Nonlinear control under wave actuator dynamics with time- and state-dependent moving boundary

We consider the stabilization of nonlinear ODE systems with actuator dynamics modeled by a wave PDE whose boundary is moving and is a function of time and of the ODE’s state. Such a problem is inspired by applications in oil drilling where the position of the drill bit is a state variable in the ODE modeling the friction-dominated drill bit dynamics while at the same time being the position of the moving boundary of the wave PDE that models the distributed torsional dynamics of the drillstring. For moving boundaries that depend only on time, we extend the global result recently developed by Bekiaris-Liberis and Krstic for constant boundaries. For moving boundaries that also depend on the ODE’s state, we develop a local result where the initial condition is restricted in such a way that it is ensured that the rate of movement of the boundary (both ‘leftward’ and ‘rightward’) is bounded by unity in closed-loop. For strict-feedforward systems under wave actuator dynamics with moving boundaries, the predictor-based feedback laws are obtained explicitly. The feedback design is illustrated through an example. Copyright © 2013 John Wiley & Sons, Ltd.