Nonlinear region of attraction analysis for flight control verification and validation

Control Engineering Practice

Volumn 19, Issue 4, 2011, Pages 335-345

  Chakraborty, Abhijit ^a   Seiler, Peter ^a   Balas, Gary J ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Flight control; Nonlinear analysis; Region of attraction; Validation and verification

Indexed keywords

CURRENT PRACTICES; FLIGHT CONTROL; GENERIC TRANSPORT MODELS; HIGH-FIDELITY SIMULATIONS; LINEAR ANALYSIS; LONGITUDINAL DYNAMICS; NONLINEAR EFFECT; NONLINEAR POLYNOMIALS; NONLINEAR REGIONS; POLYNOMIAL MODELS; POLYNOMIAL OPTIMIZATION; REGION OF ATTRACTION; SHORT PERIODS; VALIDATION AND VERIFICATION; VERIFICATION AND VALIDATION;

FLIGHT CONTROL SYSTEMS; FLIGHT SIMULATORS; MATHEMATICAL MODELS; NASA; POLYNOMIALS;

NONLINEAR ANALYSIS;

EID: 79953045571     PISSN: 09670661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.conengprac.2010.12.001     Document Type: Article

References (41)

1. Bailey, R., Hostetler, R., Barnes, K., Belcastro, C. M., & Belcastro, C. M. (2005). Experimental validation: Subscale aircraft ground facilities and integrated test capability. In AIAA GNC conference. No. AIAA 2005-6433.
2. Balas, G., Packard, A., Seiler, P., & Topcu, U. (2009). Robustness analysis of nonlinear systems, http://www.aem.umn.edu/~AerospaceControl/.
3. Chakraborty A., Seiler P., Balas G. Susceptibility of f/a-18 flight controllers to the falling leaf mode: Nonlinear analysis. Journal of Guidance, Control, and Dynamics 2010, 34(1):73-85.
4. Chiang H.-D., Thorp J. Stability regions of nonlinear dynamical systems: A constructive methodology. IEEE Transactions on Automatic Control 1989, 34(12):1229-1241.
5. Cox, D., 2009. The GTM DesignSim v0905.
6. Davison E., Kurak E. A computational method for determining quadratic Lyapunov functions for nonlinear systems. Automatica 1971, 7:627-636.
7. Gatermann K., Parrilo P. Symmetry groups, semidefinite programs, and sums of squares. Journal of Pure and Applied Algebra 2004, 192:95-128.
8. Genesio R., Tartaglia M., Vicino A. On the estimation of asymptotic stability regions: State of the art and new proposals. IEEE Transactions on Automatic Control 1985, 30(8):747-755.
9. Gregory, I.M., Cao, C., Xargay, E., Hovakimyan, N., & Zou, X. (2009). L1 adaptive control design for NASA AirSTAR flight test vehicle. In AIAA conference on decision and control conference No. AIAA 2009-5738.
10. Hachicho, O., & Tibken, B. (2002). Estimating domains of attraction of a class of nonlinear dynamical systems with LMI methods based on the theory of moments. In Proceedings of the IEEE conference on decision and control (pp. 3150-3155).
11. Hauser, J., & Lai, M. (1992). Estimating quadratic stability domains by nonsmooth optimization. In Proceedings of the American control conference (pp. 571-576).
12. Heller, M., David, R., & Holmberg, J. (2004). Falling leaf motion suppression in the F/A-18 Hornet with revised flight control software. In AIAA aerospace sciences meeting. No. AIAA-2004-542.
13. Heller, M., Niewoehner, R., & Lawson, P. K. (1999). High angle of attack control law development and testing for the F/A-18E/F Super Hornet. In AIAA conference on decision and control conference No. AIAA-1999-4051 (pp. 541-551).
14. Heller, M., Niewoehner, R., & Lawson, P. K. (2003). On the validation of safety critical aircraft systems, Part I: An overview of analytical & simulation methods. In AIAA guidance, navigation, and control conference. No. AIAA 2003-5559.
15. Jaramillo, P. T., & Ralston, J. N. (1996). Simulation of the F/A-18D falling leaf. In AIAA atmospheric flight mechanics conference (pp. 756-766).
16. Jarvis-Wloszek, Z. (2003). Lyapunov based analysis and controller synthesis for polynomial systems using sum-of-squares optimization. Ph.D. thesis, University of California, Berkeley.
17. Jarvis-Wloszek, Z., Feeley, R., Tan, W., Sun, K., & Packard, A. (2003). Some controls applications of sum of squares programming. In Proceedings of the IEEE conference on decision and control (Vol. 5, pp. 4676-4681).
18. Jarvis-Wloszek, Z., Feeley, R., Tan, W., Sun, K., & Packard, A. (2005). Controls applications of sum of squares programming. In Positive polynomials in control. Lecture notes in control and information sciences (pp. 3-22). Springer-Verlag.
19. Jordan, T. L., & Bailey, R. M. (2008). NASA Langley's AirSTAR testbed: A subscale flight test capability for flight dynamics and control system experiments. In AIAA guidance, navigation and control conference No. AIAA 2008-6660.
20. Jordan, T. L., Foster, J. V., Bailey, R. M., & Belcastro, C. M. (2006). AirSTAR: A UAV platform for flight dynamics and control system testing. In AIAA aerodynamic measurement technology and ground testing conference No. AIAA 2006-3307.
21. Lasserre J. Global optimization with polynomials and the problem of moments. SIAM Journal on Optimization 2001, 11(3):796-817.
22. Lluch, C. D. (1998). Analysis of the out-of-control falling leaf motion using a rotational axis coordinate system. Master's thesis, Virginia Polytechnic Institute and State University.
23. Lofberg, J. (2004). Yalmip: A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD conference Taipei, Taiwan. URL http://control.ee.ethz.ch/joloef/yalmip.php.
24. Murch, A. (2008). A flight control system architecture for the NASA AirSTAR flight test infrastructure. In AIAA conference on decision and control conference.
25. Murch, A., Cox, D. E., & Cunningham, K. (2009). Software considerations for subscale flight testing of experimental control laws. In AIAA infotech.
26. Murch, A., & Foster, J. (2007). Recent NASA research on aerodynamic modeling of post-stall and spin dynamics of large transport airplanes. In 45th AIAA aerospace sciences meeting.
27. Parrilo, P. (2000). Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.D. thesis, California Institute of Technology.
28. Parrilo P. Semidefinite programming relaxations for semialgebraic problems. Mathematical Programming Series B 2003, 96(2):293-320.
29. Prajna, S., Papachristodoulou, A., Seiler, P., & Parrilo, P. A. (2004). SOSTOOLS: Sum of squares optimization toolbox for MATLAB.
30. Stevens B., Lewis F. Aircraft control and simulation 1992, John Wiley & Sons.
31. Sturm, J. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 625-653.
32. Sturm, J. (2001). SeDuMi version 1.05. http://fewcal.kub.nl/sturm/software/sedumi.html.
33. Tan, W. (2006). Nonlinear control analysis and synthesis using sum-of-squares programming. Ph.D. thesis, University of California, Berkeley.
34. Tan W., Packard A. Searching for control Lyapunov functions using sums of squares programming. Allerton conference on communication, control and computing 2004, 210-219.
35. Tan W., Topcu U., Seiler P., Balas G., Packard A. Simulation-aided reachability and local gain analysis for nonlinear dynamical systems. Proceedings of the IEEE conference on decision and control 2008, 4097-4102.
36. Tibken B. Estimation of the domain of attraction for polynomial systems via LMIs. Proceedings of the IEEE conference on decision and control 2000, 3860-3864.
37. Tibken B., Fan Y. Computing the domain of attraction for polynomial systems via BMI optimization methods. Proceedings of the American control conference 2006, 117-122.
38. Topcu U., Packard A., Seiler P. Local stability analysis using simulations and sum-of-squares programming. Automatica 2008, 44(10):2669-2675.
39. Topcu U., Packard A., Seiler P., Wheeler T. Stability region analysis using simulations and sum-of-squares programming. Proceedings of the American control conference 2007, 6009-6014.
40. Vannelli A., Vidyasagar M. Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems. Automatica 1985, 21(1):69-80.
41. Vidyasagar M. Nonlinear systems analysis 1993, Prentice-Hall. 2nd ed.