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In this article, we study the adaptive stability for parabolic partial differential equation (PDE)-ordinary differential equation (ODE) cascade systems with actuator dynamics, where the actuator dynamics are nonlinear subject to unknown parameters. Compared with a class of PDE–ODE coupled systems that the control input only acts on the PDE boundary and the linear sandwiched system without uncertainty, the structure of such systems is more complex. First of all, infinite-dimensional backstepping transformation is adopted. The original PDE-ODE cascade system is changed to a new system that is easier to design. On this basis, finite-dimensional backstepping transformation and adaptive compensation technology are combined to develop a state-feedback controller. Then, the boundedness of all the signals in the closed-loop system is proved by the Lyapunov functional analysis. Furthermore, the control law and the original system states eventually converge to zero. Finally, different simulation data are presented to illustrate the validity of the theoretical results.

Accumulating evidences show that circular RNAs (circRNAs) play an important role in regulating gene expression, and involve in many complex human diseases. Identifying associations of circRNA with disease helps to understand the pathogenesis, treatment and diagnosis of complex diseases. Since inferring circRNA-disease associations by biological experiments is costly and time-consuming, there is an urgently need to develop a computational model to identify the association between them. In this paper, we proposed a novel method named KNN-NMF, which combines $K\ $Knearest neighbors with nonnegative matrix factorization to infer associations between circRNA and disease (KNN-NMF). Frist, we compute the Gaussian Interaction Profile (GIP) kernel similarity of circRNA and disease, the semantic similarity of disease, respectively. Then, the circRNA-disease new interaction profiles are established using weight $K$K nearest neighbors to reduce the false negative association impact on prediction performance. Finally, Nonnegative Matrix Factorization is implemented to predict associations of circRNA with disease. The experiment results indicate that the prediction performance of KNN-NMF outperforms the competing methods under five-fold cross-validation. Moreover, case studies of two common diseases further show that KNN-NMF can identify potential circRNA-disease associations effectively.

Dear Editor, This letter deals with the output feedback stabilization of a class of high-order nonlinear time-delay systems with more general low-order and high-order nonlinearities. By constructing reduced-order observer, based on homogeneous domination theory together with the adding a power integrator method, an output feedback controller is developed to guarantee the equilibrium of the closed system globally uniformly asymptotically stable.