Multi-Model Method Decentralized Adaptive Control for a Class of Discrete-Time Multi-Agent Systems

Abstract

This paper studies the decentralized adaptive tracking control problem for a class of discretetime multi-agent systems with unknown parameters and high-frequency gains using multi-model method. Each agent is strong coupling with its neighbors by the historical outputs. All agents are interacted either directly or indirectly. In the face of uncertainties, the projection algorithm as a normal adaptive method is adopted. In order to improve quality of identification, the multi-model method is taken to identify unknown parameters and high-frequency gains using switching sets of the multiple parameters' and high-frequency gains' estimates, and the index switching functions. Using the certainty equivalence principle, the control law for the hidden leader agent is designed by the desired reference signal; the control law for each follower agent is devised by neighbors' historical outputs. Moreover, the proposed decentralized adaptive control laws can guarantee the following performances of the system: (1) the leader agent tracks the reference trajectory and each follower agent follows the average value of its neighborhood historical outputs; (2) the synchronization of all the follower agents to the leader agent is achieved; (3) all the agents track the reference trajectory, and the closed-loop system eventually achieves strong synchronization. Finally, simulations validate the effectiveness on improving control performance of multi-model adaptive algorithm by comparing with the projection algorithm.

Multiple models for decentralised adaptive control of discrete‐time systems

“…Theorem 2. Suppose that for each of the Q LTI or LIP-N subsystems Σ i , i ∈ I Q , modelled by (5), there are M i prediction models given by (31). Let the estimates of the parameter vector Θ 0 be updated with either (35) or (36), where 𝜇 i, and 𝜇 i, respectively satisfy (14) and (15), and the input u i,k be determined using (34).…”

“…Such usage is a departure from existing works 26–29,38–40 . In contrast to references cited earlier, 30–32 our scenario is more general in that we assume all subsystems are interconnected. (The case where a subsystem is connected to its neighbours is, therefore, a particular case.)…”

“…However, they considered only normalised error signals. More recently, a system connected only to its neighbours was treated 30–32 . A master‐follower approach is used, 31 and all subsystems are expected to follow the same desired trajectory.…”

“…More recently, a system connected only to its neighbours was treated 30–32 . A master‐follower approach is used, 31 and all subsystems are expected to follow the same desired trajectory. Further, output synchronisation of heterogeneous linear agents with unknown dynamics is dealt with Reference 33, and its extension to leader‐follower synchronisation is considered 34 .…”

Distributed Adaptive Tracking Control of Hidden Leader-Follower Multi-Agent Systems with Unknown Parameters

“…Most investigations of the multi-model method of adaptive control have focused on handling the various kinds of uncertainties in a single system [35][36][37][38]. In recent years, the distributed multi-model method for adaptive tracking control of MASs has attracted the attention of scholars in the systems and control community [39,40]. For example, in [39], distributed optimal tracking control was investigated based on a correlative measured model.…”