A global continuous control scheme for the finite-time or (local) exponential stabilization of mechanical systems with constrained inputs is proposed. The approach is formally developed within the theoretical framework of local homogeneity. This has permitted to solve the formulated problem not only guaranteeing input saturation avoidance but also giving a wide range of design flexibility. The proposed scheme is characterized by a Saturating-Proportional-Derivative type term with generalized saturating and locally-homogeneous structure that permits multiple design choices on both aspects. The work includes a simulation implementation section where the veracity of the so-cited argument claiming that finite-time stabilizers are faster than asymptotical ones is studied. In particular, a way to carry out the design so as to indeed guarantee faster stabilization through finite-time controllers (beyond their finite-time convergence) is shown.
This brief proposes two alternative approaches for the global regulation of robot manipulators with input saturations. They prove to be simple extensions of the PD-with-gravity-compensation (PDgc) control law to the bounded-input case. Moreover, they turn out to be in a better position to approach (within the restricted range of the control variables) a PDgc control signal than other algorithms previously proposed under the same analytical framework. Closed-loop performance improvements are, therefore, obtained through their implementation. This is corroborated through experimental results.
In this work, a notion of local homogeneity is formally defined. Important results involving homogeneous functions or vector fields are reformulated in the consequent local context. In particular, global finite-time stability is characterized through the proposed notion of local homogeneity. As an application of the developed analytical setting, a global finite-time stabilization scheme for robot manipulators with bounded inputs is presented. The developed framework and results prove to be useful to relax analytical and synthesis constraints imposed or generated by homogeneity requirements.
We address the problem of master-slave synchronization of chaotic systems under parameter uncertainty and with partial measurements. Our approach is based on observer-design theory hence, we view the master dynamics as a system of differential equations with a state and a measurable output and we design an observer (tantamount to the slave system) which reconstructs the dynamic behavior of the master. The main technical condition that we impose is persistency of excitation (PE), a property well studied in the adaptive control literature. In the case of unknown parameters and partial measurements we show that synchronization is achievable in a practical sense, that is, with "small" error. We also illustrate our methods on particular examples of chaotic oscillators such as the Lorenz and the Lü oscillators. Theoretical proofs are provided based on recent results on stability theory for time-varying systems.
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