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arXiv · 2011.13674

Robust Orbital Stabilization: A Floquet Theory-based Approach

Christian Fredrik Sætre·Anton S. Shiriaev·Leonid B. Freidovich·Sergei V. Gusev·Leonid M. Fridman
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Abstract

The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the paper is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet-Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a transverse linearization. This ensures asymptotic stability of the periodic orbit when the system is confined to the sliding manifold, despite any system uncertainties and external disturbances satisfying a matching condition. The challenging task of oscillation control of the underactuated Cart-Pendulum system subject to both matched and unmatched disturbances/uncertainties demonstrates the efficacy of the proposed scheme.

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Christian Fredrik Sætre, Anton S. Shiriaev, Leonid B. Freidovich, Sergei V. Gusev, Leonid M. Fridman. 2020-11-27. Robust Orbital Stabilization: A Floquet Theory-based Approach. https://doi.org/10.1002/rnc.5738

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