Stochastic Control of Decentralized Singularly Perturbed Systems

Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

Abstract:

Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: Decentralized, optimal control, output, singular perturb.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1123606

References:

[1] P. Kokotovic, H. Khalil and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design, London: Academic Press, 1986.
[2] J. Leigh, Control Theory, London: The Institution of Engineering and Technology, 2004.
[3] N. Jagan, Control Systems, Hyderabad, India: BS Publications, 2007.
[4] S. Engelberg, A Mathematical Introduction to Control Theory, London: Imperial College Press, 2005.
[5] J. Speyer and D. Jacobson, Primer on Optimal Control Theory, Philadelphia: Society for Industrial and Applied Mathematics, 2010.
[6] M. Golnaraghi, B. C. and M. Golnaraghi, Automatic Control Systems, Hoboken, NJ: John Wiley & Sons. Inc., 2010.
[7] N. Sandell, P. Varaiya, M. Athans and M. Safonov, "Survey of decentralized control methods for large scale systems," IEEE Transactions on Automatic Control, vol. 23, no. 2, pp. 108-128, 1978.
[8] D. Zhang, X. Wang, and L. Meng, "Consensus problems for high-order LTI systems: a decentralized static output feedback method." International Journal of Innovative Computing, Information and Control, pp. 2143-2154, 2013.
[9] V. Seksena, J. O'Reilly and P. Kokotovic, "Singular perturbations and time-scale methods in control theory: Survey 1976–1983," Automatica, vol. 20, no. 3, pp. 273-293, 1984.
[10] Y. Zhang, D. Naidu, C. Cai and Y. Zou, "Singular perturbations and time scales in control theories and applications: an overview 202-2012," Internation Journal of Information and Systems Sciences, vol. 9, no. 1, pp. 1-36, 2014.
[11] D. Naidu, "Singular perturbations and time scales in control theory and applications: an overview," Dynamics of Continuous Discrete and Impulsive Systems Series B, vol. 9, no. 2, pp. 233-278, 2002.
[12] K. Kalsi, Decentralized Observer-Based Control of Uncertain Dynamic Systems, West Lafayette, IN: Diss. Purdue University, 2010.
[13] A. Savkin and I. Petersen, "Optimal Stabilization of Linear Systems via Decentralized Output Feedback," IEEE Transactions on Automatic Control, vol. 43, no. 2, pp. 292 - 294, 1998.
[14] B. Anderson and J. Moore, "Time-varying feedback laws for decentralized control," IEEE Transactions on Automatic Control, vol. 26, no. 5, pp. 1133-1139, 1981.
[15] J. Marden and J. Shamma, "Game theory and distributed control" In: P. Young, S. Zamir (editors), Handbook of game theory, Vol.4, Elsevier Science, 2012.
[16] J. Lynch and K. Law, "Decentralized control techniques for large-scale civil structural systems ‏" Proc. of the 20th Int. Modal Analysis Conference (IMAC XX), Los Angeles, CA, USA, February 2002.
[17] P. Ioannou, "Decentralized adaptive control of interconnected systems." IEEE Transactions on Automatic Control, vol. 31, no. 4, pp. 291-298, 1986.
[18] A. Elmahdi, A. Taha, D. Sun and J. Panchal, "An Optimal General Purpose Scheduler for Networked Control Systems." IEEE International Conference on Systems, Man and Cybernetics (SMC), pp. 234-239, 2014.
[19] I. Hyun, M.E. Sawan, D.G. Lee, and D. Kim "Robust stability for decentralized singularly perturbed unified system.‏" Proceedings of American Control Conference. 2006.‏
[20] K. Yao, "An iteration method to sub-optimal output feedback computer control of decentralized singularly-perturbed systems." Innovative Computing, Information and Control, 2007. ICICIC'07. Second International Conference on. IEEE, 2007.‏
[21] A. Haddad and P. Kokotovic, "Stochastic control of linear sigularly perturbed systems," IEEE Transactions on Automatic Control, vol. 22, no. 5, pp. 815-821, 1977.