PhD Thesis Defence | Zhanlue Liang, Formation Control of Multi-agent Systems via Impulsive Strategy

MS Teams (please email amgrad@uwaterloo.ca for the meeting link)

Candidate 

Zhanlue Liang | Applied Mathematics, University of Waterloo

Title

Formation Control of Multi-agent Systems via Impulsive Strategy

 Abstract

Multi-agent systems (MASs) involving cooperative control problems such as consensus tracking of distributed networks, flocking control with obstacle avoidance, and attitude alignment have received a considerable amount of interest over the past few decades because of their broad real-time applications in various fields. As one of the most significant aspects of cooperative control, the formation stabilization process has been studied extensively in relation to cooperative surveillance, unmanned aerial vehicles, spacecraft coordination, autonomous underwater vehicles, etc. In formation tracking control, the fundamental goal is to reach a desired configuration and align with the formation leader from any arbitrary starting position. This can be achieved using various types of distributed control protocols in practice, which facilitate efficient communication and information exchange among agents.

To begin with, we discuss the design of hybrid impulsive control protocols for the formation stabilization of multi-agent systems. By taking various sizes of time delay into account, some sufficient formation stabilization criteria are established via the Razumikhin technique and Lyapunov functional method. It is important to emphasize that the guarantee of stabilization is largely determined by the impulsive strength, the size of the time delays, and the length of the impulsive intervals. In the meantime, the general structure of collision avoidance mechanisms using artificial potential fields (APFs) or braking/gyroscopic forces is also discussed since they are critical for ensuring safety and reducing accident risk in a variety of applications. In comparison, the approach of braking and gyroscopic forces provides better performance by preventing undesired local minima. Moreover, one should realize that the inclusion of such mechanisms will raise the complexity of asymptotic formation stabilization under delay-dependent impulses. Thus, we further consider treating the collision avoidance mechanism as an external input and investigate input-to-state formation stabilization with respect to different impulse classes. In this way, stabilization can still be achieved once environmental obstacles are out of sensing range. Some sufficient conditions benefiting from stabilizing control impulses are derived by employing the Lyapunov Krasovskii functional and impulsive comparison principle. The hybrid impulsive control framework will be kept using throughout the rest of this thesis.

Then, on top of the hybrid impulsive control framework, we extend our formation stabilization results into the following aspects:

1. Multi-group formation stabilization for heterogeneous MASs with different dynamics order is investigated. In this setup, each subgroup can pursue its own control objectives, while group-wise coordination can be established via directed inter-group communication links. The stabilization is then dependent on the overall topological structure of the network.
2. The hybrid event-triggered impulsive formation stabilization associated with non-linearity strength of intrinsic dynamics is considered. By incorporating pinning mechanisms and delayed control inputs, the corresponding event-triggered strategies are developed. Based on the Lyapunonv-Razumikhin technique regarding delayed impulsive systems, some novel results for maintaining local formation stabilization are obtained.
3. We also investigate the finite-time formation tracking control of multi-agents via aperiodic intermittent communication under the hybrid impulsive control framework. In addition, the concepts of average impulsive interval and state-dependent intermittent control width are also implemented. The finite-time stabilization results illustrate the effectiveness of the proposed control protocol on the basis of the weak Lyapunov inequality condition.
4. Furthermore, we investigate the formation stabilization of vehicle platoons using switching control, which is a trending application of multi-agent systems. Based on time-dependent switching between stable and unstable control inputs, or state-dependent switching utilizing convex switching regions and chatter-free switching rules, exponential stabilization results are obtained.

Finally, numerical simulations are provided to demonstrate the effectiveness and performance of our analytical results.