Consensus of Nonlinear Multi-Agent Systems under a Directed Network and Its Applications


Student thesis: Doctoral Thesis

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Award date23 Nov 2021


Collaborative control of multi-agent systems has received increasing and extensive attention over the past decades due to its widespread applications. Typical examples include data fusion in wireless sensor networks, distributed design in power systems and cooperative surveillance of unmanned aerial vehicles, just to name a few. In particular, consensus is one of the most fundamental and critical topics in engineering applications. Its prime objective is to drive all involved agents to behave identically under distributed protocols based on local sensors’ data through communications with neighboring peers.

This thesis focuses on nonlinear agents communicated over a directed network. To cope with different scenarios, consensus criteria are theoretically established while their usages in real-world applications are explored.

First of all, we consider the leader-following consensus of coupled nonlinear agents with intermittent control. By using multiple Lyapunov functions method and the algebraic graph theory, the second-order consensus is guaranteed just by pinning a subset of followers under mild assumptions. The result provides high flexibility in control gains design, allowing multiple switching with different gains in arbitrarily-chosen time intervals. As a general design, it not only encompasses many existing intermittent control schemes but is also able to handle many practical situations, such as recovering consensus from occasional control failures.

Next, we study a more general framework with time-varying control, which is useful to counteract denial-of-service (DoS) attacks. External DoS attacks aim to impose intermittent congestion in communication channels, which in turns affects the state update in consensus processes, resulting in the failure of a consensus protocol. Recently, such a situation has been recast as a consensus problem with on-off control. However, in previous studies, undirected graphs are commonly assumed while the DoS attacks are to follow certain periodic patterns. Obviously, these assumptions hardly reflect real situations. Therefore, a redesign is needed to cope with aperiodic attacks and directed topologies. Our theoretical result reveals that consensus is still achievable, provided that the average of the DoS attack duration over a certain length of time interval is upper bounded. Compared with existing results, the newly derived consensus criterion demonstrates better generality and tractability.

Then, we explore the time-varying control in the presence of transmission delay over a communication network. To facilitate the study, a novel delayed differential inequality with time-varying coefficients is first established. By considering the consensus problem as the stability problem of a delayed differential system with time-dependent parameters, a sufficient consensus criterion is established. Our theoretical study reveals that the average of the control strength is crucial. Together with the agent dynamics and the underlying topology, this average also governs the largest admissible delay. As demonstrated, the new criterion is applicable for consensus problems with general on-off coupling under data sampling and delayed communications, respectively.

It should be pointed out that, in practical implementation, the states of agents are periodically sampled, meaning that they are only available at sampling instants. As a result, the design of sampled-data controllers is practically important. We hence consider the consensus problem for networked nonlinear agents with time-varying control gain under a synchronous periodic data sampling framework. To further reduce resource utilization, we propose both state-dependent and time-dependent event-triggered protocols, respectively. Their effectiveness is theoretically justified by the Lyapunov stability theorem, facilitated by a delayed differential inequality with time-dependent parameters. Instead of specifying a lower bound for the control gain, as others suggested, our criteria rely on its time-average and thus allow higher flexibility in controller design.

Sometimes, precise agent dynamics are hard to obtain while the model uncertainty could exert critical influences on consensus. In this case, a Gaussian process (GP) model could be an alternative solution. Moreover, to deal with practical constraints, such as actuator or state constraints, the model predictive control (MPC) is commonly applied. By integrating both techniques, we propose and design a distributed MPC based on GP (GP-DMPC) to solve consensus problems with model uncertainty and practical constraints. Specifically, the vehicle platooning problem is investigated, where the final state is to achieve a consistent velocity in the fleet and maintain a small inter-vehicle distance. GP regression is employed to model the vehicle dynamics which is practically unknown. Then, a DMPC scheme is designed to achieve the platoon with constant spacing policy, where a local open-loop optimization problem is formulated for each vehicle, taking practical physical constraints and model uncertainty, such as actuator limitation, collision avoidance and passengers’ comfort, into consideration. The stability analysis confirms that the design goals can be reached asymptotically, while its effectiveness is illustrated by numerical simulations. It is demonstrated that the vehicle platooning can be reformed in reaction to sudden acceleration or deceleration of a vehicle.