Finite-frequency fault estimation and accommodation for continuous-time Markov jump linear systems with imprecise statistics of modes transitions. (English) Zbl 1532.93267
Summary: In this paper, the issues of both fault estimation and accommodation are studied for a class of continuous-time Markov jump linear systems under actuator fault, sensor fault and external disturbance in the framework of finite frequency domain. The imprecise statistic of modes transitions are considered here, which means that the transition rates are uncertain. Firstly, the sensor fault is defined as a new state, and then an adaptive observer is developed to estimate the actuator fault and the newly defined state with the aid of the descriptor system approach. By using the obtained fault estimation, a novel fault accommodation scheme is proposed based on the sample point controller design approach to satisfy the stochastic stability requirement of the closed-loop system with a prescribed \(H_\infty\) performance bound. Moreover, for the convenience of design, the presented sample point controller design is successfully transformed into resolving a class of input-delay control issues. Finally, two numerical examples, including a practical F-404 aircraft engine system, are illustrated to show the effectiveness and applicability of the developed design methods.
MSC:
| 93C80 | Frequency-response methods in control theory |
| 93C40 | Adaptive control/observation systems |
| 93B36 | \(H^\infty\)-control |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
Markov jump linear systems; adaptive observer; fault-tolerant control; sample point controller; finite frequency domain; F-404 aircraft engine systemReferences:
| [1] | Abbaspour, A.; Yen, K. K.; Forouzannezhad, P.; Sargolzaei, A., A neural adaptive approach for active fault-tolerant control design in UAV, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50, 9, 3401-3411 (2020) |
| [2] | Boem, F.; Gallo, A. J.; Raimondo, D. M.; Parisini, T., Distributed fault-Tolerant control of large-scale systems: an active fault diagnosis approach, IEEE Transactions on Control of Network Systems, 7, 1, 288-301 (2020) · Zbl 1516.93034 |
| [3] | Briat, C., Convergence and equivalence results for the Jensen’s inequality-application to time-delay and sampled-data systems, IEEE Transactions on Automatic Control, 56, 7, 1660-1665 (2012) · Zbl 1368.26020 |
| [4] | Cao, T.; Gong, H.; Han, B., Fault tolerant attitude control design for hypersonic vehicles with actuator faults, ICIC Express Letters, Part B: Applications, 8, 6, 927-936 (2017) |
| [5] | Chen, B.; Niu, Y.; Zou, Y., Security control for Markov jump system with adversarial attacks and unknown transition rates via adaptive sliding mode technique, Journal of the Franklin Institute, 356, 6, 3333-3352 (2019) · Zbl 1411.93164 |
| [6] | Fu, L.; Ma, Y.; Wang, C., Memory sliding mode control for semi-Markov jump system with quantization via singular system strategy, International Journal of Robust and Nonlinear Control, 29, 18, 6555-6571 (2019) · Zbl 1447.93036 |
| [7] | Gao, H.; Li, X.; Yu, X., Finite frequency approaches to \(H_\infty\) filtering for continuous-time state-delayed systems, (50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA (2011)), 2583-2588 |
| [8] | Guezmil, A.; Berriri, H.; Pusca, R., Experimental investigation of passive fault tolerant control for induction machine using sliding mode approach, Asian Journal of Control, 21, 1, 520-532 (2018) · Zbl 1422.93032 |
| [9] | Gyurkovics, V., A note on Wirtinger-type integral inequalities for time-delay systems, Automatica, 61, 44-46 (2015) · Zbl 1327.93169 |
| [10] | He, W.; Chen, G.; Han, Q. L., Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control, Information Sciences, 380, 145-158 (2017) · Zbl 1429.68027 |
| [11] | Iwasaki, T.; Hara, S., Generalized KYP Lemma: Unified frequency domain inequalities with design applications, IEEE Transactions on Automatic Control, 50, 1, 41-59 (2005) · Zbl 1365.93175 |
| [12] | B. Jiang and C. Gao, Decentralized adaptive sliding mode control of large-scale semi-Markovian jump interconnected systems with dead-zone input, IEEE Transactions on Automatic Control, doi:10.1109/TAC.2021.3065658. · Zbl 1537.93025 |
| [13] | Kaviarasan, B.; Kwon, O.; Park, M. J., Mode-dependent intermediate variable-based fault estimation for Markovian jump systems with multiple faults, International Journal of Robust and Nonlinear Control, 31, 8, 2960-2975 (2021) · Zbl 1526.93255 |
| [14] | Le, V. H.; Trinh, H., Stability analysis of Two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities, Information Sciences, 367-368, 403-417 (2016) · Zbl 1429.93404 |
| [15] | Lee, W. I.; Lee, S. Y.; Park, P. G., Affine Bessel-Legendre inequality: Application to stability analysis for systems with time-varying delays, Automatica, 93, 535-539 (2018) · Zbl 1400.93247 |
| [16] | Li, X.; Gao, H., Robust frequency-domain constrained feedback design via a two-stage heuristic approach, IEEE Transactions on Cybernetics, 45, 10, 2065-2075 (2015) |
| [17] | Li, J.; Ma, Y.; Fu, L., Fault-tolerant passive synchronization for complex dynamical networks with Markovian jump based on sampled-data control, Neurocomputing, 350, 20-32 (2019) |
| [18] | Li, X.; Karimi, H. R.; Wang, Y., Robust fault estimation and fault-tolerant control for Markovian jump systems with general uncertain transition rates, Journal of the Franklin Institute, 355, 8, 3508-3540 (2018) · Zbl 1390.93762 |
| [19] | Liu, L.; Liu, Y.; Li, D.; Tong, S.; Wang, Z., Barrier Lyapunov function-based adaptive fuzzy FTC for switched systems and its applications to resistance-inductance-capacitance circuit system, IEEE Transactions on Cybernetics, 50, 8, 3491-3502 (2020) |
| [20] | Liu, Z.; Yu, J.; Zhao, L., Adaptive \(H_\infty\) sliding mode control for a class of uncertain Markovian jump systems with time-delay, ICIC Express Letters, 14, 4, 319-327 (2020) |
| [21] | Qiu, J.; Wei, Y.; Karimi, H. R., New approach to delay-dependent \(H_\infty\) control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions, Journal of the Franklin Institute, 352, 1, 189-215 (2015) · Zbl 1307.93444 |
| [22] | Rantzer, A., On the Kalman-Yakubovich-Popov lemma, Systems & Control Letters, 28, 1, 7-10 (1996) · Zbl 0866.93052 |
| [23] | Shen, Q.; Yue, C.; Goh, C. H.; Wang, D., Active fault-tolerant control system design for spacecraft attitude maneuvers with actuator saturation and faults, IEEE Transactions on Industrial Electronics, 66, 5, 3763-3772 (2019) |
| [24] | Skorokhod, A., Asymptotic methods in the theory of stochastic differential equations, Translations of Mathematical Monographs, Providence, RI: Amer. Math. Soc., 78 (1989) · Zbl 0695.60055 |
| [25] | Sun, Q.; Lim, C. C.; Shi, P.; Liu, F., Design and stability of moving horizon estimator for Markov jump linear systems, IEEE Transactions on Automatic Control, 64, 3, 1109-1124 (2019) · Zbl 1482.93611 |
| [26] | Tan, B., Production control of a pull system with production and demand uncertainty, IEEE Transactions on Automatic Control, 47, 5, 779-783 (2002) · Zbl 1364.90147 |
| [27] | Tao, J.; Lu, R.; Shi, P.; Su, H.; Wu, Z., Dissipativity-based reliable control for fuzzy Markov jump systems with actuator faults, IEEE Transactions on Cybernetics, 47, 9, 2377-2388 (2017) |
| [28] | Tian, Y.; Wang, Z., A switched fuzzy filter approach to \(H_\infty\) filtering for Takagi-sugeno fuzzy Markov jump systems with time delay: The continuous-time case, Information Sciences, 557, 236-249 (2021) · Zbl 1489.93126 |
| [29] | Wang, X.; Fei, Z.; Yu, J.; Du, Z., Passivity-based event-triggered fault tolerant control for VTOL with actuator failure and parameter uncertainties, International Journal of Systems Science, 50, 4, 817-828 (2019) · Zbl 1482.93395 |
| [30] | Wan, H.; Luan, X.; Karimi, H. R., Dynamic self-triggered controller codesign for Markov jump systems, IEEE Transactions on Automatic Control, 66, 3, 1353-1360 (2021) · Zbl 1536.93856 |
| [31] | Xiong, J.; Lam, J., Robust \(H_2\) control of Markovian jump systems with uncertain switching probabilities, International Journal of Systems Science, 40, 3, 255-265 (2009) · Zbl 1167.93335 |
| [32] | R. Yang, L. Li, P. Shi, Dissipativity-based two-dimensional control and filtering for a class of switched systems, IEEE Transactions on Systems, Man, Cybernetics: Systems, 2019, doi:10.1109/TSMC.2019.2916417. |
| [33] | Yin, Y.; Shi, J.; Liu, F., Robust fault detection of singular Markov jump systems with partially unknown information, Information Sciences, 537, 368-379 (2020) · Zbl 1478.93726 |
| [34] | Zhang, L.; Boukas, E. K., Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, Automatica, 45, 463-468 (2009) · Zbl 1158.93414 |
| [35] | Zhang, L.; Boukas, E. K.; Lam, J., Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities, IEEE Transactions on Automatic Control, 53, 10, 2458-2464 (2008) · Zbl 1367.93710 |
| [36] | Zhang, Z.; Li, H.; Wu, C., Finite frequency fuzzy \(H_\infty\) control for uncertain active suspension systems with sensor failure, IEEE/CAA Journal of Automatica Sinica, 5, 4, 777-786 (2018) |
| [37] | Zhang, X.; Gao, Z.; Qian, M., Integrated fault estimation and fault-tolerant control for rigid spacecraft attitude system with multiple actuator faults, International Journal of Innovative Computing, Information and Control, 15, 4, 1255-1270 (2019) |
| [38] | Zhou, K.; Doyle, J. C.; Glover, K., Robust and Optimal Control (1996), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0999.49500 |
| [39] | Zhou, D.; Ji, H.; He, X.; Shang, J., Fault detection and isolation of the brake cylinder system for electric multiple units, IEEE Transactions on Control Systems Technology, 26, 5, 1744-1757 (2018) |
| [40] | Zhou, D.; Qin, L.; He, X.; Yan, R.; Deng, R., Distributed sensor fault diagnosis for a formation system with unknown constant time delays, Science China: Information Science, 61, 11, Article 112205 pp. (2018) |
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.
