Adaptive control for heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients and uncertain nonlinear actuator dynamics.

In this paper, we aim to develop adaptive asymptotic stability for heterodirectional 2 × 2 hyperbolic PDEs with parametric-strict-feedback nonlinear actuator dynamics. First, we transform the heterodirectional 2 × 2 hyperbolic PDEs with spatially varying coefficients into a stable target subsystem by utilizing the infinite-dimensional backstepping transformation. Second, an adaptive state feedback controller is constructed by combining finite-dimensional state transformation and adaptive compensation technology to assure the boundedness of all the signals in the closed-loop system. Meanwhile, we show that the PDE states converge to zero pointwise in space, the nonlinear ODE states and the control input also converge to zero. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]