Davide Liuzza

Analysis and stability of consensus in networked control systems

Abstract In this paper, the consensus problem in networks of integrators is investigated. After recalling the classical diffusive protocol, we present in a unified framework some results on the rate of convergence previously presented in the literature. Then, we introduce two switching communication protocols, one based on a switching coupling law between neighboring nodes, the other on the conditional activation of links in the network. We show that the former protocol induces the monotonicity of each system in the network, enhancing the speed of convergence to consensus. Moreover, adopting this novel protocol, we are able to control the network, steering the nodes’ dynamics to a desired consensus value. The aim of the latter protocol is instead to select adaptively the activation of the edges of the network, in accordance with the dynamics of the network. After showing the effectiveness of both approaches through numerical simulations, the stability properties of these protocols are discussed.

Event-Triggered Pinning Control of Switching Networks

This paper investigates event-triggered pinning control for the synchronization of complex networks of nonlinear dynamical systems. We consider networks described by time-varying weighted graphs and featuring generic linear interaction protocols. Sufficient conditions for the absence of Zeno behavior are derived and exponential convergence of a global normed error function is proven. Static networks are considered as a special case, wherein the existence of a lower bound for interevent times is also proven. Numerical examples demonstrate the effectiveness of the proposed control strategy.

Convergence and synchronization in heterogeneous networks of smooth and piecewise smooth systems

This paper presents a framework for the study of convergence in networks where the nodes’ dynamics may be both piecewise smooth and/or nonidentical. Sufficient conditions are derived for global convergence of all node trajectories towards the same bounded region in the synchronization error space. The analysis is based on the use of set-valued Lyapunov functions and bounds are derived on the minimum coupling strength required to make all nodes in the network converge towards each other. We also provide an estimate of the asymptotic bound on the mismatch between the node state trajectories. The analysis is performed both for linear and nonlinear coupling protocols. The theoretical analysis is extensively illustrated and validated via its application to a set of representative numerical examples.

Distributed model based event-triggered control for synchronization of multi-agent systems

This paper investigates the problem of event-triggered control for the synchronization of networks of nonlinear dynamical agents; distributed model-based approaches able to guarantee the synchronization of the overall system are derived. In these control schemes all the agents use a model of their neighbourhood in order to generate triggering instants in which the local controller is updated and, if needed, local information based on the adopted control input is broadcasted to neighbouring agents. Synchronization of the network is proved and the existence of Zeno behaviour is excluded; an event-triggered strategy able to guarantee the existence of a minimum lower bound between inter-event times for broadcasted information and for control signal updating is proposed, thus allowing applications where both the communication bandwidth and the maximum updating frequency of actuators are critical. This idea is further extended in an asynchronous periodic event-triggered schemes where the agents check a trigger condition via a periodic distributed communication without requiring a model based computation.

Contraction Analysis for a Class of NonDifferentiable Systems with Applications to Stability and Network Synchronization

In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched nondifferentiable systems satisfying Caratheodory conditions for the existence and uniqueness of a solution. After generalizing the classical definition of contraction to this class of dynamical systems, we give sufficient conditions for global convergence of their trajectories. The theoretical results are then applied to solve a set of representative problems such as proving global asymptotic stability of switched linear systems, giving conditions for incremental stability of piecewise smooth systems, and analyzing the convergence of networked switched systems.

Event-triggered pinning control of complex networks with switching topologies

This paper investigates the problem of event-triggered pinning control for the synchronization of networks of nonlinear dynamical agents onto a desired reference trajectory. The pinned agents are those that have access to the reference trajectory. We consider both static and switching topologies. We prove that the system is well posed and identify conditions under which the network achieves exponential convergence. A lower bound for the rate of convergence is also derived. Numerical examples demonstrating the effectiveness of the results are provided.

Control of multi-agent systems with event-triggered cloud access

This paper investigates a multi-agent formation control problem with event-triggered control updates and additive disturbances. The agents communicate only by exchanging information in a cloud repository. The communication with the cloud is considered a shared and limited resource, and therefore it is used intermittently and asynchronously by the agents. The proposed approach takes advantage of having a shared asynchronous cloud support while guaranteeing a reduced number of communication. More in detail, each agent schedules its own sequence of cloud accesses in order to achieve a coordinated network goal. A control law is given with a criterion for scheduling the control updates recursively. The closed loop scheme is proven to be effective in achieving the control objective and a numerical simulation corroborates the theoretical results.

Synchronization of networked piecewise smooth systems

This paper is concerned with the synchronization of networks of switching dynamical systems. In particular, conditions are derived for all nodes in a network of such systems to converge towards a common synchronous evolution. The key assumption is for the vector field to be in a suitable form that we call QUAD affine. Under this assumption, we show that the network of interest synchronizes even if the vector field is discontinuous and sliding motion is possible. The theoretical results are complemented by numerical simulations on a testbed example.

Coordination of Multi-agent Systems with Intermittent Access to a Cloud Repository

A cloud-supported multi-agent system is composed of autonomous agents required to achieve a common coordination objective by exchanging data over a shared cloud repository. The repository is accessed asychronously by different agents, and direct inter-agent commuication is not possible. This model is motivated by the problem of coordinating a fleet of autonomous underwater vehicles , with the aim to avoid the use of expensive and power-hungry modems for underwater communication. For the case of agents with integrator dynamics, a control law and a rule for scheduling the cloud access are formally defined and proven to achieve the desired coordination. A numerical simulation corroborate the theoretical results.

Cloud-Supported Formation Control of Second-Order Multi-Agent Systems

This paper addresses a formation problem for a network of autonomous agents with second-order dynamics and bounded disturbances. Coordination is achieved by having the agents asynchronously upload (download) data to (from) a shared repository, rather than directly exchanging data with other agents. Well-posedness of the closed-loop system is demonstrated by showing that there exists a lower bound for the time interval between two consecutive agent accesses to the repository. Numerical simulations corroborate the theoretical results.