Time-Varying Formation-Containment Control for Heterogeneous Multi-Agent Systems With Communication and Output Delays via Observer-Based Feedback Protocol

In this article, the time-varying formation-containment control problem of heterogeneous multi-agent systems (MASs) with an observer-based state feedback protocol is studied, where both communication delays and output delays are taken into consideration. By introducing an augmented Lyapunov-Krasovskii functionals (LKFs) candidate and employing less conservative methods to estimate its derivative, an improved quasi-formation-containment criterion is derived. On this basis, some observers and controllers are designed to allow for a larger maximum upper bound (MUB) of time delays on the premise of guaranteeing the fulfillment of the time-varying formation of leaders and the bounded convergence of followers. The estimation of the MUB determines the allowable delay range for system stability under the designed observers and controllers. Moreover, a distributed algorithm is developed to calculate the MUB of time delays, the observer gains, and the controller gains. Finally, two simulation experiments are implemented to demonstrate the obtained results, which verify the superiority and practicability of the criterion and algorithm. Note to Practitioners—This paper aims to solve the problem of formation-containment for MASs. It has been extensively implemented in various practical engineering fields, such as the exploration of the ocean through autonomous underwater vehicles and the teamwork carried out by mobile robots. In real-world engineering scenarios, the interaction between agents often has the following issues: 1) The state of agents may not be directly measurable in certain environments. 2) The information communication among agents is usually affected by time delays. 3) The existing formation-containment controllers are only suitable for dealing with predetermined small time delays. Therefore, a distributed algorithm with great effectiveness is designed to handle these problems.