A systematic backstepping approach for the control of coupled ODE-PDE-ODE systems

摘要

A systematic backstepping design of state feedback controllers is addressed for coupled ODE-PDE-ODE systems, that mostly arise for distributed-parameter systems where actuator and sensor dynamics are taken into account. It allows the successive and simplified derivation of known backstepping controllers and can easily be transferred to a broader spectrum of systems, that had not yet been considered. For that, the approach makes use of the strict feedback form that is inherent in these systems. Using integrator backstepping techniques, the ODE-PDE-ODE system is stabilized step-by-step by virtual state feedbacks and mapped into error coordinates. The proposed modular design is essentially independent of whether the distributed-parameter part of the system is parabolic or hyperbolic.