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 JAMP  Vol.4 No.10 , October 2016
Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems
Abstract: This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.
Cite this paper: Zhu, J. (2016) Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems. Journal of Applied Mathematics and Physics, 4, 1859-1869. doi: 10.4236/jamp.2016.410188.
References

[1]   Sontag, E.D. (1998) Mathematical Control Theory: Deterministic Finite Dimensional Systems. 2nd Edition, Springer, New York.
http://dx.doi.org/10.1007/978-1-4612-0577-7

[2]   Pontryagin, L.S. (1964) The Mathematical Theory of Optimal Processes. Pergamon Press, Oxford, UK.

[3]   Zhu, J.H., Wu, D. and Gao, D. (2012) Applying the Canonical Dual Theory in Optimal Control Problems. Journal of Global Optimization, 54, 221-233.

[4]   Zhu, J.H. and Zhang, X. (2008) On Global Optimmizations with Polynomials. Optimization Letters, 2, 239-249.
http://dx.doi.org/10.1007/s11590-007-0054-5

[5]   Boothby, W.M. (2007) An Introduction to Differential Manifolds and Riemannian Geometry. Elsevier Pte Ltd., Singapore.

[6]   Zhu, J.H. and Liu, G.H. (2014) Solution to Optimal Control by Canonical Differential Equation. International Journal of Control, 87, 21-24.
http://dx.doi.org/10.1080/00207179.2013.819589

[7]   Brown, R.F. (1988) Fixed Point Theory and Its Applications. American Mathematical Society, New York.
http://dx.doi.org/10.1090/conm/072

 
 
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