Detection signal design for failure detection: a robust approach

Auxiliary signal design for robust multimodel identification

“…This situation has been considered in [9]. The idea is to eliminate just as we eliminated to obtain (2.10).…”

“…This leads to a descriptor system (3.2)-(3.3). In [9], a method was presented for reducing the descriptor system to a smaller, explicit system. A similar method can be used in the continuous-time case, even if the models are time varying.…”

Auxiliary signal design for robust multimodel identification

“…This situation has been considered in [9]. The idea is to eliminate just as we eliminated to obtain (2.10).…”

“…This leads to a descriptor system (3.2)-(3.3). In [9], a method was presented for reducing the descriptor system to a smaller, explicit system. A similar method can be used in the continuous-time case, even if the models are time varying.…”

Active fault diagnosis for hybrid systems based on sensitivity analysis and EKF

“…where the sensitivity is S = ∂ǫ ∂θ and λ is the eigenvalue of the Hessian matrix of H. As is obvious, the ratio in (13) is equal to the condition number (12), which shows the correspondence between the sensitivity analysis and parameter estimation algorithm based on the LMS approach.…”

Active fault diagnosis and tracking control for stochastic distribution control systems with bounded disturbance

“…However, obtaining an analytical solution for this inequality might be challenging. Therefore, for the AFD problem of multi-input systems, the MATLAB solver can be used to solve (13) to obtain the auxiliary input of the system. □ Remark 2.…”

“…At this moment, the mode of the system cannot be judged. By solving (13) and ( 18), the obtained auxiliary input is injected continuously until the fault type can be judged. The result is shown in Figure 3.…”

Auxiliary signal design for robust multimodel identification

“…This situation has been considered in [9]. The idea is to eliminate just as we eliminated to obtain (2.10).…”

“…This leads to a descriptor system (3.2)-(3.3). In [9], a method was presented for reducing the descriptor system to a smaller, explicit system. A similar method can be used in the continuous-time case, even if the models are time varying.…”

Active fault diagnosis for hybrid systems based on sensitivity analysis and EKF

“…where the sensitivity is S = ∂ǫ ∂θ and λ is the eigenvalue of the Hessian matrix of H. As is obvious, the ratio in (13) is equal to the condition number (12), which shows the correspondence between the sensitivity analysis and parameter estimation algorithm based on the LMS approach.…”

Active fault diagnosis and tracking control for stochastic distribution control systems with bounded disturbance

“…However, obtaining an analytical solution for this inequality might be challenging. Therefore, for the AFD problem of multi-input systems, the MATLAB solver can be used to solve (13) to obtain the auxiliary input of the system. □ Remark 2.…”

“…At this moment, the mode of the system cannot be judged. By solving (13) and ( 18), the obtained auxiliary input is injected continuously until the fault type can be judged. The result is shown in Figure 3.…”

Auxiliary signal design for robust multimodel identification

“…This situation has been considered in [9]. The idea is to eliminate just as we eliminated to obtain (2.10).…”

“…This leads to a descriptor system (3.2)-(3.3). In [9], a method was presented for reducing the descriptor system to a smaller, explicit system. A similar method can be used in the continuous-time case, even if the models are time varying.…”

Active fault diagnosis for hybrid systems based on sensitivity analysis and EKF

“…where the sensitivity is S = ∂ǫ ∂θ and λ is the eigenvalue of the Hessian matrix of H. As is obvious, the ratio in (13) is equal to the condition number (12), which shows the correspondence between the sensitivity analysis and parameter estimation algorithm based on the LMS approach.…”

Active fault diagnosis and tracking control for stochastic distribution control systems with bounded disturbance

“…However, obtaining an analytical solution for this inequality might be challenging. Therefore, for the AFD problem of multi-input systems, the MATLAB solver can be used to solve (13) to obtain the auxiliary input of the system. □ Remark 2.…”

“…At this moment, the mode of the system cannot be judged. By solving (13) and ( 18), the obtained auxiliary input is injected continuously until the fault type can be judged. The result is shown in Figure 3.…”