Boundary Control for Cascaded System of Nonlinear ODE/Hyperbolic PDE With Time-Varying Parameter

Boundary control for a nonlinear system actuated by a first-order time-varying hyperbolic partial differential equation is investigated. Two-step backstepping transformation is applied during the design. The first-step backstepping transformation is given to transfer the first-order hyperbolic PDE to a transport PDE, and the second-step backstepping transformation is used to design the compensator for the closed-loop system. Globally asymptotical stability of the closed-loop system is proved by constructing a Lyapunov functional. The validity of the proposed design is illustrated by an example.