Performance of Suboptimal Controllers for Affine-Quadratic Problems

Ankita Sharma; A. J. Shaiju

doi:10.4236/ijmnta.2014.35025

Home > Journals > Engineering | Physics & Mathematics > IJMNTA

IJMNTA> Vol.3 No.5, December 2014

Share This Article:

Performance of Suboptimal Controllers for Affine-Quadratic Problems ()

Abstract Full-Text HTML XML

Download as PDF (Size:2510KB) PP. 230-235

DOI: 10.4236/ijmnta.2014.35025 2,369 Downloads 2,804 Views

Author(s) Leave a comment

Ankita Sharma^*, A. J. Shaiju

Affiliation(s)

Department of Mathematics, Indian Institute of Technology Madras, Chennai, India.

ABSTRACT

In this article, affine-quadratic control problems are studied. Error bounds are derived for the difference between the performance indices corresponding to the optimal and a class of suboptimal controls. In particular, it is shown that the performance of these suboptimal controls is close to that of the optimal control whenever the error in estimating the costate initial condition is small.

KEYWORDS

Affine-Quadratic Control, Nonlinear Control, Optimal Control, Suboptimal Control

Cite this paper

Sharma, A. and Shaiju, A. (2014) Performance of Suboptimal Controllers for Affine-Quadratic Problems. International Journal of Modern Nonlinear Theory and Application, 3, 230-235. doi: 10.4236/ijmnta.2014.35025.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Anderson, B.D.O. and Moore, J.B. (1989) Optimal Control: Linear Quadratic Methods. Prentice-Hall, Inc., Upper Saddle River.

[2]	Zhou, K., Doyle, J.C. and Glover, K. (1996) Robust and Optimal Control. Prentice-Hall, Inc., Upper Saddle River.

[3]	Bardi, M. and Dolcetta, I.C. (2008) Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhauser, Boston.

[4]	Tang, L., Zhao, L.D. and Guo, J. (2009) Research on Pricing Policies for Seasonal Goods Based on Optimal Control Theory. ICIC Express Letters, 3, 1333-1338.

[5]	Garrard, W.L. and Jordan, J.M. (1977) Design of Nonlinear Automatic Flight Control Systems. Automatica, 13, 497-505. http://dx.doi.org/10.1016/0005-1098(77)90070-X

[6]	Manousiouthakis, V. and Chmielewski, D.J. (2002) On Constrained Infinite-Time Nonlinear Optimal Control. Chemical Engineering Science, 57, 105-114. http://dx.doi.org/10.1016/S0009-2509(01)00359-1

[7]	Notsu, T., Konishi, M. and Imai, J. (2008) Optimal Water Cooling Control for Plate Rolling. International Journal of Innovative Computing, Information and Control, 4, 3169-3181.

[8]	Kalman, R.E. (1960) Contributions to the Theory of Optimal Control. Matematica Mexicana, 5, 102-119.

[9]	Effati, S. and Nik, H.S. (2011) Solving a Class of Linear and Non-Linear Optimal Control Problems by Homotopy Perturbation Method. IMA Journal of Mathematical Control and Information, 28, 539-553. http://dx.doi.org/10.1093/imamci/dnr018

[10]	Sharma, A. and Shaiju, A.J. (2014) Solution of Affine-Quadratic Control Problems. Proceedings of the 19th WC-IFAC, Cape-Town.

[11]	Jajarmi, A., Pariz, N., Kamyad, A.V. and Effati, S. (2011) A Novel Series Representation Approach to Solve a Class of Nonlinear Optimal Control Problems. International Journal of Innovative Computing, Information and Control, 7, 1413-1425.

[12]	Pontryagin, L.S., et al. (1962) The Mathematical Theory of Optimal Processes. John Wiley and Sons, Inc., New York.