A novel numerical method based on the differential transformation is proposed for solving nonlinear optimal control problems in this paper. The differential transformation is a linear operator that transforms a function from the original time and/or space domain into another domain in order to simplify the differential calculations. The optimality conditions for the optimal control problems can be represented by algebraic and differential equations. Using the differential transformation, these algebraic and differential equations with their boundary conditions are first converted into a system of nonlinear algebraic equations. Then the numerical optimal solutions are obtained in the form of finite-term Taylor series by solving the system of nonlinear algebraic equations. The differential transformation algorithm is similar to the spectral element methods in that the computational region splits into several subregions but it uses polynomials of high degrees by keeping a small number of subregions. The differential transformation algorithm could solve the finite- (or infinite-) time horizon optimal control problems formulated as either the algebraic and ordinary differential equations using Pontryagin’s minimum principle or the Hamilton–Jacobi–Bellman partial differential equation using dynamic programming in one unified framework. In addition, the differential transformation algorithm can efficiently solve optimal control problems with the piecewise continuous dynamics and/or nonsmooth control. The performance is demonstrated through illustrative examples.
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e-mail: ihwang@purdue.edu
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September 2009
Research Papers
Differential Transformation and Its Application to Nonlinear Optimal Control
Inseok Hwang,
Inseok Hwang
Assistant Professor
School of Aeronautics and Astronautics,
e-mail: ihwang@purdue.edu
Purdue University
, West Lafayette, IN 47907
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Jinhua Li,
Jinhua Li
Graduate Student
School of Aeronautics and Astronautics,
e-mail: li31@purdue.edu
Purdue University
, West Lafayette, IN 47907
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Dzung Du
Dzung Du
Graduate Student
School of Aeronautics and Astronautics,
e-mail: ddu@purdue.edu
Purdue University
, West Lafayette, IN 47907
Search for other works by this author on:
Inseok Hwang
Assistant Professor
School of Aeronautics and Astronautics,
Purdue University
, West Lafayette, IN 47907e-mail: ihwang@purdue.edu
Jinhua Li
Graduate Student
School of Aeronautics and Astronautics,
Purdue University
, West Lafayette, IN 47907e-mail: li31@purdue.edu
Dzung Du
Graduate Student
School of Aeronautics and Astronautics,
Purdue University
, West Lafayette, IN 47907e-mail: ddu@purdue.edu
J. Dyn. Sys., Meas., Control. Sep 2009, 131(5): 051010 (11 pages)
Published Online: August 19, 2009
Article history
Received:
August 5, 2008
Revised:
May 7, 2009
Published:
August 19, 2009
Citation
Hwang, I., Li, J., and Du, D. (August 19, 2009). "Differential Transformation and Its Application to Nonlinear Optimal Control." ASME. J. Dyn. Sys., Meas., Control. September 2009; 131(5): 051010. https://doi.org/10.1115/1.3155013
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