Finite horizon optimal control of singularly perturbed systems: A differential Lyapunov equation approach

IEEE Transactions on Automatic Control

Volumn 55, Issue 9, 2010, Pages 2148-2152

  Nguyen, Thang ^a   Gajic, Zoran ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Algebraic Riccati equation; Differential Lyapunov Sylvester equation; Differential Riccati equation; Optimal control; Singularly perturbed systems

Indexed keywords

ALGEBRAIC RICCATI EQUATIONS; DIFFERENTIAL LYAPUNOV/SYLVESTER EQUATION; DIFFERENTIAL RICCATI EQUATION; OPTIMAL CONTROLS; SINGULARLY PERTURBED SYSTEMS;

ALGEBRA; CONTROL; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; OPTIMIZATION; PERTURBATION TECHNIQUES;

RICCATI EQUATIONS;

EID: 77956511189     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2051187     Document Type: Article

References (19)

1. P. Kokotovic, H. Khalil, and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design. Orlando, FL: Academic, 1986.
2. Z. Gajic and M. Lim, Optimal Control of Singularly Perturbed Linear Systems with Applications: High Accuracy Techniques. New York: Marcel Dekker, 2001.
3. P. Kokotovic and R. Yackel, "Singular perturbation of linear regulators: Basic theorems," IEEE Trans. Autom. Control, vol. AC-17, no. 1, pp. 29-37, Feb. 1972.
4. R. Yackel and P. Kokotovic, "A boundary layer method for the matrix Riccati equation," IEEE Trans. Autom. Control, vol. AC-18, no. 1, pp. 17-24, Feb. 1973.
5. V. Y. Glizer and M. G. Dmitriev, "Singular perturbations in a linear optimal control problem with quadratic functional," Soviet Mathematics Doklady, vol. 16, no. 6, pp. 1555-1558, 1975.
6. V. Y. Glizer and M. G. Dmitriev, "Asymptotic properties of solution of a singularly perturbed Cauchy problem encountered in optimal-control theory,"Differ. Equ. , vol. 14, no. 4, pp. 423-432, 1978.
7. T. Grodt and Z. Gajic, "The recursive reduced-order numerical solution of the singularly perturbed matrix differential Riccati equation," IEEE Trans. Autom. Control, vol. AC-33, no. 8, pp. 751-755, Aug. 1988.
8. Z. Gajic, S. Koskie, and C. Coumarbatch, "On the singularly perturbed matrix differential Riccati equation," in Proc. IEEE Conf. Decision and Control, Seville, Spain, Dec. 2005, pp. 3638-3644.
9. Z. Gajic, "Numerical fixed-point solution for near-optimum regulators of linear-quadratic Gaussian control problem for singularly perturbed systems," Int. J. Control, vol. 43, pp. 373-387, 1986.
10. T. Nguyen and Z. Gajic, "Solving the matrix differential Riccati equation: A Lyapunov equation approach," IEEE Trans. Autom. Control, vol. 55, no. 1, pp. 191-194, Jan. 2010.
11. R. E. Kalman, "Contribution to the theory of optimal control," Bol. Soc. Mat. Mex. , vol. 5, pp. 102-119, 1960.
12. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. New York: Wiley, 1972.
13. Z. Gajic and M. Qureshi, The Lyapunov Matrix Equation in System Stability and Control. New York: Dover, 2008.
14. S. Hammarling, "Numerical solution of the stable, non-negative definite Lyapunov equation," IMA J. Numer. Anal. , vol. 2, pp. 303-325, 1982.
15. W. Su, Z. Gajic, and X. Shen, "The exact slow-fast decomposition of the algebraic Riccati equation of singularly perturbed systems," IEEE Trans. Autom. Control, vol. 37, no. 9, pp. 1456-1459, Sep. 1992.
16. V. Kecman, S. Bingulac, and Z. Gajic, "Eigenvector approach for order-reduction of singularly perturbed linear-quadratic optimal control problems," Automatica, vol. 35, pp. 151-158, 1999.
17. S. Serbin and C. Serbin, "A time-stepping procedure for A" = A1 X + XA2 + D X(0) = C," IEEE Trans. Autom. Control, vol. AC-25, no. 6, pp. 1138-1141, Dec. 1980.
18. N. J. Higham, "The scaling and squaring method for the matrix exponential revisited," SIAM J. Matrix Anal. Appl. , vol. 26, pp. 1179-1193, 2005.
19. Y. Arkun and S. Ramakrishnan, "Bounds on the optimum quadratic cost of structure-constrained controllers," IEEE Trans. Autom. Control, vol. 41, no. 2, pp. 236-240, Feb. 1996.