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Characterization of Domain of Fixed-time Stability under Control Input Constraints
arXiv - CS - Systems and Control Pub Date : 2020-04-02 , DOI: arxiv-2004.01540
Kunal Garg; Dimitra Panagou

In this paper, we study the effect of control input constraints and of the upper bound on the time of convergence on the domain of attraction for systems that exhibit fixed-time stability (FxTS). We first present a new result on FxTS, where we allow a positive term in the time derivative of the Lyapunov function. We provide analytical expressions for the domain of attraction and the time of convergence in terms of the coefficients of the positive and negative terms that appear in the time derivative of the Lyapunov function. We show that this result serves as a robustness characterization of FxTS systems in the presence of additive, vanishing disturbances. We use the new FxTS result in formulating a quadratic program (QP) that computes control inputs to drive the trajectories of a class of nonlinear, control-affine systems to a goal set in the presence of control input constraints. We show that the new positive term in the FxTS result acts as a slack term in the QP constraint, and helps guarantee feasibility of the QP. We study the effect of the control authority and the convergence time on the magnitude of the coefficient of this positive term through numerical examples.
更新日期:2020-04-06

 

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