Integrated fault estimation and fault‐tolerant control for uncertain time‐varying delay nonlinear Markovian jump systems

Abstract

Summary This paper investigates the issues of fault estimation and fault‐tolerant control for a class of uncertain time‐varying delay nonlinear Markovian jump systems with simultaneous actuator and sensor faults. Firstly, by analyzing and reformulating the original system, a Markovian robust sliding‐mode observer is introduced to provide simultaneous estimations of the state and faults. Secondly, a novel stochastic integral sliding surface function is designed, and the sufficient criteria is derived in terms of linear matrix inequalities, which guarantees that the sliding‐mode dynamics and error system are asymptotically stable with definite appointed H∞ performance disturbance attenuation level. Then, a robust sliding‐mode control law scheme is sought to ensure the reachability of the sliding surface in a finite time interval. Finally, the effectiveness of the proposed methodology is verified by numerical and practical examples.

An adaptive control scheme for switched nonlinear cyber‐physical systems against state‐dependent sensor attacks and input‐dependent actuator attacks

“…If the parameter 𝜇 𝜎 (t) in the sensor attack model in our article satisfies 0 < 𝜇 𝜎 (t) < 1, and the parameter 𝜌 a,𝜎 (t) in the actuator attack model in our article satisfies 0 < 𝜌 a,𝜎 (t) < 1, this security control problem is similar to the sensor and actuator fault-tolerant problem. Specifically, many adaptive control schemes are proposed to reduce the impact of sensor and actuator faults in other works (see the work in References [37][38][39][40]. As for the sensor and actuator attack models considered in our article, the parameters 𝜇 𝜎 (t) and 𝜌 a,𝜎 (t) just satisfy 𝜇 𝜎 (t) ≠ −1 and 𝜌 a,𝜎 −1, which makes more drastic attacks be tolerated, and the considered models include the case of sensor and actuator faults.…”

“…Remark If the parameter $$$ {\mu}_{\sigma }(t) $$$ in the sensor attack model in our article satisfies $$$ 0<{\mu}_{\sigma }(t)<1 $$$, and the parameter $$$ {\rho}_{a,\sigma }(t) $$$ in the actuator attack model in our article satisfies $$$ 0<{\rho}_{a,\sigma }(t)<1 $$$, this security control problem is similar to the sensor and actuator fault‐tolerant problem. Specifically, many adaptive control schemes are proposed to reduce the impact of sensor and actuator faults in other works (see the work in References 37‐40). As for the sensor and actuator attack models considered in our article, the parameters $$$ {\mu}_{\sigma }(t) $$$ and $$$ {\rho}_{a,\sigma }(t) $$$ just satisfy $$$ {\mu}_{\sigma }(t)\ne -1 $$$ and $$$ {\rho}_{a,\sigma }(t)\ne -1 $$$, which makes more drastic attacks be tolerated, and the considered models include the case of sensor and actuator faults.…”

Simultaneous fault estimation for uncertain Markovian jump systems subjected to actuator degradation

“…Summarizing the aforementioned discussions, the problem on estimations of the state and faults for MJSs have attracted intensive attention, and some desired results have been achieved . Notably, Li et al and Yin et al devised approaches to estimate both the actuator and sensor faults at the meantime, relying upon the designs of sliding mode observers with TRs being completely known.…”

“…Summarizing the aforementioned discussions, the problem on estimations of the state and faults for MJSs have attracted intensive attention, and some desired results have been achieved. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Notably, Li et al 15 and Yin et al 17 devised approaches to estimate both the actuator and sensor faults at the meantime, relying upon the designs of sliding mode observers with TRs being completely known. Li and Zhu 18 developed an adaptive observer for MJSs with GUTRs to simultaneously provide the estimations of actuator and sensor faults, on the basis of which a fault-tolerant controller was constructed.…”