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SummaryFor finite-time optimal robust control problem of bipedal walking robot, a class of global and feasible projected Fletcher-Reeves conjugate gradient approach is proposed based on an online convex optimization algorithm. The optimal robust controllers are solved by projected Fletcher-Reeves conjugate gradient approach.The approach can rapidly converge to a stable gait cycle by selecting an initial gait. Under some suitable conditions, we provide a rigorous proof of global convergence and well-defined properties for projected Fletcher-Reeves conjugate gradient approach. To demonstrate the effectiveness of the bipedal walking robot, we will conduct numerical simulations on the model of 3-link robot with nonlinear, impulsive, and underactuated dynamics. Furthermore, to indicate the availability of high-dimensional robotic system, the main result is illustrated on a nonlinear impulsive model of a bipedal walking robot through simulations via finite-time optimal robust controller. Numerical results show that the projected Fletcher-Reeves conjugate gradient approach is feasible and effective for bipedal walking robots. Therefore, it is reasonable to infer that the optimal robust control approach can be used in practical systems.

3D topology control in underwater sensor networks is of great significance to ensuring reliable and efficient operation of the network. In this paper, by analyzing the characteristics of an underwater sensor network, we take the cube as the basic unit to perform 3D partition of the monitoring area, define the 3D partition unit and basic cluster structure of the underwater sensor network, and arrange rotating temporary control nodes in the cluster. Then, a cluster sleep-wake scheduling algorithm is proposed that compares the remaining node energy. It selects the node with the largest remaining energy as the working node, and the remaining nodes complete the transition of dormancy and waiting states as long as they reach the preset dormancy time. The node state settings of this phase are completed by the temporary control node. Temporary control nodes selecting and sleep-wake scheduling are used in the algorithm through 3D topology control, which reduces energy consumption and guarantees maximum sensing coverage of the entire network and the connection rate of active nodes. Simulation results further verify the effectiveness of the proposed algorithm.

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