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Optimal control of switching surfaces in hybrid dynamical systems. (English) Zbl 1101.93054
Summary: This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system’s mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching parameters. The optimal control problem is to minimize a cost functional, defined on the state trajectory, as a function of the switching parameters. The paper derives the gradient of the cost functional in a costate-based formula that reflects the special structure of hybrid systems. It then uses the formula in a gradient-descent algorithm for solving an obstacle-avoidance problem in robotics.

MSC:
93C85Automated control systems (robots, etc.)
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References:
[1] Arkin, R. C. 1998. Behavior Based Robotics. Cambridge, Massachusetts: The MIT Press.
[2] Bemporad, A., Giua, A., Seatzu, C. 2002. A master-slave algorithm for the optimal control of continuous-time switched affine systems. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, December, pp. 1976--1981.
[3] Boccadoro, M., Valigi, P. 2003. A modelling approach for the dynamic scheduling problem of manufacturing systems with non-negligible setup times and finite buffers. 42nd IEEE Conference on Decision and Control, Maui, Hawaii, December.
[4] Boccadoro, M., Egerstedt, M., and Wardi, Y. 2004. Optimal Control of Switching Surfaces in Hybrid Dynamic Systems. IFAC Workshop on Discrete Event Systems, Reims, France, September.
[5] Branicky, M., Borkar, V., and Mitter, S. 1998. A unified framework for hybrid control: Model and optimal control theory. IEEE Trans. Automat. Contr. 43(1): 31--45. · Zbl 0951.93002 · doi:10.1109/9.654885
[6] Brockett, R. 1995. Stabilization of motor networks. 34th IEEE Conference on Decision and Control, December. pp. 1484--1488.
[7] Egerstedt, M. 2000. Behavior based robotics using hybrid automata. Lecture Notes in Computer Science: Hybrid Systems III: Computation and Control. Pittsburgh, Pennsylvania: Springer Verlag, pp. 103--116, March. · Zbl 0938.93585
[8] Egerstedt, M., Wardi, Y., and Delmotte, F. 2003. Optimal control of switching times in switched dynamical systems. 42nd IEEE Conference on Decision and Control, Maui, Hawaii, December.
[9] Flieller, D., Louis, J. P., and Barrenscheen, J. 1998. General sampled data modeling of power systems supplied by static converter with digital and analog controller. Math. Comput. Simul. 46: 373--385. · doi:10.1016/S0378-4754(97)00149-3
[10] Giua, A., Seatzu, C., and Van Der Mee, C. 2001. Optimal control of switched autonomous linear systems. 40th IEEE Conference on Decision and Control, Orlando, Florida, December, pp. 2472--2477.
[11] Hristu-Varsakelis, D. 2001. Feedback control systems as users of shared network: Communication sequences that guarantee stability. 40th IEEE Conference on Decision and Control, Orlando, Florida, December. p. 3631. · Zbl 1098.70543
[12] Johansson, M., and Rantzer, A. 2000. Piecewise linear quadratic optimal control. IEEE Trans. Automat. Contr. 43(4): 629--637. · Zbl 0969.49016
[13] Polak, E. 1997. Optimization: Algorithms and Consistent Approximations. Springer-Verlag, New York. · Zbl 0899.90148
[14] Riedinger, P., Kratz, F., Iung, C., and Zanne, C. 1999. Linear quadratic optimization for hybrid systems. 38th IEEE Conference on Decision and Control, Phoenix, Arizona, December, pp. 3059--3064.
[15] Shaikh, M. S., Caines, P. E. 2002. On trajectory optimization for hybrid systems: Theory and algorithms for fixed schedules. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, December.
[16] Shaikh, M. S., and Caines, P. 2003. On the optimal control of hybrid systems: Optimization of switching times and combinatoric location schedules. American Control Conference, Denver, Colorado, June. · Zbl 1038.49033
[17] Sussmann, H. J. 1999. A maximum principle for hybrid optimal control problems. 38th IEEE Conference on Decision and Control, Phoenix, Arizona, December, pp. 425--430.
[18] Verriest, E. 2003. Regularization method for optimally switched and impulsive systems with biomedical applications (I). 42nd IEEE Conference on Decision and Control, Maui, Hawaii, December.
[19] Wardi, Y., Boccadoro, M., Egerstedt, M., and Verriest, E. 2004. Optimal control of switching surfaces. 43rd IEEE Conference on Decsion and Control, Nassau, Bahamas, December 14--17, pp. 1854--1859. · Zbl 1101.93054
[20] Xu, X., and Antsaklis, P. 2002. Optimal control of switched autonomous systems. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, December.
[21] Xu, X., Antsaklis, P. J. 2002. Optimal control of switched systems via nonlinear optimization based on direct differentiations of value functions. Int. J. Control 75: 1406--1426. · Zbl 1039.93005 · doi:10.1080/0020717021000023825