Distributed Cooperative Optimal Control for Multiagent Systems on Directed Graphs: An Inverse Optimal Approach

Abstract

In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

Synchronization in Networks of Linearly Coupled Dynamical Systems via Event-Triggered Diffusions

“…cλ 2 (L) > α and P Γ is semi-positive definite. For any β ′ < β, any initial condition and any time t ≤ 0, we have 1) With the updating rule (9), at least one agent has next inter-event interval, which is lower-bounded by a common constant τ O > 0. in addition, if there exists ς > 0 such that z 2 i (t) ≥ ςV (t) for all i = 1, · · · , m and t ≥ 0, then the next inter-event interval of every agent is strictly positive and is lower-bounded by a common constant.…”

“…The updating rules (9) and (10) are different but closely related to each other in some respects. It can be seen from inequalities (11) and (15) used in the derivation that the convergence behavior for (9) might be better than (10). However, it makes rule (9) more complicated than (10), since each agent should receive the message of the states of its neighborhood but rule (10) does not need.…”

“…Therefore, rule (9) costs more updating times than (10). Moreover, as shown by Theorem 2, rule (10) can guarantee the positivity of the intervals to next updating time for all agents but rule (9) can only guarantee it for at least one agent at each time or for all nodes under some specific additional conditions. III.…”

“…S YNCHRONIZATION of coupled dynamical systems have been widely studied over the past decades [1]- [9], which can be characterized by that all oscillators approach to a uniform dynamical behavior and generally assured by the couplings among nodes and/or external distributed and cooperative control.…”

Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes

“…Specifically, synchronization, as an important and interesting collective behavior of complex networks in our real life, has drawn increasing attention from different fields such as information science, biological system, image processing, secure communication, etc [9][10][11][12][13][14][15]. Up to now, there are many widely-studied synchronization schemes, which defines the correlated in-time behaviors among the nodes in a dynamical network, such as complete synchronization [16], phase synchronization [17], generalized synchronization [18], projective synchronization [19,20], lag synchronization [21], cluster synchronization [22], synchronization in multi-agent systems [23,24]. The synchronization observed in a network is usually called "inner synchronization" as it is a collective behavior within this network.…”