Control design for uncertain nonlinear systems is an important issue. Uncertaintiesalways reside in nonlinear systems due to incomplete mathematical model description orintended approximation factors in system models, e.g. linearization for system models.Furthermore, unexpected external disturbances and unmeasured system states increase theuncertainties in the systems. In this dissertation, we consider an uncertain nonlinear systems that takes the form ofa chain of integrators and introduce control design methodologies based on output feedbackcontrol: using extended high-gain observers and dynamic inversion.The proposed output feedback controller results in a closed-loop system with a three-time-scale structure; an extended high-gain observer estimates unmeasured states and un-certainties in the fastest time scale and dynamic inversion is used to deal with nonaffinecontrol inputs or input uncertainties in the intermediate time scale whereas the plant dy-namics evolves in the slowest time scale. The dynamic inversion algorithm, based on sectorconditions, results in fast convergence into inputs under state feedback control. Togetherwith the extended high-gain observer, dynamic inversion results in performance recovery ofa target system. The time-scale-separation approach is well-suited to underactuated mechanical systemsto overcome the lack of the number of inputs. Since the time separation is created betweensubsystems in plant dynamics, subsystem dynamics are viewed as virtual inputs for theother subsystems. In this dissertation, we apply the time-scale separation strategy to two examples of underactuated mechanical systems in the presence of uncertainties, the invertedpendulum on a cart and the autonomous helicopter.
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