Transient Control for Leader-follower Multi-agent Systems with Application to Spatiotemporal Logic Tasks

QC 20230411

Abstract

Over the past few decades, significant research has been directed towards addressing the problem of distributed control of multi-agent systems. The overall tasks include consensus, formation, flocking, and coverage control with the wide applications in multi-robot coordination, manufacturing and intelligent transportation systems. However, the distributed control strategies are usually for all agents and sometimes it may be redundant and costly since the desired tasks may be fulfilled by steering part of the agents through the appropriately designed local control strategy in a way that allows the whole group to complete the  intended tasks. Therefore, we instead consider a general leader-follower framework in this thesis, which is meant in the sense that a group of agents with external inputs are selected as leaders in order to drive the group of followers in a way that the entire system can achieve consensus or target formation within certain transient bounds. The followers are controlled according to some standard protocols and rely solely on their dynamic couplings with the steered leaders, without requiring any additional control effort and knowledge of the prescribed team bounds.   

Beyond the traditional considerations of stabilizing and ensuring tracking for multi-agent systems, nowadays more and more applications entail more complex tasks that cannot be easily defined as classic control objectives. Instead, a more advanced level of specification definition is required to address such high-level tasks. Therefore, formal methods based approaches are considered in this thesis in order to specify more complex and high-level task specifications. Signal Temporal Logic (STL), which is based on continuous-time signals, has the added feature of formulating both time and space constraints, and thus provides potentials to deal with quantitative transient constraints for multi-agent systems. 

In this thesis, we tackle both low-level control and high-level planning of leader-follower multi-agent systems using transient-based approaches. Firstly, in the low-level control part, we consider the classical problem of consensus or formation control for leader-follower multi-agent systems in a distributed manner using a prescribed performance strategy. Both the first and second-order cases are treated. Under the assumption of tree graphs, a distributed control law is proposed for the first-order case when the decay rate of the performance functions is within a sufficient bound. Then, two classes of tree graphs that can have additional followers are investigated. For the second-order case, we propose a distributed control law based on a backstepping approach for the group of leaders to steer the entire system achieving the target formation within the prescribed performance bounds. In the second part, we further discuss the results for general graphs with cycles, which are extended based on the previous results of tree graphs. The extension of general graphs with cycles has more practical applications and offers a complete theory for undirected graphs. In the low-level control part, we finally discuss topological conditions for leader-follower networks such that we can apply previously designed prescribed performance strategy for the leader-follower multi-agent systems to achieve target formation within the transient constraints. Specifically, we derive necessary and sufficient conditions for the leader-follower graph topology in order to achieve the desired formation while satisfying the prescribed performance transient bounds. 

In the high-level planning part, cooperative control of leader-follower  multi-agent systems subject to certain fragments of STL specifications is considered. We first propose a funnel-based control strategy for the leader-follower multi-agent systems to enforce the satisfaction of the basic STL formulas by prescribing certain transient behavior on the funnels that constrain the closed-loop trajectories. A hybrid control strategy is then leveraged to satisfy the sequential STL formulas. Later on, we consider a large scale leader-follower network which is composed of several leader-follower subsystems with coupled dynamics. Only the leaders know the related STL specifications and are designed in a distributed fashion to drive the followers in a way such that the STL specifications are globally satisfied. Under the local feasibility assumption, we propose a funnel-based control approach for each leader-follower subsystem such that the local STL specifications are achieved, which further implies the global satisfaction of all STL specifications. In order to enforce the satisfaction of the STL formulas, the funnel parameters are appropriately designed to prescribe certain transient behavior that constrains the closed-loop trajectories. 

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