Well-posedness and exponential stability of two-dimensional vibration model of a boundary-controlled curved beam with tip mass

Design of adaptive fault‐tolerant controllers for perturbed nonlinear ODE‐PDE cascaded systems

“…According to the reviewed papers, regardless of the control technology applied to the systems governed by PDE or ODE‐PDE, one can see the following deficiencies: The controllers may not be applied to nonlinear PDE or ODE‐PDE cascaded systems; these include 5‐7,9,15,17,20‐25,27,28,31‐33,36 . Noted also that dynamic equations of the plant in References 5,21‐24,27,28,31‐33 are only governed by linear PDE; and the dynamic equations in References 9,15 are linear ODE‐PDE. The controllers may not be applied to systems with unmatched perturbations; these include 5,7,8,10‐16,19‐21,23‐25,27‐30,33,36 The upper bounds of perturbations must be known beforehand; these include 7,14,15,17,20,21,24,27,28,35 …”

“…The upper bounds of perturbations must be known beforehand; these include 7,14,15,17,20,21,24,27,28,35 The possibility of actuator's failure were not considered in the design of control schemes, these include 5,6,8‐14,17‐24,26‐34,37,38 …”

“…According to the previous limitations 1–4, the motivation and the originality of this research is clear that, in this article, a FTC scheme is proposed for a class of nonlinear ODE‐PDE cascaded systems with matched and unmatched disturbances. Not only the dynamic equations one considered in this article are more extended than those in the literature, 5‐38 but also the control scheme one proposed is able to simultaneously eliminate the limitations (1)‐(4) mentioned above. In addition, the proposed control scheme provides the following advantages: Both adaptive mechanisms and perturbation estimator are utilized so that the upper bounds of perturbations and perturbation estimation errors are not required to be known beforehand. The unknown loss of effectiveness of actuator's degradation can be time‐varying variables. The controlled states of ODE and PDE of the cascaded system are able to converge to zero within a finite time. …”

“…22 Li and Jin 30 developed an output feedback regulation controller for a cascaded wave PDE-ODE system with velocity recirculation and matched disturbance. As for other aspects of control, Mei, 31 Zhou and Guo, 32 Tavasoli, 33 Strecker et al 34 applied disturbance estimators, boundary control, output tracking controllers to achieve asymptotically stable and exponentially stable, respectively.…”

“…The controllers may not be applied to nonlinear PDE or ODE-PDE cascaded systems; these include. [5][6][7]9,15,17,[20][21][22][23][24][25]27,28,[31][32][33]36 Noted also that dynamic equations of the plant in References 5,21-24,27,28,31-33 are only governed by linear PDE; and the dynamic equations in References 9,15 are linear ODE-PDE. 2.…”