A new approach is proposed for the stability problem of delayed load frequency control (LFC) scheme with fixed and timevarying delay cases included in the current article. New stability criteria with delay dependency in terms of linear matrix inequalities for LFC systems are derived by a novel augmented Lyapunov-Krasovski (L-K) functional. Our proof deployment for system stability of power grids employs the further improved integral inequality in the form of infinite series which turns out to be less conservative than Wirtinger's inequality that encompasses Jensen inequality. Simulation case studies are carried out to show the effectiveness and superiority of the presented delaydependent PI-type LFC design scheme.

This article concerns the secure containment control problem for multiple autonomous aerial vehicles. The cyber attacker can manipulate control commands, resulting in containment failure in the position loop. Within a zero-sum graphical game framework, secure containment controllers and malicious attackers are regarded as game players, and the attack-defense process is recast as a min-max optimization problem. Acquiring optimal distributed secure control policies requires solving the game-related Hamilton-Jacobi–Isaacs (HJI) equations. Based on the critic-only neural network (NN) structure, the reinforcement learning (RL) method is employed in solving coupled HJI equations. The fixed-time convergence technique is introduced to improve the convergence rate of RL, and the experience replay mechanism is utilized to relax the persistence of excitation condition. The associated NN convergence and closed-loop stability are analyzed. In the attitude loop, the optimal feedback control law is obtained by solving Hamilton-Jacobi–Bellman equations using the fixed-time convergent RL method. The simulation example and the quadrotor experiment are given to show the effectiveness of the proposed scheme.

In this paper, a new method is put forward for the closed-loop stability analysis of PI-type load frequency control (LFC) scheme with interval time-varying delay. Improved delay-dependent conditions in terms of linear matrix inequalities for single-area and multi-area LFC systems are deduced by the proposed augmented Lyapunov-Krasovski (L-K) functional. {{red}{Less conservativeness of our main results is due to an integral inequality called truncated second-order Bessel-Legendre (B-L) inequality, which can produce tighter bounds than Wirtinger-based inequality that encompasses Jensen inequality.}} Finally, the two-area interconnected power system based on Matlab/Simulink is provided to show the effectiveness and superiority of the obtained results.

This article studies how to solve the energy management (EM) problem while balancing economy and security. Firstly, a defense scheme is developed to relieve the negative effects of denial-of-service (DoS) attacks. Secondly, a secure predefined-time distributed EM algorithm via the time-base generator (TBG) is devised which can be suitable for directed graphs, and sensitive information is decomposed into two dynamic variables for key information privacy preservation. Thirdly, a dynamic event-triggered (DET) mechanism is proposed to economize communication resources. By constructing the Lyapunov energy function, it is proven that the convergence time of the devised distributed algorithm can be predefined by users independent of initial conditions. Zeno behavior is proven to be avoided, which exhibits the effectiveness of the DET approach. At last, the simulations are given to show the validity and advancement of the designed secure distributed algorithm.

In this paper, a fixed-time convergent reinforcement learning (RL) algorithm is proposed to accomplish the secure formation control of a second-order multi-agent system (MAS) under the false data injection (FDI) attack. To alleviate the FDI attack on the control signal, a zero-sum graphical game is introduced to analyze the attack-defense process, in which the secure formation controller intends to minimize the common performance index function, whereas the purpose of the attacker is the opposite. Attaining the optimal secure formation control policy located at the Nash equilibrium depends on solving the game-associated coupled Hamilton-Jacobi-Isaacs equation. Taking into account fixed-time convergence, a critic-only online RL algorithm with the experience replay technique is designed. Meanwhile, the corresponding convergence and stability proofs are provided. A simulation example is presented to show the effectiveness of the devised scheme.

The article investigates the optimal energy management (OEM) problem for microgrids. To figure out the problem in fixed time and alleviate communication load with limited resources, this article devises a novel fixed-time stability lemma and an event-triggered (ET) fixed-time distributed OEM approach. Using Lyapunov stability theory, the distributed approach has been proven to converge in fixed time and the upper bound on convergence time can be derived without dependence on the initial states. The dynamic ET method is raised to dynamically adjust the triggering threshold and reduce communication redundancy. In addition, Zeno behavior is avoided. Simulations are given to show the effectiveness and advantage of the designed distributed OEM method.