Stochastic event-based LQG control: an analysis on strict consistency. (English) Zbl 1485.93368
Summary: This paper studies the discrete-time linear-quadratic-Gaussian problem under partial-information-based sensors and event-based transmissions. By constructing a special form of stochastic event-based protocols, the optimal control policy is obtained, which minimizes an average quadratic cost function under a fixed transmission protocol. Then, analytical expressions of the corresponding transmission and control performance are derived. To evaluate the efficiency of event-based protocols, the concept of strict consistency is introduced, which requires that the control performance of event-based protocols be strictly better than that of the periodic protocol under the same transmission rate. Based on the obtained analytical expressions, the strict consistency is proved by showing that the periodic protocol corresponds to a local maximum point in the design space of parameters. To further improve the control performance of stochastic event-based protocols, an iterative parameter design algorithm (with finite iterations) is proposed for ensuring a strict reduction in cost functions after each iteration. Finally, numerical simulations are provided to illustrate the theoretical results.
MSC:
| 93C65 | Discrete event control/observation systems |
| 93C55 | Discrete-time control/observation systems |
| 93E20 | Optimal stochastic control |
| 49N10 | Linear-quadratic optimal control problems |
Keywords:
stochastic systems; linear-quadratic-Gaussian control; event-based transmissions; strict consistencyReferences:
| [1] | Anderson, B. D.O.; Moore, J. B., Optimal filtering (1979), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ, US · Zbl 0688.93058 |
| [2] | Andrén, M. T., Bernhardsson, B., Cervin, A., & Soltesz, K. (2017). On event-based sampling for LQG-optimal control. In Proc. conference on decision and control (pp. 5438-5444). |
| [3] | Antunes, D. J.; Balaghi, M. H., Consistent event-triggered control for discrete-time linear systems with partial state information, IEEE Control Systems Letters, 4, 1, 181-186 (2020) |
| [4] | Antunes, D. J., & Khashooei, B. A. (2016). Consistent event-triggered methods for linear quadratic control. In Proc. conference on decision and control (pp. 1358-1363). |
| [5] | Antunes, D. J.; Khashooei, B. A., Consistent dynamic event-triggered policies for linear quadratic control, IEEE Transactions on Control of Network Systems, 5, 3, 1386-1398 (2018) · Zbl 1515.93157 |
| [6] | Araújo, J., Teixeira, A., Henriksson, E., & Johansson, K. H. (2014). A down-sampled controller to reduce network usage with guaranteed closed-loop performance. In Proc. conference on decision and control (pp.6849-6856). |
| [7] | Årzén, K. E. (1999). A simple event-based PID controller. In Proc. ifac world congress (pp. 423-428). |
| [8] | Åström, K. J., & Bernhardsson, B. (1999). Comparison of periodic and event based sampling for first-order stochastic systems. In Proc. ifac world congress (pp. 301-306). |
| [9] | Balaghi, M. H.I.; Antunes, D. J.; Mamduhi, M. H.; Hirche, S., An optimal LQG controller for stochastic event-triggered scheduling over a lossy communication network, IFAC-PapersOnLine, 51, 23, 58-63 (2018) |
| [10] | Balaghiinaloo, M.; Antunes, D. J.; Heemels, W., An \(l_2\)-consistent event-triggered control policy for linear systems, Automatica, 125, Article 109412 pp. (2021) · Zbl 1461.93302 |
| [11] | Balaghiinaloo, M.; Antunes, D. J.; Mamduhi, M. H.; Hirche, S., Decentralized LQ-consistent event-triggered control over a shared contention-based network (2020), arXiv preprint, arXiv:1910.04582 |
| [12] | Bertsekas, D. P., Dynamic Programming and Optimal Control (1995), Athena Scientific: Athena Scientific Belmont, MA, US · Zbl 0904.90170 |
| [13] | Brunner, F. D., Set-theoretic approaches to the aperiodic control of linear systems (2017), University of Stuttgart: University of Stuttgart Germany, Logos Verlag Berlin, (Doctoral thesis) · Zbl 1415.93002 |
| [14] | Brunner, F. D.; Antunes, D.; Allögwer, F., Stochastic thresholds in event-triggered control: A consistent policy for quadratic control, Automatica, 89, 376-381 (2018) · Zbl 1388.93060 |
| [15] | Chen, W.; Shi, D.; Wang, J.; Shi, L., Event-triggered state estimation: Experimental performance assessment and comparative study, IEEE Transactions on Control Systems Technology, 25, 5, 1865-1872 (2017) |
| [16] | Demirel, B.; Leong, A. S.; Gupta, V.; Quevedo, Q. E., Tradeoffs in stochastic event-triggered control, IEEE Transactions on Automatic Control, 64, 6, 2567-2574 (2019) · Zbl 1482.93700 |
| [17] | Dolgov, M.; Fischer, J.; Hanebeck, U. D., Event-based LQG control over networks with random transmission delays and packet losses, IFAC Proceedings Volumes, 46, 27, 23-30 (2013) |
| [18] | Dolk, V. S.; Borgers, D. P.; Heemels, W., Output-based and decentralized dynamic event-triggered control with guaranteed \(\mathcal{L}_p\)-gain performance and zeno-freeness, IEEE Transactions on Automatic Control, 62, 1, 34-49 (2016) · Zbl 1359.93211 |
| [19] | Garcia, E.; Antsaklis, P. J., Model-based event-triggered control for systems with quantization and time-varying network delays, IEEE Transactions on Automatic Control, 58, 2, 422-434 (2013) · Zbl 1369.93408 |
| [20] | Girard, A., Dynamic triggering mechanisms for event-triggered control, IEEE Transactions on Automatic Control, 60, 7, 1992-1997 (2015) · Zbl 1360.93423 |
| [21] | Han, D.; Mo, Y.; Wu, J.; Weerakkody, S.; Sinopoli, B.; Shi, L., Stochastic event-triggered sensor schedule for remote state estimation, IEEE Transactions on Automatic Control, 60, 10, 2661-2675 (2015) · Zbl 1360.93672 |
| [22] | Horn, R. A.; Johnson, C. R., Matrix Analysis (1987), Cambridge Univeristy Press: Cambridge Univeristy Press Cambridge, U.K |
| [23] | Hovareshti, P., Gupta, V., & Baras, J. S. (2007). Sensor scheduling using smart sensors, In Proc. conference on decision and control (pp. 494-499). |
| [24] | Khashooei, B. A.; Antunes, D. J.; Heemels, W., A consistent threshold-based policy for event-triggered control, IEEE Control Systems Letters, 2, 3, 447-452 (2018) |
| [25] | Lunze, J.; Lehmann, A., A state-feedback approach to event-based control, Automatica, 46, 1, 211-215 (2010) · Zbl 1213.93063 |
| [26] | Meng, X.; Chen, T., Optimal sampling and performance comparison of periodic and event based impulse control, IEEE Transactions on Automatic Control, 57, 12, 3252-3259 (2012) · Zbl 1369.93576 |
| [27] | Meng, X.; Chen, T., Event triggered robust filter design for discrete-time systems, IET Control Theory & Applications, 8, 2, 104-113 (2014) · Zbl 1286.93059 |
| [28] | Payne, H.; Silverman, L., On the discrete time algebraic riccati equation, IEEE Transactions on Automatic Control, 18, 3, 226-234 (1973) · Zbl 0297.93036 |
| [29] | Resnick, S. I., Adventures in stochastic processes (1992), Birkhäuser · Zbl 0762.60002 |
| [30] | Speyer, J. L.; Chung, W. H., Stochastic processes, estimation, and control (2008), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics Philadelphia, PA, US · Zbl 1171.93006 |
| [31] | Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52, 9, 1680-1685 (2007) · Zbl 1366.90104 |
| [32] | Wang, X.; Lemmon, M. D., Event-triggering in distributed networked control systems, IEEE Transactions on Automatic Control, 56, 3, 586-601 (2011) · Zbl 1368.93211 |
| [33] | Wang, X.; Lemmon, M. D., On event design in event-triggered feedback systems, Automatica, 47, 10, 2319-2322 (2011) · Zbl 1228.93080 |
| [34] | Wu, J.; Jia, Q.; Johansson, K. H.; Shi, L., Event-based sensor data scheduling: Trade-off between communication rate and estimation quality, IEEE Transactions on Automatic Control, 58, 4, 1041-1046 (2013) · Zbl 1369.90086 |
| [35] | Wu, J.; Ren, X.; Han, D.; Shi, D.; Shi, L., Finite-horizon Gaussianity-preserving event-based sensor scheduling in Kalman filter applications, Automatica, 72, 100-107 (2016) · Zbl 1344.93102 |
| [36] | Yu, H.; Hao, F., Input-to-state stability of integral-based event-triggered control for linear plants, Automatica, 85, 248-255 (2017) · Zbl 1375.93113 |
| [37] | Yu, H.; Shang, J.; Chen, T., On stochastic and deterministic event-based state estimation, Automatica, 123, Article 109314 pp. (2021) · Zbl 1461.93499 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
