| Summary: | This master thesis is devoted to developing an adaptive control scheme for the well-
known Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique. The main
objective of this adaptive scheme is to asymptotically stabilize a class of Underactuated
Mechanical Systems (UMSs) in the presence of uncertainties (not necessarily matched). This class of
UMSs is characterized by the solvability of the Partial Differential Equation (PDE) resulting from
the IDA-PBC technique. Two propositions are stated in this work to design the adaptive IDA-PBC. One
of the main properties of these propositions is that even though the parameter estimation conver-
gence is not guaranteed, the adaptive IDA-PBC achieves asymptotic stabilization. To illustrate the
effectiveness of these propositions, this work performs simulations of the Inertia Wheel Inverted
Pendulum (IWIP) system, considering a time-dependent input disturbance, a type of physical damping,
i.e., friction (not considered in the standard
IDA-PBC methodology), and parameter uncertainties in the system (e.g., inertia). === Tesis
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