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A novel reinforcement learning (RL)-based model-free adaptive control (MFAC) strategy is proposed to address the consensus tracking control issue for multiagent systems subjected to data injection attacks launched in the communication channel. By virtue of the dynamic linearization technique, equivalent dynamic linear data models for nonlinear systems and unknown linear ideal controllers are provided with the aim of determining the controller structure. Meanwhile, to reduce the effects of injection attacks, the fuzzy logic system is used to approximate the unknown nonlinear function by an online learning approach. Moreover, an RL MFAC method is proposed by employing the actor-critic structure to optimize the parameter estimation performance. Rigorous proofs are presented to ensure that the closed-loop systems are uniformly ultimately bounded even in the presence of injection attacks. The validity and superiority of the provided algorithm are further demonstrated through representative simulations.

The distributed optimal problem is investigated in this article for uncertain nonlinear time-varying delay multiagent systems (MASs) under unknown virtual control coefficients. The primary goal is to ensure the output states converge to the ideal point of the global objective function. In comparison to the preceding results on distributed optimization, the considered MASs are subject to time delays and unknown nonlinear functions, which brought great challenges to the controller design process. To overcome this challenge, a distributed optimization algorithm is proposed via a two-stage strategy, which consists of optimization estimator design and tracking controller design. First, in the first-stage, a novel optimal signal generator is constructed by using information interaction between agents, real-time feedback value of local gradient information, so that the optimization problem is transformed into a problem of tracking control. Second, in second-stage, the fuzzy adaptive tracking control strategy is designed via backstepping technology to track the virtual signal accurately. In addition, the Lyapunov–Krasovskii functional (LKF) is applied to counteract influences brought by time-varying delays, and fuzzy logic systems are employed for handling the uncertain function in the derivative of LKF. Furthermore, an assumption is made for the time-varying delays to settle the singularity problem, which often occurs in time-delay problems. In the spirit of the convex analysis and the Barbalats lemma, the stability of the proposed algorithm is illustrated, and all variables in the closed-loop systems are bounded. Lastly, simulations are presented to validate the efficacy of the scheme.

This paper considers a prescribed performance-based event-triggered model-free adaptive control (ET-MFAC) problem for nonlinear system without and with false data injection (FDI) attacks. First, the nonlinear system is converted into an equivalent linear data model by utilizing the dynamic linearization technique. Then, the event-triggered constrained tracking control schemes for nonlinear system without and with FDI attacks under the data-driven framework are designed, which include the following three parts: 1) a prescribed performance function and converted output signal are directly employed in the cost function, and the constraint control schemes are derived by the cost function to realize the prescribed performance requirement; 2) an event-triggered mechanism is designed on the basis of the relationship between measurement error and tracking error, which can decrease the communication burden; 3) in order to reduce the negative effect of FDI attacks on nonlinear system, a resilient security control scheme is presented. Finally, a numerical example shows the efficiency of the developed control methods without and with FDI attacks. Note to Practitioners—This paper investigates an event-triggered constrained tracking error control for the nonlinear system without and with FDI attacks. To avoid utilizing accurate model information, MFAC is introduced into the design process of presented strategies. Incorporating prescribed performance control with an event-triggered mechanism, the developed constrained tracking strategy is designed for the first time to lessen the computational burden while improving the transient and steady-state performance on system. Moreover, based on the energy constraint of FDI attackers, a novel resilient security constrained tracking strategy is developed to decrease the impact of FDI attacks on considered nonlinear system. The validity of theoretical results is carried out by a simulation.

The fixed-time cooperative control is investigated for heterogeneous multiagent systems (HMASs) containing multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) under Denial of Service (DoS) attacks and external perturbations. First, for the ease of collaborative tasks, an unified model is obtained in the XY plane by transforming the dynamical models of UAVs and UGVs. Then, a fuzzy switching observer is designed to achieve unavailable state estimation during the attack zone. In particular, in virtue of the character of DoS attacks, a novel fixed-time stability theory is set up. On this foundation, a distributed fixed-time secure tracking control strategy is raised by utilizing the adaptive approach to effectively defend against DoS attacks. Notably, distinct from the existing works on finite-time stability for HMASs, the present method exhibits some brilliant features, such as fast response, high accuracy, and attack resistance. Additionally, rational proofs have substantiated that the designed control scheme can not only ensure the boundedness of each closed-loop signal but also guarantee the synchronization error converges to a predefined small neighborhood near the origin in a fixed time. Ultimately, the validity of the proposed method is demonstrated by a representative simulation.

With the rapid development of wireless technologies, the simultaneous and flexible control of amplitude and phase characteristics of the signals is highly demanded. However, none of the existing power dividers (PDs) can simultaneously achieve this tunability in a single circuit. In this article, a PD with simultaneously tunable power division ratio (PDR) and phase difference is presented for the first time. The proposed PD consists of two highly flexible arms, a matching network, and an isolation network. The arm is constructed by loading three varactor diodes on a quarter-wavelength 3-dB coupled line. A theoretical analysis is conducted to show that the input impedance and phase delay of this arm can be flexibly controlled by the capacitance of the varactor diodes. Subsequently, the PDR and phase difference between the two output ports can be tuned independently, maintaining good return loss and isolation. For demonstration purposes, a highly flexible PD operating at 2.4 GHz is designed, fabricated, and measured. A wide PDR range from −20 to 20 dB and a wide phase difference range from −180° to 180° are observed, with better than 10 dB return loss and 15 dB isolation.