Globally Stabilizing a Class of Underactuated Mechanical Systems on the Basis of Finite-Time Stabilizing Observer
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Globally exponentially stabilizing a class of underactuated mechanical systems (UMS) with nonaffine nonlinear dynamics is investigated in this paper. The considered UMS has a nonaffine nonlinear subsystem that can be globally asymptotically stabilized by saturated feedbacks, but the saturated feedback cannot be analytically expressed in closed-form. This obstacle limits the real-time applications of most controllers presented in literatures. In this paper, a hybrid feedback strategy is presented to globally exponentially stabilize the UMS with nonaffine and strict-feedback canonical forms. The hybrid feedback strategy is characterized by the composition of partial states feedback and partial virtual outputs feedback based on a higher-order finite-time stabilizing observer. The presented hybrid feedback controller can be synthesized by applying Lyapunov stability theory. Some numerical simulations associated with two underactuated nonlinear systems, the Acrobot system and the Inertia-Wheel-Pendulum (IWP) system, are employed to demonstrate the effectiveness of the proposed controller. The presented control strategy can be applied in real time, thus providing a new feasible dynamic model other than the differential flatness systems for synthesizing the mechanical systems of general underactuated legged robots.
KeywordsNon-affine nonlinear systems Underactuation Finite-time Observer Controller
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