i-manager Publications

Numerical Approach for Solving Time and Robust Time Optimal Control Problems

Mohammad Amin Rashidifar*, Ali Amin Rashidifar**

*Faculty of Mechanical Engineering, Islamic Azad University, Shadegan Branch, Shadegan, Iran.

** Computer Science, Islamic Azad University, Shadegan Branch, Shadegan, Iran.

Periodicity:November - January'2014
DOI : https://doi.org/10.26634/jme.4.1.2574

Abstract

A numerical technique for solving time and robust time-optimal control problems has been presented. The method relies on the special feature that the optimal control structure contains as many free parameters as there are interior or boundary conditions. Two Boundary Value Problems (BVPs) are formulated for the state variables and co-states independently, thus, reducing the dimension of the original problem into half. Then, a numerical algorithm is developed, that is based on the shooting method, to solve the resulting BVPs. The computed optimal solution is verified by comparing the control input resulting from the first BVP with the switching function obtained by solving the second BVP. Next, the numerical technique is modified to solve robust time-optimal control problems. The capability of the proposed method is demonstrated through numerical examples, whose output optimal solution is shown to be identical to those presented in the literature. These examples include linear as well as non-linear systems. Finally, the numerical technique is utilized to design a time-optimal control for a rest-to-rest maneuver of flexible structure while eliminating the residual vibrations at the end of the maneuver.

Keywords

Time Optimal Control, Boundary Value Problem, Shooting Method, Nonlinear System

How to Cite this Article?

Rashidifar, M. A., and Rashidifar, A. A. (2014). Numerical Approach for Solving Time-and Robust Time-Optimal Control Problems. i-manager's Journal on Mechanical Engineering, 4(1), 1-9. https://doi.org/10.26634/jme.4.1.2574

References

[1]. Singh, T., and Vadali, S., (1994). "Robust Time-Optimal Control: Frequency Domain Approach," Journal of Guidance, Control, and Dynamics, Vol. 17, No. 2, pp. 346- 353.

[2]. Ben-Asher, J., Burns, J., and Cliff, E., (1992). "Time-Optimal Slewing of Flexible Spacecraft," Journal of Guidance Control, and Dynamics, Vol. 15, No. 2, pp. 360-367.

[3]. Liu, Q., and Wie, B., (1992). "Robust Time-Optimal Control of Uncertain Flexible Spacecraft," Journal of Guidance, Control, and Dynamics, Vol. 15, No. 3, pp. 597- 604.

[4]. Singh, G., Kabamba, P., and McClamroch, N., Planar, (1989). “Time-Optimal, Rest-to-Rest Slewing Maneuvers of Flexible Spacecraft," Journal of Guidance, Control, and Dynamics, Vol. 12, No. 1, pp. 71-81.

[5]. Pao, L., (1996). "Minimum-Time Control Characteristics of Flexible Structures," Journal of Guidance, Control, and Dynamics, Vol. 19, No. 1, pp. 123-129.

[6]. Meier, E., and Bryson, A., (1990). "An Efficient Algorithm for Time-Optimal Control of a Two-Link Manipulator," Journal of Guidance, Control, and Dynamics, Vol. 13, No. 5, pp. 859-866.

[7]. Scrivener, S., and Thompson, R., (1994). "Survey of Time-Optimal Attitude Maneuvers," Journal of Guidance, Control, and Dynamics, Vol. 17, No. 2, pp. 225-233.

[8]. Maurer, H., and Wiegand, M., (1992). "Numerical Solution of a Drug Displacement Problem with Bounded State Variables," Optimal Control Applications and Methods, Vol. 13, pp. 43-55.

[9]. Kirk, D., (1970). Optimal Control Theory, Prentice Hall, New Jersey.

[10]. Ryan, E., (1982). Optimal Relay and Saturating Control System Synthesis, Peter Peregrinus, London.

[11]. Lastman, G. J., (1978). "Shooting Method for Solving Two-Point Boundary Value Problems, Arising from Non- Singular Bang-Bang Optimal Control Problems," International Journal of Control, Vol. 27, No. 4, pp. 513-524.

[12]. Li, F., and Bainum, P. M., (1990). "An Improved Shooting Method for Solving Minimum-Time Maneuver Problems," American Society of Mechanical Engineering, Winter Annual Meeting, Dallas, TX, Nov. 26-30.

[13]. Liu, S., and Singh, T., (1996). "Robust Time-Optimal Control of Flexible Spacecraft with Structured Uncertainties," AIAA Guidance, Navigation, and Control Conference, San Diego, CA, July 29-31.

If you have access to this article please login to view the article or kindly login to purchase the article

Single Article

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Online	15	15

ADD TO CART

Options for accessing this content:

If you would like institutional access to this content, please recommend the title to your librarian.
If you already have i-manager's user account: Login above and proceed to purchase the article.
New Users: Please register, then proceed to purchase the article.