Motivated by the thermoelastic coupling effect arising in microelectromechanical systems (MEMS), event-triggered control of second-order ODE-heat systems coupled at intermediate point is investigated. The event-triggered control includes two parts, one is the feedback control signal, and the other is the event-triggered mechanism that decides when to update the control input. First, we design an event-triggered controller by using Zero-Order Hold to a continuous-time controller. Then, a dynamic triggering condition is established. Next, we derive that the existence of a minimal dwell-time, which avoids the occurrence of Zeno behavior. By utilizing Lyapunov-Krasovskii functional method, the global exponential stability of the closed-loop system is demonstrated. Finally, the simulation data based on the thermoelastic coupling system is displayed to demonstrate the availability of the theoretical results.

In this article, we are devoted to the global stabilization for ordinary differential equation (ODE)-parabolic partial differential equation (PDE)-ODE-coupled systems subject to spatially varying coefficient, where a nonlinear ODE is located at the driving end and a linear ODE is located at the other end. By means of infinite-dimensional and finite-dimensional backstepping transformations, both state-feedback and output-feedback controllers are established to assure the global exponential stability of the resulting closed-loop system. Besides, the boundedness and exponential convergence of the controllers are also investigated. Finally, the availability of the theoretical results is illustrated by simulation data.

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.

This paper focuses on establishing an adaptive boundary observer for fully coupled reaction-diffusions partial differential equations (PDEs) containing unknown parameters. Firstly, the state error system is transformed into an intermediate system by finite dimensional backstepping-like transformation, and then we convert the intermediate system to a target system by infinite dimensional backstepping transformation. Secondly, a least-squares type parameter adaptive law is given. Thirdly, exploiting an ad hoc persistent excitation condition, the exponentially convergent of the observer will be established by applying Lyapunov functional. Finally, we use simulation analysis for Chemical Tubular Reactor model to demonstrate the validity of the results.