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Fault estimation and optimization for uncertain disturbed singularly perturbed systems with time-delay

The first author is supported by Youth Foundation of Beijing Nature Science Grant (No.4154068), the Youth Talent Cultivation Program of Beijing, the National Natural Science Foundation of China (No.61473002, No.61573024), North China University of Technology Yuyou Talent Support Program and the Fundamental Research Funds for Beijing Universities (No.110052971921/030)
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  • This paper presents a observer-based fault estimation method for a class of singularly perturbed systems subjected to parameter uncertainties and time-delay in state and disturbance signal with finite energy. To solve the estimation problem involving actuator fault and sensor fault for the uncertain disturbed singularly perturbed systems with time-delay, the problem we studied is firstly transformed into a standard $ H_\infty $ control problem, in which the performance index $ \gamma $ represents the attenuation of finite energy disturbance. By adopting Lyapunov function with the $ \varepsilon $-dependence, a sufficient condition can be derived which enables the designed observer to estimate different kinds of fault signals stably and accurately, and the result obtained by dealing with small perturbation parameter in this way is less conservative. A novel multi-objective optimization scheme is then proposed to optimal disturbance attenuation index $ \gamma $ and system stable upper bound $ \varepsilon^* $, in this case, the designed observer can estimate the fault signals better in the presence of interference when the systems guarantee maximum stability bound. In the end, the validity and correctness of proposed scheme is verified by comparing the error between the estimated faults and the actual faults.


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  • Figure 1.  Curves of estimated actuator fault

    Figure 2.  Curves of estimated actuator fault

    Figure 3.  Curves of the actuator fault estimation error

    Figure 4.  Curves of the actuator fault estimation error

    Figure 5.  Curves of estimated sensor fault

    Figure 6.  Curves of estimated sensor fault

    Figure 7.  Curves of the sensor fault estimation error

    Figure 8.  Curves of the sensor fault estimation error

    Figure 9.  Estimation error curves of fault state vector

    Figure 10.  Estimation error curves of original system state vector

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