This article addresses algebraic criteria for consensus problems of continuous-time networked systems with fixed and switching topology. A special eigenvector ω of the Laplacian matrix is first constructed and correlated with the connectivity of digraph. And then, some necessary and/or sufficient algebraic conditions are presented by employing the vector ω, which can directly determine whether the consensus problem can be solved. More importantly, for the switching topology case, the obtained algebraic conditions for the average consensus problem are necessary and sufficient. Furthermore, the presented results clearly show that only the agents corresponding to the positive elements of ω contribute to the group decision value and decide the collective behaviour of the system. Particularly for the fixed topology case, the role of each agent is exactly measured by the value of the corresponding element of ω. Based on these results, some extended protocols are further proposed to solve the average consensus problem, in which the interaction digraphs are not needed to be balanced. Numerical examples are included to illustrate the obtained results.

The pectoral fin propulsion of a bionic robotic fish always consists of two phases: propulsion and recovery. The robotic fish moves in a burst-and-coast swimming manner. This study aims to analyze a pair of bionic robotic fish with rigid pectoral fin propulsion with three degrees of freedom and optimize the elliptical propulsion curve with the minimum recovery stroke resistance using computational fluid dynamics methods. Then, the time allocated to the propulsion and recovery phases is investigated to maximize the propulsion performance of the bionic robotic fish. The numerical simulation results show that when the time ratio of the propulsion and recovery phases is 0.5:1, the resistance during the movement of the robotic fish is effectively reduced, and the drag-reducing effect is pronounced. According to a further analysis of pressure clouds and vortex structures, the pressure difference between the upstream and downstream fins of the pectoral fin varies with different stroke ratios. The increase in recovery phase time helps to prevent premature damage to the vortex ring structure generated during the propulsion process and improves propulsion efficiency.

The robotic fish of BCF/MPF hybrid propulsion achieves efficient and stable swimming through the synergistic control of pectoral fins and body. However, the control problem has been less studied of fins-body coupling with multiple degrees of freedom. This study focuses on the development and synergistic control of robotic fish with fins-body. First, a robotic fish with pectoral fin and body co-propulsion was designed, and a gait controller of fin-body synergic was constructed by a central pattern generator (CPG). Specifically, the control parameters were simplified, and the synergic movement was realized of fin-body coupling with multiple degrees of freedom. Secondly, the dataset was obtained with computational fluid dynamics (CFD) simulations and six-dimensional force sensors, and the offline hydrodynamic model was obtained by bidirectional long-short-time memory networks (BiLSTM) identification, which is the relationship between the control parameters and force/torque of the robotic fish. The model parameters were updated online with experimental data. Finally, a control framework is constructed for offline-online model and event-triggered nonlinear model predictive control (ENMPC), which compensates for the driving force of the robotic fish, achieves tracking trajectory precisely, and reduces the computational cost.