Optimal Control of a Linear Distributed Parameter System via Shifted Legendre Polynomials
The optimal control problem of a linear distributed
parameter system is studied via shifted Legendre polynomials (SLPs)
in this paper. The partial differential equation, representing the
linear distributed parameter system, is decomposed into an n - set
of ordinary differential equations, the optimal control problem is
transformed into a two-point boundary value problem, and the twopoint
boundary value problem is reduced to an initial value problem
by using SLPs. A recursive algorithm for evaluating optimal control
input and output trajectory is developed. The proposed algorithm is
computationally simple. An illustrative example is given to show the
simplicity of the proposed approach.
[1] Sage, A. P. and White III, C .C., Optimal Systems Control, Englewood
cliffs, NJ: Prentice Hall, 1977.
[2] Mahapatra, G. B., Solution of optimal control problem of linear diffusion
equations via Walsh functions, IEEE Trans. on Automatic Control, Vol.
25, No. 2, pp: 319-321, 1980.
[3] Wang, M. L. and Chang, R. Y., Optimal control of linear distributed
parameter systems by shifted Legendre polynomial functions, Trans. of
ASME J. of Dynamic Systems, Measurement, and Control, Vol. 105, pp:
222-226, 1983.
[4] Horng, I. R. and Chou, J. H., Application of shifted Chebyshev series to
the optimal control of linear distributed parameter systems, Int. J. of
Control, Vol. 42, No. 1, pp: 233-241, 1985.
[5] Chang, R. Y. and Yang, S. Y., Solution of two-point boundary value
problems by generalized orthogonal polynomials and application to
optimal control of lumped and distributed parameter systems, Int. J.
of Control, Vol. 43, No. 6, pp: 1785-1802, 1986.
[6] Zhu, J. M. and Lu, Y. Z., Application of single step method of block-pulse
functions to the optimal control of linear distributed parameter systems,
Int. J. of Systems Sci., Vol. 19, No. 12, pp: 2459-2472, 1988.
[7] Datta, K. B. and Mohan, B. M., Orthogonal Functions in Systems and
Control, Singapore: World Scientific, 1995.
[8] Razzaghi, M. and Habibi, M., Application of Legendre series to the
control problems governed by linear parabolic equations, Mathematics
and Computers in Simulation, Vol. 42, pp: 77-84, 1996.
[9] Sadek, I. S. and Bokhari, M. A., Optimal control of a parabolic distributed
parameter system via orthogonal functions, Optimal Control Applications
and Methods, Vol. 19, pp: 205-213, 1998.
[1] Sage, A. P. and White III, C .C., Optimal Systems Control, Englewood
cliffs, NJ: Prentice Hall, 1977.
[2] Mahapatra, G. B., Solution of optimal control problem of linear diffusion
equations via Walsh functions, IEEE Trans. on Automatic Control, Vol.
25, No. 2, pp: 319-321, 1980.
[3] Wang, M. L. and Chang, R. Y., Optimal control of linear distributed
parameter systems by shifted Legendre polynomial functions, Trans. of
ASME J. of Dynamic Systems, Measurement, and Control, Vol. 105, pp:
222-226, 1983.
[4] Horng, I. R. and Chou, J. H., Application of shifted Chebyshev series to
the optimal control of linear distributed parameter systems, Int. J. of
Control, Vol. 42, No. 1, pp: 233-241, 1985.
[5] Chang, R. Y. and Yang, S. Y., Solution of two-point boundary value
problems by generalized orthogonal polynomials and application to
optimal control of lumped and distributed parameter systems, Int. J.
of Control, Vol. 43, No. 6, pp: 1785-1802, 1986.
[6] Zhu, J. M. and Lu, Y. Z., Application of single step method of block-pulse
functions to the optimal control of linear distributed parameter systems,
Int. J. of Systems Sci., Vol. 19, No. 12, pp: 2459-2472, 1988.
[7] Datta, K. B. and Mohan, B. M., Orthogonal Functions in Systems and
Control, Singapore: World Scientific, 1995.
[8] Razzaghi, M. and Habibi, M., Application of Legendre series to the
control problems governed by linear parabolic equations, Mathematics
and Computers in Simulation, Vol. 42, pp: 77-84, 1996.
[9] Sadek, I. S. and Bokhari, M. A., Optimal control of a parabolic distributed
parameter system via orthogonal functions, Optimal Control Applications
and Methods, Vol. 19, pp: 205-213, 1998.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54561", author = "Sanjeeb Kumar Kar", title = "Optimal Control of a Linear Distributed Parameter System via Shifted Legendre Polynomials", abstract = "The optimal control problem of a linear distributed
parameter system is studied via shifted Legendre polynomials (SLPs)
in this paper. The partial differential equation, representing the
linear distributed parameter system, is decomposed into an n - set
of ordinary differential equations, the optimal control problem is
transformed into a two-point boundary value problem, and the twopoint
boundary value problem is reduced to an initial value problem
by using SLPs. A recursive algorithm for evaluating optimal control
input and output trajectory is developed. The proposed algorithm is
computationally simple. An illustrative example is given to show the
simplicity of the proposed approach.", keywords = "Optimal control, linear systems, distributed parametersystems, Legendre polynomials.", volume = "4", number = "8", pages = "1113-6", }