## Design of stochastic fault tolerant control for $$H_{2}$$ performance.(English)Zbl 1132.93043

Summary: The controller synthesis problem for fault tolerant control systems (FTCS) with stochastic stability and $$H_{2}$$ performance is studied. System faults of random nature are modelled by a Markov chain. Because the real system fault modes are not directly accessible in the context of FTCS, the controller is reconfigured based on the output of a fault detection and identification (FDI) process, which is modelled by another Markov chain. Then state feedback and output feedback control are developed to achieve the mean square stability (MSS) and the $$H_{2}$$ performance for both continuous-time and discrete-time systems with model uncertainties.

### MSC:

 93E10 Estimation and detection in stochastic control theory 93E15 Stochastic stability in control theory 93B50 Synthesis problems 60J27 Continuous-time Markov processes on discrete state spaces
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### References:

 [1] , . Fault Diagnosis in Dynamic System, Theory and Applications. Prentice-Hall: New York, 1989. [2] Fault tolerant control: the 1997 situation. Proceedings of IFAC SAFEPROCESS’97. Hull, United Kingdom, August 1997; 1033–1055. [3] . Robust Model-based Fault Diagnosis for Dynamic Systems. Kluwer Academic Publishers: Boston, 1999. · Zbl 0920.93001 [4] Zhang, IEEE Transactions on Automatic Control 49 pp 1259– (2004) [5] Tao, Automatica 38 pp 1027– (2002) [6] Diao, IEEE Transactions on Control Systems Technology 9 pp 494– (2001) [7] Wu, International Journal of Adaptive Control and Signal Processing 14 pp 775– (2000) [8] Srichander, International Journal of Control 57 pp 433– (1993) · Zbl 0808.93067 [9] Mahmoud, IEEE Transactions on Automatic Control 46 pp 1810– (2001) [10] Mahmoud, Stochastic Analysis and Applications 21 pp 673– (2002) [11] , . Active Fault Tolerant Control Systems: Stochastic Analysis and Synthesis. Springer: Berlin, 2003. · Zbl 1036.93002 [12] Cheng, Dynamics of Continuous Discrete and Impulsive Systems, Series B Applications and Algorithms 11 pp 123– (2004) [13] . Synthesis of fault tolerant control with random FDI dealy. Proceedings of the 44th IEEE Conference on Decision and Control. Seville, Spain, December 2005; 3844–3849. [14] Shi, Journal of Optimization and Applications 95 pp 75– (1997) [15] Shi, Optimal Control Applications and Methods 24 pp 85– (2003) [16] , , . H stochastic stabilization of active fault tolerant control systems: convex approach. Proceedings of the 44th IEEE Conference on Decision and Control. Seville, Spain, December 2005; 3783–3788. [17] Ghaoui, International Journal of Robust and Nonlinear Control 6 pp 1015– (1997) [18] de Farias, IEEE Transactions on Automatic Control 45 pp 944– (2000) [19] Fang, IEEE Transactions on Automatic Control 47 pp 1590– (2002) [20] Costa, International Journal of Control 66 pp 557– (1997) [21] Costa, Automatica 35 pp 259– (1999) [22] Costa, International Journal of Control 73 pp 11– (2000) [23] , . Discrete-time Markov Jump Linear Systems. Springer: Berlin, 2005. · Zbl 1081.93001 [24] Fragoso, Stochastic Analysis and Applications 22 pp 99– (2004) [25] do Val, Automatica 38 pp 343– (2002) [26] Adaptive dual control methods: an overview. 5th IFAC Symposium on Adaptive Systems in Control and Signal Processing, Budapest, Hungary, June 14–16 1995; 67–73. [27] Barmish, Journal of Optimization Theory and Applications 46 pp 399– (1985) [28] Apkarian, IEEE Transactions on Automatic Control 46 pp 1941– (2001) [29] de Oliveira, Systems and Control Letters 37 pp 261– (1999) [30] Ghaoui, IEEE Transactions on Automatic Control 42 pp 1171– (1997) [31] Leibfritz, SIAM Journal of Control and Optimization 39 pp 1711– (2001) [32] Mudge, IEE- Control Theory and Applications 135 pp 275– (1988)
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