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Summary The distributed convex optimization problem subject to time‐varying communication delays and switching network topologies is addressed in this paper. Based on continuous‐time Zero‐Gradient‐Sum scheme, the novel distributed algorithms are proposed to minimize the global objective function which is composed of a sum of strictly convex local cost functions. In the fixed network topology case, by constructing a new Lyapunov‐Krasovskii function, two explicit sufficient conditions for the maximum admissible time delay are derived to guarantee that all agents' states converge to the optimal solution. In the switching network topology case, the stability condition is derived by the common Lyapunov function theory. In addition, two sufficient conditions about the maximum admissible time delays are also derived for the fixed and switching weight‐balanced network topologies, respectively. Several simulation tests are used to illustrate the effectiveness of our obtained theoretical results.

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The basic biomechanical laws that apply to the clawed toes of animals with powerful digging abilities and the optimal bionic design of curved soil cultivating components with an analogous contour were researched in a novel way. First, the curvature and profile of the inside contour line of a field mouse's clawed toe were analyzed. The finite element method (FEM) was then used to simulate the working process in order to study the changing characteristics of the working resistance of bionic soil-engaging surfaces and the stress field of the processed soil. A straight-line cultivating component was used for comparative analysis. In accordance with the simulation results, a series of soil cultivating components of varying design were manufactured. An indoor soil bin experiment was carried out to measure their working resistance and validate the results of the FEM analysis. The results of this research would have important values in the optimization design of cultivating components for energy and cost savings.