Reduced-order suboptimal control design for a class of nonlinear distributed parameter systems using POD and θ-D techniques

Optimal Control Applications and Methods

Volumn 29, Issue 3, 2008, Pages 191-224

  Padhi, Radhakant ^a   Xin, Ming ^b   Balakrishnan, S N ^c  

^a INDIAN INSTITUTE OF SCIENCE   (India)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

^c Architectural and Environmental Engineering   (United States)

Author keywords

Distributed parameter system; Finite difference; Heat transfer; Proper orthogonal decomposition; Suboptimal control design; Temperature control

Indexed keywords

CONTROL SYSTEMS; CONTROL THEORY; FEEDBACK; INTELLIGENT CONTROL; MATHEMATICAL MODELS; MILITARY DATA PROCESSING; OPTIMAL CONTROL SYSTEMS; STATE FEEDBACK; SYSTEMS ENGINEERING; VIBRATION CONTROL;

BASIS FUNCTIONS; BENCH-MARK PROBLEMS; CLOSED FORM SOLUTIONS; COMPUTATIONAL TOOLS; CONTROL PROBLEMS; DISTRIBUTED PARAMETER SYSTEM (DPS); GALERKIN PROJECTIONS; IN CONTROL; LUMPED PARAMETER APPROXIMATION; LUMPED PARAMETER SYSTEMS (LMS); MODEL REDUCTIONS; NONLINEAR TEMPERATURE; NUMERICA L RESULTS; OPTIMAL CONTROL DESIGN; ORIENTED BASIS FUNCTIONS; PROPER ORTHOGONAL DECOMPOSITION (POD); REDUCED ORDER; STATE FEEDBACK; SUBOPTIMAL CONTROL DESIGN; SYSTEMATIC METHODOLOGY; TIME-DOMAIN CONTROL;

DISTRIBUTED PARAMETER CONTROL SYSTEMS;

EID: 46749158282     PISSN: 01432087     EISSN: 10991514     Source Type: Journal    
DOI: 10.1002/oca.822     Document Type: Article

References (33)

1. Lasiecka I. Control of systems governed by partial differential equations: a historical perspective. Proceedings of the 34th Conference on Decision and Control, New Orleans, LA, U.S.A., 1995; 2792-2796.
2. Curtain RF, Zwart HJ. An Introduction to Infinite Dimensional Linear Systems Theory. Springer: New York, 1995.
3. Bameih B. The structure of optimal controllers of spatially-invariant distributed parameter systems. Proceedings of the Conference on Decision and Control, San Diego, CA, U.S.A., 1997; 1056-1061.
4. Burns JA, King BB. Optimal sensor location for robust control of distributed parameter systems. Proceedings of the Conference on Decision and Control, Lake Buena Vista, FL, U.S.A., 1994; 3967-3972.
5. Holmes P, Lumley JL, Berkooz G. Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press: Cambridge, 1996; 87-154.
6. Sadek S, Bokhari MA. Optimal control of a parabolic distributed parameter system via orthogonal polynomials. Optimal Control Applications and Methods 1998; 19:205-213.
7. Banks HT, Rosario RCH, Smith RC. Reduced-order model feedback control design: numerical implementation in a thin shell model. IEEE Transactions on Automatic Control 2000; 45:1312-1324.
8. Burns J, King BB. A Reduced basis approach to the design of low-order feedback controllers for nonlinear continuous systems. Journal of Vibration and Control 1998; 4:297-323.
9. Ravindran SS. A reduced-order approach for optimal control of fluids using proper orthogonal decomposition. International Journal for Numerical Methods in Fluids 2000; 34:425-448.
10. Singh SN, Myatt JH, Addington GA. Adaptive feedback linearizing control of proper orthogonal decomposition nonlinear flow models. Proceedings of the American Control Conference, Arlington, VA, U.S.A., 2001; 1533-1538.
11. Hinze M, Kunisch K. On suboptimal control strategies for the Navier-Stokes equations. ESAIM Proceedings, vol. 4, 1998; 181-198.
12. Bryson AE, Ho YC. Applied Optimal Control. Taylor and Francis: London, 1975.
13. Lewis F. Applied Optimal Control and Estimation. Prentice-Hall: Englewood Cliffs, NJ, 1992.
14. Garrard WL. Design of nonlinear automatic flight control systems. Automatica 1997; 13:497-505.
15. Garrard WL, Enns DF, Snell SA. Nonlinear feedback control of highly maneuverable aircraft. International Journal of Control 1992; 56:799-812.
16. Krikelis NJ, Kiriakidis KI. Optimal feedback control of nonlinear systems. International Journal of Systems Science 1992; 23:2141-2153.
17. Saridis GN, Lee CG. An approximation theory of optimal control for trainable manipulators. IEEE Transactions on Systems, Man, and Cybernetics 1979; 9:152-159.
18. Beard RW, Saridis GN, Wen JT. Galerkin approximations of the generalized Hamilton-Jacobi-Bellman equation. Automatica 1997; 33:2156-2177.
19. Mracek CP, Cloutier JR. Control designs for the nonlinear benchmark problem via the state-dependent Riccati equation method. International Journal of Robust and Nonlinear Control 1998; 8:401-433.
20. Qu Z, Cloutier JR. A new suboptimal control design for cascaded nonlinear systems. Optimal Control Applications and Methods 2002; 23:303-328.
21. Erdem EB, Alleyne AG. Design of a class of nonlinear controllers via state-dependent Riccati equations. IEEE Transactions on Control Systems Technology 2004; 12:133-137.
22. Bhoir N, Singh SN. Control of unsteady aeroelastic system via state-dependent Riccati equation method. AIAA Journal of Guidance, Control and Dynamics 2005; 28:78-84.
23. Xin M, Balakrishnan SN. A new method for suboptimal control of a class of nonlinear systems. Optimal Control Applications and Methods 2005; 26:55-83.
24. Gupta SK. Numerical Methods for Engineers. Wiley Eastern Ltd.: New Delhi, 1995.
25. Schiesser WE. Computational Mathematics in Engineering and Applied Science: ODEs, DAEs and PDEs. CRC Press: Boca Raton, FL, 1994.
26. Sirovich L. Turbulence and the dynamics of coherent structures: Part I-III. Quarterly of Applied Mathematics 1987; 45:561-590.
27. Haykin S. Neural Networks. Macmillan: New York, 1994.
28. Xin M, Balakrishnan SN, Stansbery DT, Ohlmeyer EJ. Nonlinear missile autopilot design with theta-D technique. AIAA Journal of Guidance, Control and Dynamics 2004; 27:406-417.
29. Khalil HK. Nonlinear Systems (2nd edn). Prentice-Hall: Englewood Cliffs, NJ, 1996.
30. Sage AP. Gradient and quasi-linearization computational techniques for distributed parameter systems. International Journal of Control 1967; 6:81-98.
31. Padhi R. Optimal control of distributed parameter systems using adaptive critic neural networks. Ph.D. Dissertation, University of Missouri, Rolla, U.S.A., 2001.
32. Padhi R, Balakrishnan SN. Proper orthogonal decomposition based feedback optimal control synthesis of distributed parameter systems using neural networks. Proceedings of American Control Conference, U.S.A., 2002.
33. Miller AF. Basic Heat and Mass Transfer. Richard D.Irwin Inc.: Concord, MA, 1995.