This paper concentrates on the fixed-time optimal consensus issue of multi-agent systems (MASs) under false data injection (FDI) attacks. To mitigate FDI attacks on sensors and actuators that may cause systems to deviate from the reference trajectory, a zero-sum game framework is established, where the secure control protocol aims at the better system performance, yet the attacker plays a contrary role. By solving the Hamilton–Jacobi–Isaacs (HJI) equation related to the zero-sum game, an optimal secure tracking controller based on the event-triggered mechanism (ETM) is obtained to decrease the consumption of system resources while the fixed-time consensus can be guaranteed. Moreover, a critic-only online reinforcement learning (RL) algorithm is proposed to approximate the optimal policy, in which the critic neural networks are constructed by the experience replay-based approach. The unmanned aerial vehicle (UAV) systems are adopted to verify the feasibility of the presented approach.

This article concentrates on the practical prescribed-time leader-following consensus problem of second-order multi-agent systems (MASs) under disconnected time-varying topologies. Firstly, a new practical prescribed-time stability criterion is presented, where the time-varying scaling function is related to connected moments and the derivative inequality is increasing in the disconnected intervals. Secondly, inspired by the backstepping design framework, the practical prescribed-time control protocol is designed, including the distributed velocity estimator, virtual velocity and dynamic event-triggered controller. Thirdly, some consensus conditions for achieving leader-following consensus are established and the Zeno behavior is excluded. Finally, simulation results on unmanned aerial vehicle (UAV) formation tracking are provided to demonstrate the effectiveness of the proposed method.

This paper focuses on the fixed-time distributed optimization problem with time-varying cost functions in multi-agent systems (MASs). For the scenario where all agents share the same Hessian matrix, a control framework for minimizing the global cost function is proposed based on the zero-gradient-sum (ZGS) algorithm. Specifically, integral sliding mode is employed to achieve the initial optimality of local objective functions, thereby satisfying the initial conditions required by the ZGS algorithm. Furthermore, for the case with heterogeneous Hessian matrices among agents, a distributed optimization algorithm integrating distributed gradient estimation and the prediction-correction method (PCM) is designed. Specifically, the distributed gradient estimation enables each agent to reconstruct the global objective gradient information of the system within a fixed time. Both proposed algorithms can achieve fixed-time convergence, and the inverse of the Hessian matrix is approximated online using a zeroing neural network (ZNN), which significantly improves computational efficiency. Finally, numerical simulations are conducted based on the charge balance problem in smart grids to verify the effectiveness and superiority of the proposed algorithms.