Predefined-time distributed optimal formation control of networked marine surface vehicles based on a nonsingular segmented terminal sliding mode method

Generally, traditional cooperative control schemes for networked control systems face challenges in balancing optimality and convergence speed. For this reason, this paper proposes a predefined-time distributed optimal formation algorithm for the networked marine surface vehicles (NMSVs) to address these issues. Under this algorithm, each vehicle is assigned a cost function for achieving optimal performance such as energy consumption, collision avoidance, and so on. The main control objective is to actuate the NMSVs to form a designed formation pattern while minimizing the total cost function within a predefined time. The proposed algorithm is built by a distributed optimization layer and a local controller layer. For more details, the first layer employs a consensus-based distributed optimization protocol to compute the optimal position and velocity based on the given cost functions. The second layer integrates a predefined-time non-singular terminal sliding mode controller to realize the optimal formation of NMSVs with the derived optimal solution as the formation centre in a user-specified time. Through Lyapunov-based stability analysis, the sufficient conditions for guaranteeing the effectiveness of the proposed scheme are derived. Simulation results also confirm the effectiveness and robustness of the proposed method.