Robust and resilient state-dependent control of continuous-time nonlinear systems with general performance criteria

Systems Science and Control Engineering

Volumn 2, Issue 1, 2014, Pages 34-40

  Wang, Xin ^a   Yaz, Edwin E ^b   Long, James ^c  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b Marquette University   (United States)

^c OREGON INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Nonlinear systems; Optimal control; Robust control

Indexed keywords

ASYMPTOTIC STABILITY; LINEAR MATRIX INEQUALITIES; NONLINEAR CONTROL SYSTEMS; NONLINEAR SYSTEMS; QUADRATIC PROGRAMMING; ROBUST CONTROL; STABILITY CRITERIA; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

CONTINUOUS TIME NONLINEAR SYSTEMS; DISTURBANCE REDUCTION; OPTIMAL CONTROLS; PERFORMANCE CRITERION; POSITIVE REAL CONTROL; QUADRATIC DISSIPATIVE; QUADRATIC REGULATORS; UNSTRUCTURED UNCERTAINTY;

CONTINUOUS TIME SYSTEMS;

EID: 84982966219     PISSN: None     EISSN: 21642583     Source Type: Journal    
DOI: 10.1080/21642583.2013.877859     Document Type: Article

References (27)

1. Basar, T., & Bernhard, P. (1995). H-infinity optimal control and related minimax design problems – A dynamic game approach (2nd ed.). Boston: Birkhauser.
2. Boyd, S., Ghaoui, L. E., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM.
3. Cloutier, J. R. (1997). State-dependent Riccati equation techniques: An overview. Proceedings of the 1997 American Control Conference, pp. 932–936, Albuquerque, MN.
4. Cloutier, J. R., D’Souza, C. N., & Mracek, C. P. (1996). Nonlinear regulation and nonlinear H-infinity control via the state-dependent Riccati equation technique: Part 1 theory, part 2 examples. Proceedings of 1st international conference on nonlinear problems in aviation and aerospace, pp. 117–141, Daytona Beach, FL.
5. Doyle, J. C., Glover, K., Khargonekar, P. P., & Francis, B. A. (1989). State space solution to the standard H2 and H-infinity control problems. IEEE Transactions on Automatic Control, 34, 831–847.
6. Gupta, S., & Joshi, S. M. (1994). Some properties and stability results for sector bounded LTI systems. Proceedings of 33rd IEEE conference on decision and control, pp. 2973–2978, Orlando, USA.
7. Haddad, W. M., & Bernstein, D. S. (1991). Robust stabilization with positive real uncertainty, beyond the small gain theorem. Systems and Control Letters, 17, 191–208.
8. Hill, D. J., & Moylan, P. J. (1975). Cyclo-dissipativeness, dissipativeness and losslessness for nonlinear dynamical systems (Technical Report EE7526). Department of Electrical and Computer Engineering, University of Newcastle, Australia.
9. Hill, D. J., & Moylan, P. J. (1976). Stability of nonlinear dissipative systems. IEEE Transactions on Automatic Control, 21, 708–711.
10. Hill, D. J., & Moylan, P. J. (1980). Dissipative dynamical systems: Basic input-output and state properties. Journal of the Franklin Institute, 309, 327–357.
11. Huang, Y., & Lu, W-M. (1996). Nonlinear optimal control: alternatives to Hamilton-Jacobi equation. Proceedings of 35th conference on decision and control, pp. 3942–3947, Kobe, Japan.
12. Khargonekar, P. P., Petersen, I. R., & Zhou, K. (1990). Robust stabilization of uncertain linear systems: quadratic stabilizability and H-infinity control theory. IEEE Transactions on Automatic Control, 35, 356–361.
13. Mohseni, J., Yaz, E., & Olejniczak, K. (1998). State dependent LMI control of discrete-time nonlinear systems. Proceedings of the 37th IEEE conference on decision and control, pp. 4626–4627, Tampa, FL.
14. Petersen, I. R. (1987). A stabilization algorithm for a class of uncertain systems. Systems and Control Letters, 8, 181–188.
15. Safonov, M. G., Jonckheere, E. A., Verma, M., & Limebeer, D. J. N. (1987). Synthesis of positive real multivariable feedback systems. International Journal of Control, 45, 817–842.
16. Shim, D. (1996). Equivalence between positive real and norm-bounded uncertainty. IEEE Transactions on Automatic Control, 41, 1190–1193.
17. Sun, W., Khargonekar, P. P., & Shim, D. (1994). Solution to the positive real control problem for linear time-invariant systems. IEEE Transactions on Automatic Control, 39, 2034–2046.
18. Tan, Z., Soh, Y. C., & Xie, L. (2000). Dissipative control of linear discrete-time systems with dissipative uncertainty. International Journal of Control, 73(4), 317–328.
19. Van der Shaft, A. J. (1993). Nonlinear state space H-infinity control theory. In H. J. Trentelman & J. C. Willems (Eds.), Perspectives in control, pp. 153–190. Groningen: Birkhauser.
20. Wang, X., & Yaz, E. E. (2009). The state dependent control of continuous time nonlinear systems with mixed performance criteria. Proceedings of IASTED international conference on identification and control applications, pp. 98–102, Honolulu, HI.
21. Wang, X., Yaz, E. E., & Jeong, C. S. (2010). Robust nonlinear feedback control of discrete-time systems with mixed performance criteria. Proceedings of American control conference, pp. 6357–6362, Baltimore, MD.
22. Wang, X., Yaz, E. E., & Yaz, Y. I. (2010). Robust and resilient state dependent control of continuous time nonlinear systems with general performance criteria. Proceedings of the 49th IEEE conference on decision and control, pp. 603–608, Atlanta, GA.
23. Wang, X., Yaz, E. E., & Yaz, Y. I. (2011). Robust and resilient state dependent control of discrete time nonlinear systems with general performance criteria. Proceedings of the 18th IFAC congress, pp. 10904–10909, Milano, Italy.
24. Willems, J. C. (1972a). Dissipative dynamical systems – Part 1: General theory. Archives for Rational Mechanics and Analysis, 45, 321–351.
25. Willems, J. C. (1972b). Dissipative dynamical systems – Part 2: Linear systems with quadratic supply rates’. Archives for Rational Mechanics and Analysis, 45, 352–393.
26. Xie, S., Xie, L., & De Souza, C. E. (1998). Robust dissipative control for linear systems with dissipative uncertainty. International Journal of Control, 70(2), 169–191.
27. Zhou, K., & Khargonekar, P. P. (1988). An algebraic Riccati equation approach to H-infinity optimization. Systems and Control Letters, 11, 85–91.