A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems

HSCC'10 - Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control

Volumn , Issue , 2010, Pages 51-60

  Gonzalez, Humberto ^a   Vasudevan, Ram ^a   Kamgarpour, Maryam ^a   Sastry, S Shankar ^a   Bajcsy, Ruzena ^a   Tomlin, Claire J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Constrained optimal control; Switched hybrid systems

Indexed keywords

CONSTRAINED OPTIMAL CONTROL; CONTINUOUS INPUT; CONTROL PARAMETERS; CONVEX OPTIMAL CONTROL; COST FUNCTIONALS; DISCRETE COMPONENTS; DISCRETE OPTIMIZATION PROBLEMS; FINAL COSTS; FIXED MODES; HIERARCHICAL OPTIMIZATION; NUMERICAL EXAMPLE; NUMERICAL SOLUTION; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; SINGLE MODE; SWITCHED DYNAMICAL SYSTEMS;

ALGORITHMS; CONTROL SYSTEM ANALYSIS; ELECTRIC GROUNDING; HYBRID COMPUTERS; HYBRID SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS; NUMERICAL ANALYSIS;

OPTIMIZATION;

EID: 77953077500     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1755952.1755961     Document Type: Conference Paper

References (27)

1. H. Axelsson, Y. Wardi, M. Egerstedt, and E. Verriest. Gradient Descent Approach to Optimal Mode Scheduling in Hybrid Dynamical Systems. Journal of Optimization Theory and Applications, 136(2):167-186, 2008.
2. A. Bemporad, F. Borrelli, and M. Morari. Piecewise Linear Optimal Controllers for Hybrid Systems. In American Control Conference, 2000. Proceedings of the 2000, volume 2, 2000.
3. D. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientific Belmont, MA, 1995.
4. F. Borrelli, M. Baotić, A. Bemporad, and M. Morari. Dynamic Programming for Constrained Optimal Control of Discrete-Time Linear Hybrid Systems. Automatica, pages 1709-1721, June 2005.
5. M. Branicky, V. Borkar, and S. Mitter. A Unified Framework for Hybrid Control: Model and Optimal Control theory. IEEE Transactions on Automatic Control, 43(1):31-45, 1998.
6. R. Brockett. Stabilization of Motor Networks. In Decision and Control, 1995., Proceedings of the 34th IEEE Conference on, volume 2, 1995.
7. M. Egerstedt and Y. Wardi. Multi-Process Control Using Queuing Theory. In IEEE Conference on Decision and Control, volume 2, pages 1991-1996. IEEE; 1998, 2002.
8. M. Egerstedt, Y. Wardi, and H. Axelsson. Transition-Time Optimization for Switched-Mode Dynamical Systems. IEEE Transactions on Automatic Control, 51(1):110-115, 2006. (Pubitemid 43137937)
9. M. Egerstedt, Y. Wardi, and F. Delmotte. Optimal Control of Switching Times in Switched Dynamical Systems. In Proceedings 42nd IEEE Conference on Decision and Control, pages 2138- 2143, Dec. 2003.
10. R. Ghosh and C. Tomlin. Hybrid System Models of Biological Cell Network Signaling and Differentiation. In Proceedings of the Annual Allerton Conference on Communication Control and Computing, volume 39, pages 942-951, 2001.
11. A. Giua, C. Seatzu, and C. Van Der Mee. Optimal Control of Switched Autonomous Linear systems. In IEEE Conference on Decision and Control, volume 3, pages 2472-2477. IEEE; 1998, 2001.
12. H. Gonzalez, R. Vasudevan, M. Kamgarpour, S. S. Sastry, R. Bajcsy, and C. Tomlin. A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems: Appendix. Technical Report UCB/EECS-2010-2019, EECS Department, University of California, Berkeley, Jan 2010.
13. S. Hedlund and A. Rantzer. Optimal Control of Hybrid Systems. In Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, Dec. 1999.
14. G. Hoffmann, H. Huang, S. Waslander, and C. Tomlin. Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment. In Proc. of the AIAA Guidance, Navigation, and Control Conference. Citeseer, 2007.
15. B. Lincoln and A. Rantzer. Optimizing Linear System Switching. In IEEE Conference on Decision and Control, volume 3, pages 2063-2068. IEEE; 1998, 2001.
16. D. Mayne and E. Polak. First-Order Strong Variation Algorithms for Optimal Control. Journal of Optimization Theory and Applications, 16(3):277-301, 1975.
17. E. Polak. Optimization: Algorithms and Consistent Approximations. Springer, 1997.
18. L. Pontryagin, V. Boltyanskii, R. Gamkrelidze, and E. Mishchenko. The Mathematical Theory of Optimal Processes. Interscience New York, 1962.
19. A. Rantzer and M. Johansson. Piecewise Linear Quadratic Optimal Control. IEEE Transactions on Automatic Control, 45(4):629-637, 2000.
20. H. Rehbinder and M. Sanfridson. Scheduling of a Limited Communication Channel for Optimal Control. Automatica, 40(3):491-500, 2004.
21. M. Rinehart, M. Dahleh, D. Reed, and I. Kolmanovsky. Suboptimal Control of Switched Systems with an Application to the Disc Engine. IEEE Transactions on Control Systems Technology, 16(2):189-201, 2008.
22. M. Shaikh and P. Caines. On the Optimal Control of Hybrid Systems: Optimization of Trajectories, Switching Times, and Location Schedules. Lecture Notes in Computer Science, 2623:466-481, 2003.
23. R. Vinter. Optimal control, Systems & Control: Foundations & Applications, 2000.
24. G. Walsh, H. Ye, L. Bushnell, et al. Stability Analysis of Networked Control Systems. IEEE Transactions on Control Systems Technology, 10(3):438-446, 2002. (Pubitemid 34630818)
25. X. Xu and P. Antsaklis. Optimal Control of Switched Systems via Nonlinear Optimization Based on Direct Differentiation of Value Functions. International Journal of Control, 75, 16(17):1406-1426, 2002.
26. X. Xu and P. Antsaklis. Results and Perspective on Computational Methods for Optimal Control of Switched Systems. Lecture Notes in Computer Science, 2623:540-556, 2003.
27. W. Zhang, A. Abate, and J. Hu. Stabilization of Discrete-Time Switched Linear Systems: A Control-Lyapunov Function Approach. In R. Majumdar and P. Tabuada, editors, Hybrid Systems: Computation and Control, volume 5469 of Lecture Notes in Computer Science, pages 411-425. Springer, 2009.