Leader‐following consensus of stochastic dynamical multi‐agent systems with fixed and switching topologies under proportional‐integral protocols

Abstract

With the rapid development of swarm intelligence, consensus problem for multi‐agent systems (MASs) has attracted substantial attention. To deal with the leader‐following consensus problems in stochastic dynamical MASs with fixed and switching topologies, this article designed proportional‐integral (PI) control protocols. On the basis of algebraic graph theory and stochastic analysis techniques, by selecting appropriate Lyapunov functions, it is theoretically shown that leader‐following consensus of MASs with stochastic dynamics underlying fixed and switching topologies can be achieved in mean square, respectively. Sufficient criteria are derived for selecting the PI control gains. Finally, the theoretical results are illustrated through several numerical simulations.

Risk‐sensitive large‐population linear‐quadratic‐Gaussian Games with major and minor agents

“…This section is devoted to analyzing the asymptotic Nash equilibrium property of the decentralized control strategies specified by (17).…”

“…The large-population systems with mean field couplings arise in fields such as engineering, social science, economics and finance, operational research, and management (see earlier studies [12][13][14][15][16][17][18][19][20][21] and the related references therein). The agents in large-population system interact with the average (or so-called mean field) effect of other agents via couplings in their individual dynamics and individual cost functions.…”

Input‐constrained optimal output synchronization of heterogeneous multiagent systems via observer‐based model‐free reinforcement learning

“…Lemma 5. Let V * i (r i (k)) ∶ R n i +l → R be a continuously differentiable function with respect to the augmented state r i (k), as a positive definite solution to Bellman Equation (16), and u * i (k) is the corresponding control policy given by ( 20) regarding V * i . Then, the following equation holds for any admissible control policy u i (k).…”

“…According to whether there is a leader or not, it can be essentially categorized as leaderless consensus [6][7][8] and leader-follower synchronization [9][10][11] problems. In particular, state synchronization problems have been well established for both linear [12][13][14] and nonlinear [15][16][17] leader-follower MASs, and some output-feedback-based extensions have also been developed [18,19]. However, a general assumption on this topic is that these systems are homogeneous; that is, all agents have identical dynamics.…”

Design of a Robust Synchronization-Based Topology Observer for Complex Delayed Networks with Fixed and Adaptive Coupling Strength

“…Furthermore, numerous case studies have been conducted on different real-world networks, yielding insights from various perspectives. These studies have encompassed predicting collective behaviors [ 3 , 4 ], applications in control systems [ 5 , 6 ], and other areas. These achievements have made significant contributions to the theory of multi-connected models, which significantly increases the working efficiency of networked systems.…”