ABSTRACT
This paper proposes a novel application of differential evolution to solve a difficult dynamic optimisation or optimal control problem. The miss distance in a missile-target engagement is minimised using differential evolution. The difficulty of solving it by existing conventional techniques in optimal control theory is caused by the nonlinearity of the dynamic constraint equation, inequality constraint on the control input and inequality constraint on another parameter that enters problem indirectly.
The optimal control problem of finding the minimum miss distance has an analytical solution subject to several simplifying assumptions. In the approach proposed in this paper, the initial population is generated around the seed value given by this analytical solution. Thereafter, the algorithm progresses to an acceptable final solution within a few generations, satisfying the constraints at every iteration. Since this solution or the control input has to be obtained in real time to be of any use in practice, the feasibility of online implementation is also illustrated.
- Linkens, D. A., and Nyongesa, H. O., "Genetic algorithms for fuzzy control part 2; online system development and application", IEE Proc. -- Control Theory Appl., Vol. 142, No. 3, May 1995.Google Scholar
- Zarchan P., Tactical and Strategic Missile Guidance, Progress in Astronautics and Aeronautics, Vol. 199, Fourth Ed., AIAA, Reston, Virginia, 2002.Google Scholar
- Chen, B. S., Chen, Y. Y., and Lin, C. L., 'Nonlinear Fuzzy H∞ Guidance Law With Saturation of Actuators Against Maneuvering Targets', IEEE Transactions on Control Systems Technology, vol. 10, no. 6, Nov. 2002, pp. 769--779.Google ScholarCross Ref
- J. Shinar, and T. Shima, 'Guidance Law Evaluation in Highly Nonlinear Scenarios -- Comparison to Linear Analysis,' in AIAA Guidance, Navigation and Control Conference, 1999, Paper no. 99--4065, pp. 651--661.Google Scholar
- Thangavelu. R. , and Pradeep, S., 'A Differential Evolution Tuned Optimal Guidance Law,' in Mediterannean Conference on Control and Automation, June 2007, Paper no. T13--002.Google Scholar
- D. S. Naidu, Optimal Control Systems, CRC Press LLC, Boca Raton, Florida, 2003 Google ScholarDigital Library
- John T. Betts, Practical Methods for Optimal Control Using Nonlinear Programming, Society for Industrial and Applied Mathematics, Philadelphia, 2001, pp. 84. Google ScholarDigital Library
- H. Seywald, R. R. Kumar, and S. M. Deshpande, "Genetic Algorithm Approach for Optimal Control Problems with Linearly Appearing Controls," Journal of Guidance, Control, and Dynamics, Vol. 18, No. 1, Jan.--Feb. 1995, pp. 177--182.Google Scholar
- Differential Evolution home page. Available: http://www.icsi.berkeley.edu/~storn/code.htmlGoogle Scholar
- Y. C. Sim, S. B. Leng, and V. Subramaniam, "A combined genetic algorithms-shooting method approach to solving optimal control problems," International Journal of Systems Science, Vol 31, No. 1, 2000, pp. 83--89.Google Scholar
Index Terms
- An online implementable differential evolution tuned optimal guidance law
Recommendations
Blowup Time Optimal Control for Ordinary Differential Equations
This paper studies a time optimal control problem governed by a classical controlled system of nonlinear ordinary differential equations. Corresponding to certain controls, the solutions of the system have the behavior of blowup; namely, they blow up at ...
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
AbstractWe survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution ...
A hybrid algorithm for approximate optimal control of nonlinear Fredholm integral equations
In this paper, a novel hybrid method based on two approaches, evolutionary algorithms and an iterative scheme, for obtaining the approximate solution of optimal control governed by nonlinear Fredholm integral equations is presented. By converting the ...
Comments