Stabilization of sets with application to multi-vehicle coordinated motion |
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Authors: | Sergey G. Nersesov [Author Vitae] Parham Ghorbanian [Author Vitae] |
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Affiliation: | a Department of Mechanical Engineering, Villanova University, Villanova, PA 19085-1681, United States b Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada H3G 1M8 |
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Abstract: | In this paper, we develop stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems using vector Lyapunov functions. Several Lyapunov functions arise naturally in multi-agent systems, where each agent can be associated with a generalized energy function which further becomes a component of a vector Lyapunov function. We apply the developed control framework to the problem of multi-vehicle coordinated motion to design distributed controllers for individual vehicles moving in a specified formation. The main idea of our approach is that a moving formation of vehicles can be characterized by a time-varying set in the state space, and hence, the problem of distributed control design for multi-vehicle coordinated motion is equivalent to the design of stabilizing controllers for time-varying sets of nonlinear dynamical systems. The control framework is shown to ensure global exponential stabilization of multi-vehicle formations. Finally, we implement the feedback stabilizing controllers for time-invariant sets to achieve global exponential stabilization of static formations of multiple vehicles. |
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Keywords: | Stabilization of sets Vector Lyapunov functions Multi-vehicle systems Coordinated motion Cooperative control |
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