Adaptive Preassigned Finite-Time Tracking Control for PDE-ODE Systems With Dead-Zone Input and Actuator Failures

This paper presents a finite-time tracking control for PDE-ODE coupled systems with dead-zone input and actuator failures. To begin with, a novel finite-time performance function and error transformation are designed for a reaction-diffusion equation to improve the transient and steady-state performance for PDE-ODE systems. In addition, to overcome the difficulties generated by the uncertain actuator failures and dead-zone input for coupled systems, a finite-time tracking controller and the adaptive laws are designed to compensate for the drastic effect of unknown nonlinearities. By applying neural networks approximation technology, the computational complexity and difficulty of controller design are significantly reduced. Unlike the existing stability results in the PDE-ODE systems, the developed method can guarantee the given transient performance by adaptive parameter tuning and the tracking error converges to the specified region in finite time. Moreover, the boundedness and convergence of all the signals in the closed-loop coupled systems are proved. Finally, the simulation example exhibits the effectiveness of the proposed control scheme. Note to Practitioners-The PDE-ODE coupled systems in modern mechanical engineering scenarios require better transient and steady-state performance as well as more agility of adjustment method. Because of the special infinite-dimensional characteristics of coupled systems compared to single PDE or ODE systems, it is more complex to design the adaptive finite-time controller for PDE-ODE systems. The finite-time performance function and error transformation designed in this paper aim to improve the stability of the coupled systems and adjust the preassigned performance more flexible. The settling time is independent and free of the parameters and initial values of the coupled systems which can be chosen by users according to actual requirements. Meanwhile, the constraints of actuator failures and dead-zone nonlinearity are compensated simultaneously for PDE-ODE systems via the presented adaptive neural networks finite-time control scheme.