Cost Functions for Scheduling Tasks in Cyber-physical Systems

Abhinna Jain, C. M. Krishna, Israel Koren, Zahava Koren

2012

Abstract

In Cyber Physical Systems (CPS), computational delays can cause the controlled plant to exhibit degraded control. The traditional approach to scheduling in such systems has been to define controller task deadlines, based on the dynamics of the controlled plant. Controller tasks are then scheduled to meet these deadlines; meeting the deadline is considered the sole criterion for scheduling success.\\ This traditional approach has the advantage of simplicity, but overlooks the fact that the quality of control depends on the actual task response times. Two different schedules, each satisfying the task deadlines, can provide very different levels of control quality, if their task response times are different.\\ In this paper, we consider using cost functions of task response time to capture the impact of computational delay on the quality of control. Since the controller workload typically consists of multiple tasks, these cost functions are multivariate in nature. Furthermore, since these tasks are generally coupled, the response time of one control task can affect the sensitivity of the controlled plant to the response times of other tasks.\\ In this paper, we first demonstrate how a multivariate cost function can be formulated to quantify the effect of computational delays in vehicles. We then develop cost-sensitive real-time control task scheduling algorithms. We use as an application example an automobile: the controller workload consists of steering and torque control. Our results indicate that cost-function-based scheduling provides superior control to the traditional deadline-only-based approach.

References

  1. Astrom, K. and Wittemark, B. (1997). Controlled Systems. Prentice-Hall.
  2. Camacho, E. and Bordons, C. (2003). Model Predictive Control. Springer.
  3. F.L. Lewis, D. V. and Syrmos, V. (2012). Optimal Control. Wiley.
  4. Hegde, U. and Krishna, C. (1994). Scheduling real-time tasks with cost functions. In Journal of Information Science and Technology, Vol. 4, No. 1, pp. 1-7.
  5. K.G. Shin, C. K. and Lee, Y.-H. (1985). A unified method for evaluating real-time computer controllers and its application. In IEEE Transactions on Automatic Control, Vol. AC-30, No. 4, pp. 357-366.
  6. Krishna, C. and Shin, K. (1983). Performance measures for multiprocessor controllers. In Performance.
  7. Krishna, C. and Shin, K. (1987). Performance measures for control computers. In IEEE Transactions on Automatic Control, Vol. AC-32, No. 6, pp. 467-473.
  8. Kuo, B. (1992). Digital Control Systems. Oxford University Press.
  9. Liu, C. and Layland, J. (1973). Scheduling algorithms for multiprogramming in a hard real-time environment. In Journal of the ACM, Vol. 20, No. 1, pp. 4661.
  10. Peng, S. (2007). On one approach to constraining the combined wheel slip in the autonomous control of a 4ws4wd vehicle. In IEEE Transactions on Control System Technology, Vol. 15, No. 1, pp. 168-175.
  11. S. Samii, P. Eles, Z. P. P. T. and Cervin, A. (2010). Dynamic scheduling and control-quality optimization of self-triggered control applications. In IEEE Real-Time Systems Symposium, pp. 95-104.
  12. Sage, A. and III, C. W. (1977). Optimum Systems Control. Prentice Hall.
  13. Tabuada, P. (2007). Event-triggered real-time scheduling of stabilizing control tasks. In IEEE Transactions on Automatic Control, Vol. 52, No. 9, pp. 1680-1685.
  14. Vasyutynskyy, V. and Kabitzh, K. (2010). Event-based control: Overview and generic model. In IEEE International Workshop on Factory Communication Systems, pp. 271-279.
  15. Wang, X. and Lemmon, M. (2009). Self-triggered feedback control systems with finite gain l2 stability. In IEEE Transactions on Automatic Control, Vol. 54, No. 3, pp. 452-467.
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Paper Citation


in Harvard Style

Jain A., M. Krishna C., Koren I. and Koren Z. (2012). Cost Functions for Scheduling Tasks in Cyber-physical Systems . In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8565-21-1, pages 412-421. DOI: 10.5220/0004046704120421


in Bibtex Style

@conference{icinco12,
author={Abhinna Jain and C. M. Krishna and Israel Koren and Zahava Koren},
title={Cost Functions for Scheduling Tasks in Cyber-physical Systems},
booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2012},
pages={412-421},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004046704120421},
isbn={978-989-8565-21-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Cost Functions for Scheduling Tasks in Cyber-physical Systems
SN - 978-989-8565-21-1
AU - Jain A.
AU - M. Krishna C.
AU - Koren I.
AU - Koren Z.
PY - 2012
SP - 412
EP - 421
DO - 10.5220/0004046704120421