Robust constrained model predictive control using linear matrix inequalities

Automatica

Volumn 32, Issue 10, 1996, Pages 1361-1379

  Kothare, Mayuresh V ^a,d   Balakrishnan, Venkataramanan ^b,d   Morari, Manfred ^c,d  

^a California Institute of Technology   (United States)

^b PURDUE UNIVERSITY   (United States)

^c ETH ZURICH   (Switzerland)

^d CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Convex optimization; Linear matrix inequalities; Model predictive control; Multivariable control systems; On line operation; Robust control; Robust stability; State feedback; Time varying systems

Indexed keywords

CONSTRAINT THEORY; FEEDBACK CONTROL; FREQUENCY DOMAIN ANALYSIS; LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; MULTIVARIABLE CONTROL SYSTEMS; OPTIMIZATION; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; TIME DOMAIN ANALYSIS; TIME VARYING CONTROL SYSTEMS;

DISTURBANCE REJECTION; HORIZON STATE FEEDBACK CONTROL DESIGN; LINEAR MATRIX INEQUALITIES; ROBUST CONSTRAINED MODEL PREDICTIVE CONTROL; SETPOINT TRACKING; TRAJECTORY TRACKING;

PREDICTIVE CONTROL SYSTEMS;

EID: 0030260606     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/0005-1098(96)00063-5     Document Type: Article

References (34)

1. Alizadeh, F., J.-P. A. Haeberly and M. L. Overton (1994). A new primal-dual interior-point method for semidefinite programming. In Proc. 5th SIAM Conf. on Applied Linear Algebra, Snowbird, UT, June 1994.
2. Allwright, J. C. and G. C. Papavasiliou (1992). On linear programming and robust model-predictive control using impulse-responses. Syst. Control Lett., 18, 159-164.
3. Bernussou, J., P. L. D. Peres and J. C. Geromel (1989). A linear programming oriented procedure for quadratic stabilization of uncertain systems. Syst. Control Lett., 13, 65-72.
4. Bitmead, R. R., M. Gevers and V. Wertz (1990). Adaptive Optimal Control. Prentice-Hall, Englewood Cliffs, NJ.
5. Boyd, S. and L. El Ghaoui (1993). Methods of centers for minimizing generalized eigenvalues. Lin. Algebra Applies, 188, 63-111.
6. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan (1994). Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia.
7. Campo, P. J. and M. Morari (1986). ∞-norm formulation of model predictive control problems. In Proc. American Control Conf., Seattle, WA, pp. 339-343.
8. Campo, P. J. and M. Morari (1987). Robust model predictive control. In Proc. American Control Conf., Minneapolis, MN, pp. 1021-1026.
9. Clarke, D. W. and C. Mohtadi (1989). Properties of generalized predictive control. Automatica, 25, 859-875.
10. Clarke, D. W., C. Mohtadi and P. S. Tuffs (1987). Generalized predictive control - II. Extensions and interpretations. Automatica, 23, 149-160.
11. Feron, E., V. Balakrishnan and S. Boyd (1992). Design of stabilizing state feedback for delay systems via convex optimization. In Proc. 31st IEEE Conf. on Decision and Control, Tucson, AZ, Vol. 1, pp. 147-148.
12. Gahinet, P., A. Nemirovski, A. J. Lamb and M. Chilali (1995). LMI Control Toolbox: For Use with MATLAB. The Mathworks, Inc., Natick, MA.
13. Garcia, C. E. and M. Morari (1982). Internal model control 1. A unifying review and some new results. Ind. Engng Chem. Process Des. Dev., 21, 308-232.
14. Garcia, C. E. and M. Morari (1985a). Internal model control 2. Design procedure for multivariable systems. Ind. Engng Chem. Process Des. Dev., 24, 472-484.
15. García, C. E. and M. Morari (1985b). Internal model control 3. Multivariable control law computation and tuning guidelines. Ind. Engng Chem. Process Des. Dev., 24, 484-494.
16. García, C. E., D. M. Prett and M. Morari (1989). Model predictive control: theory and practice - a survey. Automatica, 25, 335-348.
17. 1-norm model predictive control. AIChE J. 39, 1954-1965.
18. Geromel, J. C., P. L. D. Peres and J. Bernussou (1991). On a convex parameter space method for linear control design of uncertain systems. SIAM J. Control Optim., 29, 381-402.
19. Kwakernaak, H. and R. Sivan (1972). Linear Optimal Control Systems. Wiley-Interscience, New York.
20. Liu, R. W. (1968). Convergent systems. IEEE Trans. Autom. Control, AC-13, 384-391.
21. Muske, K. R. and J. B. Rawlings (1993). Model predictive control with linear models. AIChe J. 39, 262-287.
22. Nesterov, Yu. and A. Nemirovsky (1994). Interior-point Polynomial Methods in Convex Programming. SIAM, Philadelphia.
23. Packard, A. and J. Doyle (1993). The complex structured singular value. Automatica, 29, 71-109.
24. Polak, E. and T. H. Yang (1993a). Moving horizon control of linear systems with input saturation and plant uncertainty - 1: robustness. Int. J. Control, 53, 613-638.
25. Polak, E. and T. H. Yang (1993b). Moving horizon control of linear systems with input saturation and plant uncertainty - 2: disturbance rejection and tracking. Int. J. Control, 58, 639-663.
26. Rawlings. J. B. and K. R. Muske (1993). The stability of constrained receding horizon control. IEEE Trans. Autom. Control, AC-38, 1512-1516.
27. Tsirukis, A. G. and M. Morari (1992). Controller design with actuators constraints. In Proc. 31st IEE Conf. on Decision and Control, Tucson, AZ, pp. 2623-2628.
28. Vandenberghe, L. and S. Boyd (1995). A primal-dual potential reduction method for problems involving linear matrix inequalities. Math. Program., 69, 205-236.
29. Wie, B. and D. S. Bernstein (1992). Benchmark problems for robust control design. J. Guidance, Control, Dyn., 15, 1057-1059.
30. Yakubovich, V. A. (1992). Nonconvex optimization problem: the infinite-horizon linear-quadratic control problem with quadratic constraints. Syst. Control Lett., 19, 13-22.
31. Zafiriou, E. (1990). Robust model predictive control of processes with hard constraints. Comput. Chem. Engng, 14, 359-371, 1990.
32. Zafiriou, E. and A. Marchal (1991). Stability of SISO quadratic dynamic matrix control with hard output constraints. AIChE J., 37, 1550-1560.
33. Zheng, A., V. Balakrishnan and M. Morari (1995). Constrained stabilization of discrete-time systems. Int. J. Robust Nonlin. Control, 5, 461-485.
34. Zheng, Z. Q. and M. Morari (1993). Robust stability of constrained model predictive control. In Proc. American Control Conf., San Francisco, CA, pp. 379-383.