We investigate the use of distributed proportional-integral-derivative (PID) actions to achieve consensus in networks of homogeneous and heterogeneous linear systems. Convergence of the strategy is proved for both cases using appropriate state transformations and Lyapunov functions. The effectiveness of the theoretical results is illustrated via its application to a representative power-grid model recently presented in the literature.

In this paper, we propose a multiplex proportional–integral approach, for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Sufficient conditions for convergence are derived that depend upon the structure of the network, the parameters and topologies characterizing the control layers and the node dynamics. The effectiveness of the theoretical results is illustrated numerically on a set of representative examples including a power network model.

We propose an adaptive ramp control strategy with self-tuning offset and amplitude, as a simple yet effective solution for controlling dc-dc power converters despite load and input voltage variations. It is shown that our control technique is able to suppress chaos and subharmonic oscillations for a wide range of input voltage and loads. Furthermore, a systematic methodology based on bifurcation diagrams for tuning the controller is proposed. Stability and performance analysis have been done together with a proper comparison of our technique, and the classical control strategies often used in the literature. Particularly, Vin feedforward and adaptive slope compensation controllers have been considered for the buck and boost converters, respectively. Finally, the effectiveness of the control technique is validated for the buck converter via experimental setup.

The ability of a network of nonlinear systems to synchronize onto the desired reference trajectory in the presence of one or more leader nodes is known as the pinning controllability problem. This paper studies the pinning controllability of multi-agent networks subject to three different types of noise diffusion processes; namely, noise affecting the node dynamics, the communication links, and the pinning control action itself. By using appropriate stochastic Lyapunov functions, sufficient pinning controllability conditions are derived depending on the node dynamics, network structure, noise intensity, and control parameters. Counterintuitively, it is found that under some specific conditions noise may enhance the pinning controllability of the network making it easier to drive all agents towards the desired collective behavior. The effectiveness of the theoretical results is illustrated via two application examples arising in the context of gene regulatory networks and synchronization of chaotic systems.

Understanding how animals navigate complex environments is a fundamental challenge in biology and a source of inspiration for the design of autonomous systems in engineering. Animal orientation and navigation is a complex process that integrates multiple senses, whose function and contribution are yet to be fully clarified. Here, we propose a data-driven mathematical model of adult zebrafish engaging in counter-flow swimming, an innate behavior known as rheotaxis. Zebrafish locomotion in a two-dimensional fluid flow is described within the finite-dipole model, which consists of a pair of vortices separated by a constant distance. The strength of these vortices is adjusted in real time by the fish to afford orientation and navigation control, in response to of the multi-sensory input from vision, lateral line, and touch. Model parameters for the resulting stochastic differential equations are calibrated through a series of experiments, in which zebrafish swam in a water channel under different illumination conditions. The accuracy of the model is validated through the study of a series of measures of rheotactic behavior, contrasting results of real andin-silicoexperiments. Our results point at a critical role of hydromechanical feedback during rheotaxis, in the form of a gradient-following strategy.