Finite‐time distributed control with time transformation. (5th October 2020)

• Record Type: Journal Article
• Authors: Arabi, Ehsan; Yucelen, Tansel; Singler, John R.
• Is Part Of: International journal of robust and nonlinear control. Volume 31:Number 1(2021)
• Page Start: 107
• Page End: 130
• Publication Date: 2020-10-05
• Subjects: finite‐time distributed control -- multiagent systems -- robustness -- system stability -- time transformation; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.5264
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: In this article, we propose distributed control algorithms for first‐ and second‐order multiagent systems for addressing finite‐time control problem with a priori given, user‐defined finite‐time convergence guarantees. The proposed control frameworks are predicated on a recently developed time transformation approach. Specifically, our contribution is twofold: First, a generalized time transformation function is proposed that converts the user‐defined finite‐time interval to a stretched infinite‐time interval, where one can design a distributed control algorithm on this stretched interval and then transform it back to the original finite‐time interval for achieving a given multiagent system objective. Second, for a specific time transformation function, we analytically establish the robustness properties of the resulting finite‐time distributed control algorithms against vanishing and nonvanishing system uncertainties. By contrast to existing finite‐time approaches, it is shown that the proposed algorithms can preserve a priori given, user‐defined finite‐time convergence regardless of the initial conditions of the multiagent system, the graph topology, and without requiring a knowledge of the upper bounds of the considered class of system uncertainties. Illustrative numerical examples are included to further demonstrate the efficacy of the presented results.