Research ArticleOpen AccessGoogle Scholar indexed
Numerical Solution of a Class of Nonlinear Optimal Control Problems Using Linearization and Discretization
- 1
- 2
Copy link · social · email
Abstract
In this paper, a new approach using linear combination property of intervals and discretization is proposed to solve a class of nonlinear optimal control problems, containing a nonlinear system and linear functional, in three phases. In the first phase, using linear combination property of intervals, changes nonlinear system to an equivalent linear system, in the second phase, using discretization method, the attained problem is converted to a linear programming problem, and in the third phase, the latter problem will be solved by linear programming methods. In addition, efficiency of our approach is confirmed by some numerical examples.
KeywordsLinear and Nonlinear Optimal ControlLinear Combination Property of IntervalsLinear ProgrammingDiscretizationDynamical Control Systems
- M. Diehl, H. G. Bock and J. P. Schloder, “A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control,” Siam Journal on Control and Optimization, Vol. 43, No. 5, 2005, pp.1714-1736. doi:10.1137/S0363012902400713
- M. Diehl, H. G. Bock, J. P. Schloder, R. Findeisen, Z. Nagyc and F. Allgower, “Real-Time Optimization and Nonlinear Model Predictive Control of Processes Governed by Differential-Algebraic Equations,” Journal of Process Control, Vol. 12, No. 4, 2002, pp. 577-585.
- M. Gerdts and H. J. Pesch, “Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems,” Journal of Optimization Theory and Applications, Vol. 117, No. 2, 2003, pp. 267-294. doi:10.1023/A:1023679622905
- H. J. Pesch, “A Practical Guide to the Solution of Real- Life Optimal Control Problems,” 1994. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.53.5766&rep=rep1&type=pdf
- J. A. Pietz, “Pseudospectral Collocation Methods for the Direct Transcription of Optimal Control Problems,” Master Thesis, Rice University, Houston, April 2003.
- O. V. Stryk, “Numerical Solution of Optimal Control Problems by Direct Collocation,” International Series of Numerical Mathematics, Vol. 111, No. 1, 1993, pp. 129-143.
- A. H. Borzabadi, A. V. Kamyad, M. H. Farahi and H. H. Mehne, “Solving Some Optimal Path Planning Problems Using an Approach Based on Measure Theory,” Applied Mathematics and Computation, Vol. 170, No. 2, 2005, pp. 1418-1435.
- M. Gachpazan, A. H. Borzabadi and A. V. Kamyad, “A Measure-Theoretical Approach for Solving Discrete Optimal Control Problems,” Applied Mathematics and Computation, Vol. 173, No. 2, 2006, pp. 736-752.
- A.V. Kamyad, M. Keyanpour and M. H. Farahi, “A New Approach for Solving of Optimal Nonlinear Control Problems,” Applied Mathematics and Computation, Vol. 187, No. 2, 2007, pp. 1461-1471.
- A. V. Kamyad, H. H. Mehne and A. H. Borzabadi, “The Best Linear Approximation for Nonlinear Systems,” Applied Mathematics and Computation, Vol. 167, No. 2, 2005, pp. 1041-1061.
- K. P. Badakhshan and A. V. Kamyad, “Numerical Solution of Nonlinear Optimal Control Problems Using Nonlinear Programming,” Applied Mathematics and Computation, Vol. 187, No. 2, 2007, pp. 1511-1519.
- K. P. Badakhshan, A. V. Kamyad and A. Azemi, “Using AVK Method to Solve Nonlinear Problems with Uncertain Parameters,” Applied Mathematics and Computation, Vol. 189, No. 1, 2007, pp. 27-34.