Certainty Equivalence Control of Discrete-Time Multiagent Systems: A Framework for Uniform Global Exponential Stability

作者：Su, Youfeng; Lee, Ti-Chung^*; Cai, He; Chen, Xiaofeng

来源：IEEE Transactions on Automatic Control, 2023, 68(12): 7660-7675.

DOI：10.1109/TAC.2023.3290776

• Certainty equivalence principle
• Krasovskii-LaSalle theorem
• multiagent systems
• perturbed switched systems
• weak zero-state detectability

The solvability of certainty equivalence control problems for discrete-time multiagent systems over uniformly jointly connected switching networks relies on the stability/attractivity analysis for a class of perturbed switched systems with respect to a set of switching signals. To tackle this issue, in this article, a novel systematic and unified framework is established consisting of three key stability/attractivity results. First, the uniform global exponential stability for two dual cases of the nominal dynamics is analyzed in a unified way by checking the weak zero-state detectability from the limiting systems. Second, the uniform global exponential attractivity of the perturbed switched systems accommodating both first-order and zero-order time-varying perturbations is studied without resorting to any Lyapunov function for the entire perturbed switched systems. Third, the uniform global kappa-exponential stability for a class of cascaded switched systems is investigated. These stability/attractivity results together lay the foundation to thoroughly solve two kinds of typical certainty equivalence control problems, and also improve two specific cooperative control designs. Moreover, a relaxed dwell-time condition is considered, which makes the obtained results tolerable in the extreme case of instantaneous link failure and restoration. Finally, the control performances are shown by numerical simulations.

• 单位
  中山大学; 福州大学