Synchronization via output feedback for multi-agent singularly perturbed systems with guaranteed cost

Abstract

This paper focuses on the problem of designing a decentralized output feedback control strategy for synchronization of homogeneous multi-agent systems with global performance guarantees. The agents under investigation are described as linear singularly perturbed dynamics representing a wide class of physical systems characterized by processes evolving on two time-scales. The collaborative decentralized control is achieved using only output information from neighboring agents and considering that the only available graph information consists in its connectivity, that is, there is no centralized information related to the interconnection network structure. As methodology, the synchronization problem is rewritten as a dynamic output feedback robust stabilization of a singularly perturbed uncertain linear system with guaranteed cost. We show that these problems can be solved by using convex conditions expressed by LMIs and by decoupling the slow and fast dynamics. As an advantage, the fast dynamic matrix can be singular (nonstandard systems) and unstable. The proposed conditions circumvent some drawbacks of the existing works on this topic by providing a dynamic controller that does not depend on the singular parameter or by allowing the design of slow controllers when the fast system is stable. Numerical examples are presented to demonstrate the effectiveness of the proposed protocol and design method.

Cooperative Control of Multi-Time-Scale Agent Networks Under Digraphs

“…Recently, the results in [24] are extended to different situations. [25] designs a distributed dynamic output-feedback consensus protocol to achieve asymptotically consensus with global performance guarantees, while [26] combines two Zeno-free event-triggered mechanisms and event-triggered controller to achieve guaranteed-cost consensus for two-time-scale agent networks. [27] further proposes both the static and dynamic event-triggered mechanisms and distributed synchronization protocols for two-time-scale agent networks with switching topology.…”

“…However, the achieved consensus criteria therein depend on the agent's dynamics and the size of networks, which maybe are unsolved as the size of networks is too larger. Although these contributions, some facts should be highlighted: 1) the communication topologies in above works are special cases of directed topologies with a spanning tree; 2) Apart from [25], [28], the proposed consensus protocols given above rely heavily on the relative states of agent, which are usually impossible or too expensive in practice. Therefore, a natural question arises: Is it possible to develop an suitable consensus protocol for multi-time-scale agent networks with a general directed graphs by using the relative states or the relative output states of agents?…”

Singular-Perturbations-Based Analysis of Dynamic Consensus in Directed Networks of Heterogeneous Nonlinear Systems

“…In the former, for networks of simple integrators through sector nonlinearities, and in the latter, for linear homogeneous systems interconnected through time-varying persistently-exciting gains a la [8]. On the other hand, in [33,34], networks of linear homogeneous singularly-perturbed systems are considered. Thus, in all of the above, the setting is fundamentally different from the one adopted here.…”

A bilinear system approach with input saturation to control the agreement value of multi-agent systems

“…The work of I.-C. Morȃrescu was supported by ANR under the grants HANDY ANR-18-CE40-0010 and NICETWEET ANR-20-CE48-0009. 1 Daniel R. Alkhorshid and Eduardo S. Tognetti are with the Department of Electrical Engineering, University of Brasilia -UnB, 70910-900, Brasília, DF, Brazil, dralkhorshid@gmail.com, estognetti@ene.unb.br constantin.morarescu@univ-lorraine.fr global control effort constraints (see [11], [13], [14]).…”