Robot formation control has several advantages that make it interesting for research. Multiple works have been published in the literature using different control approaches. This work presents the control of different groups of robots to achieve a desired formation based on pinning control of complex networks and coordinate translation. The implemented control law comprises complex network bounding, proportional, and collision avoidance terms. The tests for this proposal were performed via simulation and experimental tests, considering different networks of differential robots. The selected robots are Turtlebot3^® Waffle Pi robots. The Turtlebot3^® Waffle Pi is a differential mobile robot with the Robot Operating System (ROS). It has a light detection and ranging (LiDAR) sensor used to compute the collision avoidance control law term. Tests show favorable results on different formations testing on various groups of robots, each composed of a different number of robots. From this work, implementation on other devices can be derived, as well as trajectory tracking once in formation, among other applications.

This paper proposes an impulsive control scheme for a complex network that helps reduce the spread of two epidemic diseases: influenza type A and COVID-19. Both are respiratory infections; thus, they have a similar form of transmission, and it is possible to use the same control scheme in both study cases. The objective of this work is to use neural impulsive inverse optimal pinning control for complex networks to reduce the effects of propagation. The dynamic model is considered unknown, for which we design a neural identifier that, through training using the extended Kalman filter algorithm, provides the appropriate nonlinear model for this complex network. The dynamics of the network nodes are represented by the Susceptible-Infected-Removed (SIR) compartmental model in their discrete form. The results of the simulations are presented and addressed, applying the same control scheme but with different parameter values for each case study.

In this paper, we present an impulsive pinning control algorithm for discrete-time complex networks with different node dynamics, using a linear algebra approach and a neural network as an identifier, to synthesize a learning control law. The model of the complex network used in the analysis has unknown node self-dynamics, linear connections between nodes, where the impulsive dynamics add feedback control input only to the pinned nodes. The proposed controller consists of the linearization for the node dynamics and a reorder of the resulting quadratic Lyapunov function using the Rayleigh quotient. The learning part of the control is done with a discrete-time recurrent high order neural network used for identification of the pinned nodes, which is trained using an extended Kalman filter algorithm. A numerical simulation is included in order to illustrate the behavior of the system under the developed controller. For this simulation, a 20-node complex network with 5 different node dynamics is used. The node dynamics consists of discretized versions of well-known continuous chaotic attractors.

In complex dynamical networks, pinning control techniques are often applied to control a small fraction of the nodes in order to stabilize the network with reduced control effort and energy, facilitating adequate development of the complex network. Selecting the controlled nodes is a key challenge to achieving optimal performance. Theoretical analysis of the network provides the minimum quantity of nodes to control but does not specify which ones should be controlled. Analytically, controllability analysis of the entire network would be ideal, but this becomes difficult for complex networks with a large number of nodes and non-linear dynamics. Another option is to evaluate all possible combinations with the minimum number of necessary nodes or the nodes that can be controlled, but this presents a computational challenge due to the large number of possible combinations. Therefore, the remaining option is the use of metaheuristic algorithms for the rapid and practical evaluation of these combinations. In this work, we propose to optimize the selection of nodes for pinning control based on binary optimization algorithms, subject to control and development constraints. The proposed approach involves finding a binary combination with a fixed number of controlled nodes that best stabilizes the network state to zero. This paper includes a comparative study among state-of-the-art binary optimization algorithms and modified classic optimization algorithms. The applicability of the proposed approach is validated through simulations considering a dynamical discrete-time complex network.

In this work, a neural impulsive pinning controller for a twenty-node dynamical discrete complex network is presented. The node dynamics of the network are all different types of discrete versions of chaotic attractors of three dimensions. Using the V-stability method, we propose a criterion for selecting nodes to design pinning control, in which only a small fraction of the nodes is locally controlled in order to stabilize the network states at zero. A discrete recurrent high order neural network (RHONN) trained with extended Kalman filter (EKF) is used to identify the dynamics of controlled nodes and synthesize the control law.

This paper presents the mathematical model Susceptible-Infected-Recovered SIR with parameters that describe the COVID-19 dynamics. This model is based on a system of ordinary differential equations in which appropriate conditions and starting parameter values such as transmission rates and recovery rates are considered known. These parameters are utilized to obtain a simulation of COVID-19 behavior, in order to establish a possible solution to avoid a greater chance of disease transmission. On the proposed scheme, we use a neural impulsive inverse optimal control for a complex network in which the dynamic of each node is a discrete version of SIR model that describe the dynamics of COVID-19. The neural network is trained with an extended Kalmans filter and is used as a neural identifier for the selected nodes of the system. The control law used represents a hypothetical treatment for COVID-19. This work aims to simulate the interaction of different populations during an epidemic outbreak in which populations are represented by the complex network nodes