Truncated Predictor Feedback for Periodic Linear Systems With Input Delays With Applications to the Elliptical Spacecraft Rendezvous

IEEE Transactions on Control Systems Technology

Volumn 23, Issue 6, 2015, Pages 2238-2250

  Zhou, Bin ^a   Li, Zhao Yan ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Elliptical spacecraft rendezvous; periodic linear systems; time delay systems; truncated predictor feedback (TPF)

Indexed keywords

DELAY CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; LINEAR SYSTEMS; SPACECRAFT; TIME DELAY;

CHARACTERISTIC MULTIPLIER; CONTROL MATRICES; ITS APPLICATIONS; LINEAR TIME-DELAY SYSTEM; MULTIPLE INPUT DELAYS; OPEN LOOP SYSTEMS; PERIODIC LINEAR SYSTEMS; TIME-VARYING INPUT DELAY;

SPACE RENDEZVOUS;

EID: 84925875908     PISSN: 10636536     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCST.2015.2411228     Document Type: Article

References (38)

1. B. D. O. Anderson and J. B. Moore, "New results in linear system stability," SIAM J. Control, vol. 7, no. 3, pp. 398-414, 1969.
2. Z. Artstein, "Linear systems with delayed controls: A reduction," IEEE Trans. Autom. Control, vol. 27, no. 4, pp. 869-879, Aug. 1982.
3. M. Bando and A. Ichikawa, "Graphical generation of periodic orbits of Tschauner-Hempel equations," J. Guid., Control, Dyn., vol. 35, no. 3, pp. 1002-1007, 2012.
4. N. E. Barabanov, "Periodic linear systems with delays: Stability and H∞ control problem," in Proc. 17th IMACS World Congr., 2005, paper T5-I-01-0041.
5. S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control. London, U.K.: Springer-Verlag, 2008.
6. T. E. Carter, "State transition matrices for terminal rendezvous studies: Brief survey and new example," J. Guid., Control, Dyn., vol. 21, no. 1, pp. 148-155, 1998.
7. H. C. Cho and M. S. Fadali, "Nonlinear network-induced time delay systems with stochastic learning," IEEE Trans. Control Syst. Technol., vol. 19, no. 4, pp. 843-851, Jul. 2011.
8. N. K. Gary, B. P. Mann, N. H. Kim, and M. H. Kurdi, "Stability of a time-delayed system with parametric excitation," J. Dyn. Syst., Meas., Control, vol. 129, no. 2, pp. 125-135, 2007.
9. J. K. Hale, Theory of Functional Differential Equations (Applied Mathematical Sciences), vol. 3. New York, NY, USA: Springer-Verlag, 1977.
10. L. Huang, The Theory Foundation of Stability and Robustness, (in Chinese). Beijing, China: Science Press, 2003.
11. A. Ichikawa, "Null controllability with vanishing energy for infinite dimensional periodic systems," in Proc. 7th Int. Symp. Math. Theory Netw. Syst., 2006, pp. 638-642.
12. T. A. Johansen, D. Sui, and R. Nybo, "Regularized nonlinear movinghorizon observer with robustness to delayed and lost data," IEEE Trans. Control Syst. Technol., vol. 21, no. 6, pp. 2114-2128, Nov. 2013.
13. B. P. Lampe and E. N. Rosenwasser, "Stability investigation for linear periodic time-delayed systems using Fredholm theory," Autom. Remote Control, vol. 72, no. 1, pp. 38-60, 2011.
14. X. Li, D. Sun, and J. Yang, "Preserving multirobot connectivity in rendezvous tasks in the presence of obstacles with bounded control input," IEEE Trans. Control Syst. Technol., vol. 21, no. 6, pp. 2306-2314, Nov. 2013.
15. Z. Lin and H. Fang, "On asymptotic stabilizability of linear systems with delayed input," IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 998-1013, Jun. 2007.
16. Y.-J. Liu, L. Tang, S. Tong, C. L. P. Chen, and D.-J. Li, "Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems," IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 1, pp. 165-176, Jan. 2015.
17. Y.-J. Liu, S.-C. Tong, D. Wang, T.-S. Li, and C. L. P. Chen, "Adaptive neural output feedback controller design with reduced-order observer for a class of uncertain nonlinear SISO systems," IEEE Trans. Neural Netw., vol. 22, no. 8, pp. 1328-1334, Aug. 2011.
18. M. Lovera, E. De Marchi, and S. Bittanti, "Periodic attitude control techniques for small satellites with magnetic actuators," IEEE Trans. Control Syst. Technol., vol. 10, no. 1, pp. 90-95, Jan. 2002.
19. P. Massioni, T. Keviczky, E. Gill, and M. Verhaegen, "A decompositionbased approach to linear time-periodic distributed control of satellite formations," IEEE Trans. Control Syst. Technol., vol. 19, no. 3, pp. 481-492, May 2011.
20. P. Millan, L. Orihuela, I. Jurado, and F. R. Rubio, "Formation control of autonomous underwater vehicles subject to communication delays," IEEE Trans. Control Syst. Technol., vol. 22, no. 2, pp. 770-777, Mar. 2014.
21. M. E. Polites, "Technology of automated rendezvous and capture in space," J. Spcecraft Rockets, vol. 36, no. 2, pp. 280-291, 1999.
22. J. Sheng, O. Elbeyli, and J. Q. Sun, "Stability and optimal feedback controls for time-delayed linear periodic systems," AIAA J., vol. 42, no. 5, pp. 908-911, 2004.
23. M. Shibata and A. Ichikawa, "Orbital rendezvous and flyaround based on null controllability with vanishing energy," J. Guid., Control, Dyn., vol. 30, no. 4, pp. 934-945, 2007.
24. N. K. Son and N. Van Su, "Linear periodic control systems: Controllability with restrained controls," Appl. Math. Optim., vol. 14, no. 1, pp. 173-185, 1986.
25. 2-gain of systems with input delays and controller temporary failure: Zero-order hold model," IEEE Trans. Control Syst. Technol., vol. 19, no. 3, pp. 699-706, May 2011.
26. A. Varga, "On solving periodic differential matrix equations with applications to periodic system norms computation," in Proc. 44th IEEE Conf. Decision Control, Eur. Control Conf., Dec. 2005, pp. 6545-6550.
27. J. R. Wertz and R. Bell, "Autonomous rendezvous and docking technologies: Status and prospects," Proc. SPIE, pp. 20-30, Aug. 2003, paper 5088-3.
28. Z.-G. Wu, P. Shi, H. Su, and J. Chu, "Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data," IEEE Trans. Cybern., vol. 43, no. 6, pp. 1796-1806, Dec. 2013.
29. Z.-G. Wu, J. Lam, H. Su, and J. Chu, "Stability and dissipativity analysis of static neural networks with time delay," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 2, pp. 199-210, Feb. 2012.
30. K. Yamanaka and F. Ankersen, "New state transition matrix for relative motion on an arbitrary elliptical orbit," J. Guid., Control, Dyn., vol. 25, no. 1, pp. 60-66, 2002.
31. S. Yi, P. W. Nelson, and A. G. Ulsoy, "Proportional-integral control of first-order time-delay systems via eigenvalue assignment," IEEE Trans. Control Syst. Technol., vol. 21, no. 5, pp. 1586-1594, Sep. 2013.
32. B. Zhou and G.-R. Duan, "Periodic Lyapunov equation based approaches to the stabilization of continuous-time periodic linear systems," IEEE Trans. Autom. Control, vol. 57, no. 8, pp. 2139-2146, Aug. 2012.
33. 2 semi-global stabilisation of continuous-time periodic linear systems with bounded controls," Int. J. Control, vol. 86, no. 4, pp. 709-720, 2013.
34. B. Zhou, Z. Lin, and G.-R. Duan, "Truncated predictor feedback for linear systems with long time-varying input delays," Automatica, vol. 48, no. 10, pp. 2387-2399, 2012.
35. B. Zhou and Z. Lin, "Truncated predictor feedback stabilization of polynomially unstable linear systems with multiple time-varying input delays," IEEE Trans. Autom. Control, vol. 59, no. 8, pp. 2157-2163, Aug. 2014.
36. B. Zhou, Z. Lin, and G.-R. Duan, "Lyapunov differential equation approach to elliptical orbital rendezvous with constrained controls," J. Guid., Control, Dyn., vol. 34, no. 2, pp. 345-358, 2011.
37. B. Zhou, Q. Wang, Z. Lin, and G.-R. Duan, "Gain scheduled control of linear systems subject to actuator saturation with application to spacecraft rendezvous," IEEE Trans. Control Syst. Technol., vol. 22, no. 5, pp. 2031-2038, Sep. 2014.
38. B. Zhou, "Pseudo-predictor feedback stabilization of linear systems with time-varying input delays," Automatica, vol. 50, no. 11, pp. 2861-2871, 2014.