This paper investigates the problem of synchronization for nonlinear systems. Following a Lyapunov approach, we first study the global synchronization of nonlinear systems in the canonical control form with both distributed proportional-derivative and proportional-integral-derivative control actions of any order. To do so, we develop a constructive methodology and generate in an iterative way inequality constraints on the coupling matrices that guarantee the solvability of the problem or, in a dual form, provide the nonlinear weights on the coupling links between the agents such that the network synchronizes. The same methodology allows us to include a possible distributed integral action of any order to enhance the rejection of heterogeneous disturbances. The considered approach does not require any dynamic cancellation, thus preserving the original nonlinear dynamics of the agents. The results are then extended to linear and nonlinear systems admitting a canonical control transformation. Numerical simulations validate the theoretical results.

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.

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.

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.

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.

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.

This paper investigates the problem of eventtriggered 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.