Orthogonal Functions Approach to LQG Control
In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1063258Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1483
 Athans, M., The role and use of the stochastic linear-quadratic- Gaussian problem in control system design, IEEE Trans. Automatic Control, vol. 16, no. 6, pp: 529-552, 1971.
 Sage, A. P. and White, C .C., Optimum Systems Control, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977.
 Brewer, J. W., Kronecker products and matrix calculus in system theory, IEEE Trans. Circuits and Systems, vol. 25, no. 9, pp: 772-781, 1978.
 Rao, G. P., Piecewise Constant Orthogonal Functions and Their Application to Systems and Control, LNCIS 55, Springer, Berlin, 1983.
 Hwang, C. and Chen, M. Y., Analysis and optimal control of timevarying linear systems via shifted Legendre polynomials, Int. J. Control, vol. 41, no. 5, pp: 1317-1330, 1985.
 Chang, Y. F. and Lee, T. T., General orthogonal polynomials approximations of the linear-quadratic-Gaussian control design, Int. J. Control, vol. 43, no. 6, pp: 1879-1895, 1986.
 Jiang, Z. H. and Schaufelberger, W., Block-Pulse Functions and Their Applications in Control Systems, LNCIS 179, Spinger, Berlin, 1992.
 Datta, K. B. and Mohan, B. M., Orthogonal Functions in Systems and Control, Advanced Series in Electrical and Computer Engineering, vol. 9, World Scientific, Singapore, 1995.
 Patra, A. and Rao, G. P., General Hybrid Orthogonal Functions and Their Applications in Systems and Control, LNCIS 213, Springer, London, 1996.
 Gupta, V., Hassibi, B. and Murray, R. M., Optimal LQG control across packet-dropping links, Systems & Control Letters, vol. 56, no. 6, pp: 439-446, 2007.
 Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K. and Sastry, S., Optimal linear LQG control over lossy networks without packet acknowledgment, Asian J. Control, vol. 10, no. 1, pp: 3-13, 2008.
 Kar, S. K., Orthogonal functions approach to optimal control of linear time-invariant systems described by integro-differential equations, KLEKTRIKA, vol. 11, no 1, pp: 15-18, 2009.
 Mohan, B. M. and Kar, S. K., Optimal Control of Multi-Delay Systems via Orthogonal Functions, Int. J. Advanced Research in Engineering and Technology, vol. 1, no. 1, pp: 1-24, 2010.
 Kar, S. K., Optimal control of a linear distributed parameter system via shifted Legendre polynomials, Int. J. Electrical and Computer Engineering (WASET), vol. 5, no. 5, pp: 292-297, 2010.
 Mohan, B. M. and Kar, S. K., Orthogonal functions approach to optimal control of delay systems with reverse time terms, J. The Franklin Institute, vol. 347, no. 9, pp: 1723-1739, 2010.
 Mohan, B. M. and Kar, S. K., Optimal Control of Singular Systems via Orthogonal Functions, Int. J. Control, Automation and Systems, vol. 9, no. 1, pp: 145-152, 2011.
 Mohan, B. M. and Kar, S. K., Optimal control of multi-delay systems via shifted Legendre polynomials, Int. Conf. on Energy, Automation and Signals (ICEAS), Bhubaneswar, INDIA, December 28-30, 2011.
 Mohan, B. M. and Kar, S. K., Optimal control of nonlinear systems via orthogonal functions, Int. Conf. on Energy, Automation and Signals (ICEAS), Bhubaneswar, INDIA, December 28-30, 2011.