A pursuit–evasion game is a classical maneuver confrontation problem in the multi-agent systems (MASs) domain. An online decision technique based on deep reinforcement learning (DRL) was developed in this paper to address the problem of environment sensing and decision-making in pursuit–evasion games. A control-oriented framework developed from the DRL-based multi-agent deep deterministic policy gradient (MADDPG) algorithm was built to implement multi-agent cooperative decision-making to overcome the limitation of the tedious state variables required for the traditionally complicated modeling process. To address the effects of errors between a model and a real scenario, this paper introduces adversarial disturbances. It also proposes a novel adversarial attack trick and adversarial learning MADDPG (A2-MADDPG) algorithm. By introducing an adversarial attack trick for the agents themselves, uncertainties of the real world are modeled, thereby optimizing robust training. During the training process, adversarial learning was incorporated into our algorithm to preprocess the actions of multiple agents, which enabled them to properly respond to uncertain dynamic changes in MASs. Experimental results verified that the proposed approach provides superior performance and effectiveness for pursuers and evaders, and both can learn the corresponding confrontational strategy during training.

In this paper, we focus on the fourth-order nonlinear Schrödinger equation, which can describe the optical system and the Heisenberg spin system. We consider a continuous wave perturbed by the one-dimensional random rough surface as the initial condition. First, we numerically resolve the eigenvalues under different control parameters utilizing the Fourier collocation method. Then, we simulate the evolution of this equation under the above initial conditions via the symmetrical split-step Fourier method. Moreover, we investigate the “steady” chaotic state by evolving a large number of initial conditions for the same control parameters. We find that the control parameters of the initial condition affect the number and intensity of rogue waves (RWs) in integrable turbulence. In particular, we locate the inflection point where the control parameter affects the velocities of solitons and the inconsistency within the parameter of the contribution to the generation of RWs. We further verify that the collision between breathers, solitons, and breathers and solitons can generate RWs. These results will enable us to understand the turbulent state and the formation mechanism of RWs.