Adaptive constrained tracking control for dynamical actuator driven linear 2 × 2 hyperbolic PDE systems with nonlinear uncertainties.

The paper develops an adaptive constrained tracking control technique for a class of 2 × 2 hyperbolic partial differential equation (PDE) systems with boundary actuator dynamics, which are described by a set of ordinary differential equations (ODEs) in the presence of unknown parametric nonlinearities. Since the control input only appears in the uncertain ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite difficult and the existing direct boundary control approaches are ineffective. Moreover, in this paper, a more challenging problem is considered such that the controlled output and the states of ODE actuators are constrained. To this end, by utilizing finite and infinite dimensional backstepping techniques, barrier Lyapunov functions (BLFs) and adaptive methods, a novel adaptive tracking control approach is proposed. It is the first time that such a constrained tracking control problem is addressed for the PDE-ODE coupled systems considered in this paper. On the basis of the presented method, the rigorous theoretical proof is provided to show that the PDE controlled output and all the states of the ODE actuator stay within the predefined compact sets. Finally, the results are illustrated via a comparative numerical simulation. [Display omitted] • For a linear 2 × 2 hyperbolic PDE systems, the high-order unknown nonlinear actuator dynamics described by a set of ODEs are considered in the boundary point of the PDE. A tracking controller with adaptive dynamic compensation mechanism is developed such that the tracking control problem is addressed for the PDE-ODE coupled system considered in this paper. • For practical requirements for state constraints such as safe operations, physical limitations and so on, the Barrier Lyapunov function is employed to constrain the spatially distributed output of infinite-dimensional system and all the actuator states. [ABSTRACT FROM AUTHOR]