Abstract
In this paper we consider the problem of designing controllers for linear plants to be implemented in embedded platforms under stringent real-time constraints. These include preemptive scheduling schemes, under which the maximum execution time allowed for control software tasks is uncertain. We propose an “anytime control” design approach, consisting in a hierarchy of controllers for the same plant. Higher controllers in the hierarchy provide better closed-loop performance, while typically requiring a larger worst-case execution time. We provide a procedure for the design of controllers which, together with a conditioning process of the stochastic scheduling, provides better performance than prevailing worst case-based design, while guaranteeing almost sure stability of the resulting switching system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Liu, C.L., Layland, J.W.: Scheduling algorithms for multiprogramming in a hard-real-time environment. Journal of the Association for Computing Machinery 20(1) (1973)
Liu, J.W.S.: Real–Time Systems. Prentice Hall Inc., Upper Saddle River, NJ (2000)
Buttazzo, G.: Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications. Kluwer Academic Publishers, Boston (1997)
Liu, J.W.S., Lin, K.J., Shih, W.K., Bettati, R., Chung, J.Y.: Imprecise computation. Proceedings of the IEEE 82(1), 83–93 (1994)
Liu, J.W.S., Lin, K.J., Shih, W.K., Yu, A.C.S., Chung, J.Y., Zhao, W.: Algorithms for scheduling imprecise computations. Computer 24(5), 58–68 (1991)
Perrin, N., Ferri, B.: Digital filters with adaptive length for real–time applications. In: Le Royal Meridien, K.E., (ed.) Proc. IEEE Real-Time and Embedded Technology and Applications Symposium, Toronto, Canada (May 2004)
Bhattacharya, R., Balas, G.J.: Implementation of control algorithms in an environment of dynamically scheduled CPU time using balanced truncation. In: AIAA Guidance, Navigation, and Control Conference and Exhibit, Monterey, CA (August 2002)
Bhattacharya, R., Balas, G.J.: Anytime control algorithm: Model reduction approach. Journal of Guidance, Control, and Dynamics 27(5), 767–776 (2004)
Branicky, M.S.: Stability of hybrid systems: State of the art. In: Proc. 36th IEEE Conf. On Decision and Control, San Diego, California, USA, pp. 120–125 (December 1997)
DeCarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. IEEE Proceedings 88(7), 1069–1082 (2000)
Liberzon, D., Morse, A.S.: Basic problems in stability and design of switched systems. IEEE Contr. Syst. Mag. 19(5), 59–70 (1999)
Ye, H., Michel, A.N., Hou, L.: Stability theory for hybrid dynamical systems. IEEE Trans. Automat. Contr. 43(4), 461–474 (1998)
Hespanha, J.P., Morse, A.S.: Switching between stabilizing controllers. Automatica 38(11), 1905–1917 (2002)
Wicks, M.A., Peleties, P., DeCarlo, R.: Construction of piecewise Lyapunov functions for stabilizing switched systems. In: Proc. 33rd IEEE Conf. On Decision and Control, Lake Buena Vista, FL, pp. 3492–3497 (December 1994)
Wicks, M., DeCarlo, R.: Solution of coupled Lyapunov equations for the stabilization of multimodal linear systems. In: Proc. American Control Conf., Albuquerque, NM, pp. 1709–1713 (June 1997)
Pettersson, S., Lennartson, B.: Stabilization of hybrid systems using a min-projection strategy. In: Proc. American Control Conf., Arlington, Virginia, pp. 223–228 (June 2001)
Greco, L., Fontanelli, D., Bicchi, A.: Almost sure stability of anytime controllers via stochastic scheduling. In: Proc. IEEE Int. Conf. on Decision and Control, New Orleans, LO (December 2007)
Fang, Y., Loparo, K.A., Feng, X.: Almost sure and δ-moment stability of jump linear systems. Int. J. Control 59(5), 1281–1307 (1994)
Bolzern, P., Colaneri, P., De Nicolao, G.: On almost sure stability of discrete-time Markov jump linear systems. In: Proc. 43rd IEEE Conf. On Decision and Control, vol. 3, pp. 3204–3208 (2004)
Cervin, A., Lincoln, B., Eker, J., Årzén, K.E., Buttazzo, G.: The jitter margin and its application in the design of real-time control systems. In: Proc. 10th Int. Conf. on Real-Time and Embedded Computing Systems and Applications, Gothenburg, Sweden (August 2004)
Liberzon, D., Hespanha, J.P., Morse, A.S.: Stability of switched systems: A Lie-algebraic condition. Systems & Control Letters 37(3), 117–122 (1999)
Åström, K.J., Wittenmark, B.: Computer Controlled Systems. Prentice-Hall, Englewood Cliffs (1996)
Furuta, K., Yamakita, M., Kobayashi, S.: Swing-up control of inverted pendulum using pseudo-state feedback. Proceedings of the Institution of Mechanical Engineers. Pt.I. Journal of Systems and Control Engineering 206(I4), 263–269 (1992)
Bupp, R., Bernstein, D., Coppola, V.: A benchmark problem for nonlinear control design: Problem statement, experimental testbed and passive, nonlinear compensation. In: Proc. Amer. Contr. Conf, pp. 4363–4367 (1995)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fontanelli, D., Greco, L., Bicchi, A. (2008). Anytime Control Algorithms for Embedded Real-Time Systems. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-78929-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78928-4
Online ISBN: 978-3-540-78929-1
eBook Packages: Computer ScienceComputer Science (R0)