This paper proposes a couple of consensus algorithms for multiagent systems in which agents have first-order nonlinear dynamics, reaching the consensus state at a predefined time independently of the initial conditions. The proposed consensus protocols are based on the so-called time base generators (TBGs), which are time-dependent functions used to build time-varying control laws. Predefined-time convergence to the consensus is proved for connected undirected communication topologies and directed topologies having a spanning tree. Furthermore, one of the proposed protocols is based on the super-twisting controller, providing robustness against disturbances while maintaining the predefined-time convergence property. The performance of the proposed methods is illustrated in simulations, and it is compared with finite-time, fixed-time, and predefined-time consensus protocols. It is shown that the proposed TBG protocols represent an advantage not only in the possibility to define a settling time but also in providing smoother and smaller control actions than existing finite-time, fixed-time, and predefined-time consensus.

This paper aims to analyze the stability of a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks composed of agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a nonlinear function of the consensus error is performed per each node. The classical assumption of switching among connected graphs is dropped here, allowing to represent failures and intermittency in the communications between agents. Thus, conditions to guarantee finite and fixed-time convergence, even while switching among disconnected graphs, are provided. Moreover, the algorithms of the considered class are computationally simpler than previously proposed finite-time consensus algorithms for dynamic networks, which is an essential feature in scenarios with computationally limited nodes and energy efficiency requirements such as in sensor networks. Simulations illustrate the performance of the proposed consensus algorithms. In the presented scenarios, results show that the settling time of the considered algorithms grows slower than other consensus algorithms for dynamic networks as the number of nodes increases.

Fluidization constitutes a relaxation technique to study discrete event systems through a continuous approximated model, thus overcoming the state explosion problem. In this paper, the approximation of the average marking of Markovian Petri nets by the marking of the corresponding timed continuous Petri nets, under infinite-server semantics, is studied. This represents a sort of legitimization for the use of a continuous Petri net as a relaxation of a discrete Petri net. The main contribution is the addition of Gaussian noise in order to improve the approximation when the number of active servers (enabling degree) is large. The improvement is more evident when the system evolves “close” to the boundary of regions. In such a case, not only the expected value but also the probability distribution function of the marking may be approximated.

This paper is concerned with controllability of Timed Continuous Petri nets, under infinite server semantics, with uncontrollable transitions, which are a class of hybrid systems (piecewise-linear). This class of hybrid systems is suitable for representing biological systems, high traffic information networks, heavily loaded supply chains, etc. By adopting a Control Theory approach, the contribution of this paper is the characterisation of controllability over sets of equilibrium markings (potential equilibrium points), first inside a single marking region (or linear mode) and later extended to several regions.