An Approach to Parameter Optimization Problem for a Class of Compromise Solutions Under Vector Valued Performance Criteria

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The design of optimal control systems with vector valued performance index has been a challenge for researchers in the field of control engineering. The paper addresses the problem of parameter optimization in the context of vector valued optimal control design. The solution presents a class of compromise solutions with optimum value of the parameter involved in the design. The performance index in general is defined in the form of a norm which can be expressed as the sum of p¬¬th power of deviations of the different performance index elements from their optimal values considering individual performance measures separately. The norm is minimized in k dimensional performance index space to obtain a set of non inferior systems corresponding to a class of compromise solutions. The choice of a single system from the class of compromise solutions obtained is made by a suitable choice of the parameter ‘p’ depending upon the application and design specifications.
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Parameter Optimization; Vector Valued Performance Criteria; Optimal Control Design; Multi Criteria Optimal Control

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D. E. Kirk, Optimal Control Theory (Prentice Hall, 1970).

D. S. Naidu, Optimal Control Systems (CRC Press, NewYork, 2003).

Brian D.O.Anderson, John B. Moore,Optimal Control – Linear Quadratic Methods (Prentice Hall, 2004)

Roman.B. Statnikov, Multicriteria Design: Optimization and Identification, (Kluuwer Academic Publishers,1999).

M. Murat Köksalan, Jyrki Wallenius, Stanley Zionts, Multiple Criteria Decision Making: From Early History to the 21st Century, (World Scientific Publishing Company, 2011).

Zadeh L .A., Optimality and Non Scalar Valued Performance Criteria, IEEE Transactions on Automatic Control, Volume AC-8, (No. 1): 59-60, January 1963.

Essameddin Badreddin and Adrian Gambier, Multi-objective Optimal Control: An Overview. 16th IEEE International Conference on Control Applications, Part of IEEE Multi Conference on Systems and Control, Singapore, 1-3 October 2007.

Adrian Gambier and Meike Jipp, Multi-objective Optimal Control: An Introduction, Proceedings of the Asian Control Conference (ASCC-2011), Taiwan, May 15-18, 2011.

Jaganthan, S., Palaniswami, S., Application of multi objective optimization to optimal power dispatch problem with facts devices using refined BFA, (2012) International Review on Modelling and Simulations (IREMOS), 5 (5), pp. 2146-2159.

Marius-ConstantinPopescu, Luminiţa-GeorgetaPopescu, Florin Grofu, Optimal Control of Driving Systems, (2009) International Review of Automatic Control (IREACO), (2) 6, pp. 645-653.

Abdellah, A., Abdelhafid, A., Mostafa, R., Combining sliding mode and linear quadratic regulator to control the inverted pendulum, (2013) International Review of Automatic Control (IREACO), 6 (1), pp. 69-76.

B. Baigzadeh, V. Nazarzehi, H. Khaloozadeh, Evaluation and Comparison of the Performance of Two Techniques on Two Cart-Inverted Pendulum System, (2011) International Review of Automatic Control (IREACO), (4) 4, pp. 503-509.

Salukvadze M E., Vector Valued Optimisation Problems in Control Theory (Academic Press, New York, 1979).

Nandakumar M P. and B Sarkar, On a Class of Compromise Solutions for Vector Valued Optimal Control Problems, Proceedings of 9th National Systems Conference (NSC – 85), Allahabad, 1985.

Nandakumar M P., Optimal Control Systems Design with Vector Valued Performance Index, Ph.D. Thesis, Indian Institute of Technology, Kanpur, September 1986.

Hadi, H., Tajul, L., Hamzas, M.F.M.A., Hussin, M.S., Zailani, Z.A., Radzi, M.H.M., Parameter optimization for JIS S45C steel turning process based on Taguchi method, (2012) International Review of Mechanical Engineering (IREME), 6 (3), pp. 462-467.


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