This paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results.

In this paper, we investigate the oscillatory expression in Escherichia coli mediated by microRNA with time delays and reaction-diffusion terms. First of all, the integrated effects of delays and diffusions are first introduced into the genetic regulatory networks involving microRNAs, and a general model of genetic regulatory networks is then formulated. Second, two functional issues on gene regulatory networks, i.e. stability and oscillation of such model, are addressed in detail, and an explicit algorithm determining the properties of periodic oscillation is also presented. We demonstrate that the oscillatory expression of Escherichia coli is not only crucially dependent on the transcriptional and translational delays, but also heavily influenced by the diffusion coefficients. The conclusion is practically verified by a lot of biological experiments and observations. We also find that if the diffusion coefficients of miRNA, mRNA, and protein are suitably small, it can predict that inhomogeneous periodic oscillations can occur unless there only exhibits spatially homogeneous periodic oscillations. The obtained results indicate that the effects of transcriptional and translational delays are essential factors for designing or controlling genetic regulatory networks, in the meantime the functions of reaction-diffusion must beconsidered. Finally, numerical examples are presented to illustrate and visualize theoretical results.

In this study, a distributed consensus protocol is proposed for second‐order multi‐agent systems having input time delays. A distinctive feature of the algorithm is to address consensus problems for second‐order multi‐agent systems with local instantaneous interaction, where each agent can only exchange the position information with its neighbours at a series of discrete‐time instants and update its velocity state in the form of abrupt jumps setting. The authors also establish the consensus conditions over fixed and switching network topologies, respectively. It is shown that consensus can be exponentially reached if the interaction graph of the system is connected and the interaction intervals are less than a given threshold value. Subsequently, numerical simulations are given to illustrate and visualise the effectiveness and feasibility of the theoretical results.