Output feedback control in the presence of uncertainties: Using extended high-gain observers with dynamic inversion

Control design for uncertain nonlinear systems is an important issue. Uncertainties always reside in nonlinear systems due to incomplete mathematical model description or intended approximation factors in system models, e.g. linearization for system models. Furthermore, unexpected external disturbances and unmeasured system states increase the uncertainties in the systems.;In this dissertation, we consider an uncertain nonlinear systems that takes the form of a chain of integrators and introduce control design methodologies based on output feedback control: 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 uncertainties in the fastest time scale and dynamic inversion is used to deal with nonaffine control inputs or input uncertainties in the intermediate time scale whereas the plant dynamics evolves in the slowest time scale. The dynamic inversion algorithm, based on sector conditions, results in fast convergence into inputs under state feedback control. Together with the extended high-gain observer, dynamic inversion results in performance recovery of a target system.;The time-scale-separation approach is well-suited to underactuated mechanical systems to overcome the lack of the number of inputs. Since the time separation is created between subsystems in plant dynamics, subsystem dynamics are viewed as virtual inputs for the other subsystems. In this dissertation, we apply the time-scale separation strategy to two examples of underactuated mechanical systems in the presence of uncertainties, the inverted pendulum on a cart and the autonomous helicopter.