, Numerical Algorithms, 1-18.

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PublishedJune 2014

Usage tracking begins September 1, 2026.

History Published

Issue

Vol. 3 No. 2 (2014): Regular Issue

Section

Research Articles

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Unless an article landing page states a Creative Commons or other article-specific license, the article is published by L&H Scientific Publishing, LLC and all rights are reserved. The article-level license and copyright notice govern access and reuse.

How to Cite

Gavina, A., Matos, J., & Vasconcelos, P. (2026). Tau Method for Linear Quadratic Regulator Problems. Journal of Applied Nonlinear Dynamics, 3(2), 139-146. https://doi.org/10.5890/JAND.2014.06.004

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