Linear-quadratic tracking of coupled slow fast targets

Mathematics of Control, Signals, and Systems

Volumn 10, Issue 1, 1997, Pages 1-30

  Artstein, Zvi ^a   Gaitsgory, Vladimir ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Averaging; Infinite horizon; Limit design; Linear quadratic tracking; Near optimal control; Singular perturbations

Indexed keywords

CONTROL SYSTEMS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; TRACKING (POSITION);

COUPLED TARGETS; INFINITE HORIZON;

CONTROL THEORY;

EID: 0030692263     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01219773     Document Type: Article

References (25)

1. Z. Artstein, Chattering variational limits of control systems. Forum Math. 5 (1993), 369-403.
2. Z. Artstein and V. Gaitsgory, Tracking fast trajectories along a slow dynamics: A singular perturbation approach. SIAM J. Control Optim., to appear.
3. Z. Artstein and A. Leizarowitz, Tracking periodic signals with the overtaking criterion. IEEE Trans. Automat. Control 30 (1985), 1123-1126.
4. Z. Artstein and A. Vigodner, Singularly perturbed ordinary differential equations with dynamic limits. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 541-569.
5. M. Athans and P. L. Falb, Optimal Control. McGraw-Hill, New York, 1966.
6. R. W. Brockett, Finite Dimensional Linear Systems. Wiley, New York, 1970.
7. D. A. Carlson, A. B. Haurie, and A. Leizarowitz, Infinite Horizon Optimal Control. Springer-Verlag, Berlin, 1987.
8. J. H. Chow and P. V. Kokotovic, A decomposition of near-optimum regulators for systems with slow and fast modes. IEEE Trans. Automat. Control 21 (1976), 701-705; reprinted in [KK].
9. A. L. Donchev, Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems. Lecture Notes in Control and Information Science, vol. 52, Springer-Verlag, Berlin, 1983.
10. W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York, 1993.
11. V. Gaitsgory, Suboptimization of singularly perturbed control systems. SIAM J. Control Optim. 30 (1992), 1228-1249.
12. V. Gaitsgory, Suboptimal control of singularly perturbed systems and periodic optimization. IEEE Trans. Automat. Control 38 (1993), 888-903.
13. A. H. Haddad and P. V. Kokotovic, Note on singular perturbation of linear state regulator. IEEE Trans. Automat. Control 16 (1971), 279-281; reprinted in [KK].
14. R. E. Kalman, Contributions to the theory of optimal control. Bol. Soc. Mat. Mexicana 5 (1960), 102-119.
15. P. V. Kokotovic and H. K. Khalil, Singular Perturbations in Systems and Control. IEEE Selected Reprint Series, IEEE Press, New York, 1986.
16. P. V. Kokotovic, H. K. Khalil, and J. O'Reilly, Singular Perturbations in Control Analysis and Design. Academic Press, New York, 1986.
17. P. V. Kokotovic and R. A. Yackel, Singular perturbations of linear regulators: basic theorems. IEEE Trans. Automat. Control 17 (1972), 29-37; reprinted in [KK].
18. P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd edition. Academic Press, Orlando, FL, 1985.
19. R. E. O'Malley, Jr., The singularly perturbed linear state regulator problem. SIAM J. Control 10 (1972), 399-413; reprinted in [KK].
20. R. E. O'Malley, Jr., Singular perturbation of the time invariant linear state regulator problem. J. Differential Equations 12 (1972), 117-128.
21. R. E. O'Malley, Jr., On two methods of solution for a singularly perturbed linear state regulator problem. SIAM Rev. 17 (1975), 16-37.
22. R. E. O'Malley, Jr., and C. F. Kung, On the matrix Riccati approach to a singularly perturbed regulator problem. J. Differential Equations 16 (1974), 413-427.
23. R. E. O'Malley, Jr., and C. F. Kung, The singularly perturbed linear state regulator problem, II. SIAM J. Control 13 (1975), 327-337.
24. P. Sannuti and P. V. Kokotovic, Near-optimum design of linear systems by a singular perturbation method. IEEE Trans. Automat. Control 14 (1969), 15-22.
25. V. M. Volosov, Averaging in systems of ordinary differential equations. Russian Math. Surveys 17(6) (1962), 1-126.