The adaptive stabilization is investigated for a class of coupled PDE-ODE systems withmultiple uncertainties. The presence of the multiple uncertainties and the interactionbetween the sub-systems makes the systems to be considered more general andrepresentative, and moreover it may result in the ineffectiveness of the conventionalmethods on this topic. Motivated by the existing literature, an infinite-dimensionalbacksteppping transformation with new kernel functions is first introduced to change theoriginal system into a target system, from which the control design and performanceanalysis of the original system will become quite convenient. Then, by certaintyequivalence principle and Lyapunov method, an adaptive stabilizing controller issuccessfully constructed, which guarantees that all the closed-loop system states arebounded while the original system states converging to zero. A simulation example isprovided to validate the proposed method.

Control laws are described for solving the task of stabilization of motion and force of interaction of a robot with its environment with a prescribed quality of transient processes with respect to position and in the presence of control, motion, and interaction force constraints. The robustness of these laws to parametric perturbations and their stability with respect to initial and external perturbations and measuring sensor errors have been proven.