This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one ...This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem,an invertible transformation is first introduced to change the system into an observer canonical form,from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.展开更多
The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient,via state-feedback or output-feedback.The system is more general than that of the related literatu...The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient,via state-feedback or output-feedback.The system is more general than that of the related literature due to the presence of the spatially varying coefficient which makes the problem more difficult to solve.By infinite-dimensional backstepping method,both state-feedback and output-feedback stabilizing controllers are explicitly constructed,which guarantee that the closed-loop system is exponentially stable in the sense of certain norm.It is worthwhile pointing out that,in the case of output-feedback,by appropriately choosing the state observer gains,the severe restriction on the ODE sub-system in the existing results is completely removed.A simulation example is presented to illustrate the effectiveness of the proposed method.展开更多
This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigat...This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigation essentially different from those of the existing literature,and hence induces more technique obstacles in control design. Motivated by the related literature, an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one, from which the control design becomes much convenient. It is worthwhile pointing out that, since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded, the desirable kernel functions are more difficult to derive than those of the closely related literature. Then, by Lyapunov method and a dynamics compensated technique, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero. Finally, a simulation example is provided to validate the proposed method.展开更多
基金supported by the National Natural Science Foundations of China under Grant Nos.61821004,61873146 and 61773332the Special Fund of Postdoctoral Innovation Projects in Shandong Province under Grant No.201703012。
文摘This paper investigates the adaptive stabilization for a class of uncertain PDE-ODE cascaded systems. Remarkably, the PDE subsystem allows unknown control coefficient and spatially varying parameter, and only its one boundary value is measurable. This renders the system in question more general and practical, and the control problem more challenging. To solve the problem,an invertible transformation is first introduced to change the system into an observer canonical form,from which a couple of filters are constructed to estimate the unmeasurable states. Then, by adaptive technique and infinite-dimensional backstepping method, an adaptive controller is constructed which guarantees that all states of the resulting closed-loop system are bounded while the original system states converging to zero. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundations of China under Grant Nos.60974003,61143011,61273084,and 61233014the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China under Grant No.JQ200919the Independent Innovation Foundation of Shandong University under Grant No.2012JC014
文摘The paper is concerned with the stabilization of a class of coupled PDE-ODE systems with spatially varying coefficient,via state-feedback or output-feedback.The system is more general than that of the related literature due to the presence of the spatially varying coefficient which makes the problem more difficult to solve.By infinite-dimensional backstepping method,both state-feedback and output-feedback stabilizing controllers are explicitly constructed,which guarantee that the closed-loop system is exponentially stable in the sense of certain norm.It is worthwhile pointing out that,in the case of output-feedback,by appropriately choosing the state observer gains,the severe restriction on the ODE sub-system in the existing results is completely removed.A simulation example is presented to illustrate the effectiveness of the proposed method.
基金supported by the National Natural Science Foundations of China under Grant Nos.61403327,61325016,61273084 and 61233014
文摘This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigation essentially different from those of the existing literature,and hence induces more technique obstacles in control design. Motivated by the related literature, an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one, from which the control design becomes much convenient. It is worthwhile pointing out that, since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded, the desirable kernel functions are more difficult to derive than those of the closely related literature. Then, by Lyapunov method and a dynamics compensated technique, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero. Finally, a simulation example is provided to validate the proposed method.
