Adaptive stabilization for ODE systems via boundary measurement of uncertain diffusion‐dominated actuator dynamics

This paper is concerned with the adaptive stabilization for the ODE systems via boundary measurement of uncertain diffusion‐dominated actuator dynamics. It is worth pointing out that, in the related works, all the states of the diffusion‐dominated actuator are required to be measurable, and this means that an infinite number of sensors are needed to implement the controllers, which is impossible in practice. Quite differently in this paper, only one boundary state of the diffusion‐dominated actuator is measurable and available for feedback design. Moreover, the actuator dynamics contains parameter unknown. Motivated by the existing results, a state observer is first designed to estimate the unmeasurable actuator states, which consists of an input filter and an output filter. Then, by introducing an infinite‐dimensional backstepping transformation, a pivotal target system is obtained from which it is more convenient to design controller and analyze the performance of the original system. Finally, an adaptive controller is constructed by adaptive technique and Lyapunov method, which guarantees that the states of the original system converge to zero, whereas the other states of the closed‐loop system keeping bounded. A simulation example is provided to illustrate the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.