Distributed Fixed-Time Optimization for Marine Aerial-Surface Heterogeneous Systems With Prescribed Performance

The aim of this paper is to investigate the distributed fixed-time optimization problem in marine aerial-surface heterogeneous systems consisting of unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs) with prescribed performance constraints. Although distributed optimization problems have been extensively studied, the critical challenge here arises from handling heterogeneous agents with different dynamic models, while requiring convergence to an optimal solution that satisfies the constraints within a fixed time. To overcome the above challenge, a distributed bilayer fixed-time optimization scheme is proposed to address two main problems: (1) the distributed fixed-time optimization estimation problem, and (2) the distributed fixed-time local tracking problem. Specifically, the optimization estimator is designed based on a gradient descent method, enabling UAVs and USVs to infer the state and velocity of a virtual leader within a fixed time and obtain the optimal decision variables through minimizing the objective function. On the basis of backstepping, coordinate transformation and sliding mode control, a disturbance-rejection nonsingular local tracking controller is constructed to ensure that the vehicles can accurately track the optimal signal while satisfying both transient and steady-state performance requirements in position errors. Furthermore, the settling time of the hierarchical optimization process depends on having the appropriate control parameters, irrespective of the initial system state. Finally, numerical simulations validate the effectiveness of the theoretical results.