Performance of Self-Triggered Control Approaches
The self-triggered control produces non-periodic sampling sequences that vary depending on design factors related to stability and performance of the controlled system. Within this framework, two approaches aimed at minimizing a quadratic cost have been developed recently, considering an optimal performance and pursuing the same control objective; each approach follows a different sampling rule. One approach is based on maintaining the current control value as long as possible, while an optimal performance threshold is not passed. The other approach is based on the generation of a piecewise control signal, which approximates a continuous optimal control signal subject to certain constraints. This article presents a comparative study between the two approaches, providing a useful insight for conducting future research. Control performance and resource utilization were considered as metrics of interest and to evaluate them, the average sampling interval and the standardized cost were taken into account. It was shown that the different search space of each approach poses a challenge to design an equitable framework of comparison, and that both approaches exceed the periodic sampling.
Astrom, K., & Bernhardsson, B. (1999). Comparison of periodic and event based sampling for first-order stochastic systems. 14th IFAC World Congress. Recuperado de https://lup.lub.lu.se/search/ws/files/6208782/8520116.pdf
Astrom, K., & Wittenmark, B. (1997). Computer-Controlled System. Theory and Design. Third edition. Prentice Hall.
Bini, E., and Buttazzo, G. (2014). The optimal sampling pattern for linear control systems. IEEE Transactions on Automatic Control, 59(1), pp. 78-90, doi: https://doi.org/10.1109/TAC.2013.2279913
Gommans, T. (2015). Resource-aware control and estimation: an optimization-based approach. Eindhoven University of Technology Library. Recuperado de https://pure.tue.nl/ws/files/12652231/20160118_Gommans.pdf
Gommans, T., Antunes, D., Donkers, T., Tabuada, P., and Heemels, M. (2014). Self-triggered linear quadratic control. Automatica, 50(4), pp. 1279-1287, http://dx.doi.org/10.1016/j.automatica.2014.02.030
Heemels, W., Johansson, K., & Tabuada, P. (2012). An introduction to event-triggered and self-triggered control. IEEE 51st Annual Conference on Decision and Control (CDC), pp. 3270-3285, doi: https://doi.org/10.1109/CDC.2012.6425820
Meng, X., and Chen, T. (2012). Optimal sampling and performance comparison of periodic and event based impulse control. IEEE Transactions on Automatic Control, 57(12), pp. 3252-3259. doi: https://doi.org/10.1109/TAC.2012.2200381
Molin, A., and Hirche, S. (2013). On the optimality of certainty equivalence for event-triggered control systems. IEEE Transactions on Automatic Control, 58(2), pp. 470-474. doi: https://doi.org/10.1109/TAC.2012.2206719
Murray, R.M. (2006). Control and Dynamical Systems: LQR Control. California Institute of Technology. Recuperado de http://www.cds.caltech.edu/~murray/courses/cds110/wi06/lqr.pdf
Rabi, M., Johansson, K., & Johansson, M. (2008). Optimal stopping for event-triggered sensing and actuation. 47th IEEE Conference on Decision and Control, pp. 3607-3612. doi: https://doi.org/10.1109/CDC.2008.4739489
Velasco, M., Fuertes, J., & Martí, P. (2003). The self triggered task model for real-time control systems. IEEE 24th Real-Time Systems Symposium, pp. 67-70. Recuperado de http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.164.3868&rep=rep1&type=pdf
Velasco, M., Martí, P., and Bini, E. (2009). Equilibrium sampling interval sequences for event-driven controllers. 2009 European Control Conference, pp. 3773-3778. Recuperado de http://ieeexplore.ieee.org/document/7074987/
Velasco, M., Martí, P., and Bini, E. (2015). Optimal-sampling-inspired self triggered control. 1st IEEE International Conference on Event-based Control, Communication, and Signal Processing, pp. 1-8, doi: https://doi.org/10.1109/EBCCSP.2015.7300648
Velasco, M., Martí, P., Yépez, J., Ruiz, F., Fuertes, J., and Bini, E. (2011). Qualitative analysis of a one-step finite-horizon boundary for event-driven controllers. 50th IEEE Conference on Decision and Control and European Control Conference, pp. 1662-1667. doi: https://doi.org/10.1109/CDC.2011.6161106
This work is licensed under a Creative Commons 3.0 BY EC License.