This article investigates the coordination control problem for heterogeneous uncrewed-aerial-vehicle–uncrewed-ground-vehicle systems subject to switching topology. To address the complexity and limited applicability arising from separate modeling, a unified linearized model is established to describe the joint dynamics of both aerial and ground agents. Furthermore, a novel barrier-enhanced dynamic event-triggered mechanism is proposed, wherein a barrier function is embedded to dynamically modulate the triggering threshold. This design effectively balances the tradeoff between strict collision avoidance and communication efficiency. Building on this mechanism, a distributed controller and a reference modifier are codesigned to ensure simultaneous coordination tracking and safety. To handle switching topology, the stability analysis employs dwell-time segmentation and convex combination techniques. This approach guarantees the monotonic decrease of the Lyapunov–Krasovskii functional at switching instants, thereby reducing conservatism. Finally, a numerical simulation and a real-world experiment are conducted to demonstrate the effectiveness and practicality of the proposed approach.

This article investigates secure formation control of a heterogeneous multi-unmanned aerial vehicle (UAV)-unmanned ground vehicle (UGV) system (HMUUS) under nonidentical malicious injection attacks and switching topologies. A unified motion description framework is established to address the system's heterogeneity. By decomposing attacked output signals into nonattacked and attack-related components, two observers are designed to estimate the leader and follower states based solely on nonattacked components, while simultaneously estimating the attack signal for each agent. Based on the estimated states, a distributed controller is designed to ensure that HMUUS can achieve formation. Sufficient conditions are derived to ensure the monotonic decrease of the Lyapunov–Krasovskii functional (LKF) over the entire time domain of HMUUS with communication delays by constructing a piecewise linear time-varying LKF, which significantly reduces conservatism. Simulations and experiments for the HMUUS are conducted to validate the formation under switching topologies and injection attacks.

This paper introduces a novel hierarchical control approach for feature matching, real-time tracking and inter-UAV collision avoidance in multiple unmanned aerial vehicle-unmanned ground vehicle (multi-UAV-UGV) collaborative tracking. Our approach divides into three layers: optimal feature matching, tracking control by reinforcement learning (RL), and collision avoidance using control barrier functions (CBFs). First, a distance cost matrix is cleverly constructed based on the feature matching capabilities of UAVs and UGVs to determine the optimal matching configuration. It allows UAVs to perform the tracking task while minimizing travel distance. Second, a RL-based tracker is developed to achieve precise real-time tracking without depending on UAV dynamic models. The tracker is trained in a single UAV-UGV environment, which reduces policy convergence difficulty by simplifying state space and interactions compared with training in complex multi-UAV-UGV scenarios. Third, a collision avoidance mechanism based on CBFs is introduced to transform RL commands into collision-free actions by solving a quadratic programming (QP) problem. Extensive simulations and real-world experiments demonstrate the effectiveness of the proposed approach.

This paper presents a novel control framework that combines reinforcement learning (RL) with filtered position barrier certificate (FPBC) for distributed collision-free multi-agent systems (MASs) control. By introducing a filtered position model on the basis of a velocity-controlled double-integral system, the collision avoidance analysis is greatly simplified. The proposed FPBC is designed based on this filtered position model and enables collision-free interaction among agents using a less conservative first-order control barrier function (CBF), thereby eliminating the need for complex high-order CBFs (HOCBFs). The proposed FPBC is used in a Quadratic Program (QP)-based safety filter that enforces collision avoidance on the actions generated by a RL controller. This RL controller only needs to be trained in a single-agent setting and can learn an effective policy through a stability-optimality reward function to reduce computing resource consumption. Furthermore, a deadlock resolution mechanism is proposed to prevent agent stagnation and task failure in large-scale MASs. Extensive simulations and real-world experiments in UGV and UAV environments validate the proposed framework, which demonstrates superior safety and performance compared to conventional HOCBFs. The experiment video and other supplementaries are available at https://github.com/mahafeeling/FPBC.

In this paper, we propose a new noise-tolerant neurodynamic algorithm with fixed-time convergence to solve mixed variational inequality problems (MVIPs) and design the circuit framework for its hardware implementation. We prove that the proposed neurodynamic algorithm converges to a unique solution within fixed-time under some conditions and give its convergence time upper bound, which is independent of the initial states. Meanwhile, the robustness of the neurodynamic algorithm under additive perturbations is also demonstrated. In addition, the proposed neurodynamic algorithm is implemented using numerical simulation, analog circuits, and field-programmable gate array (FPGA) respectively. Finally, the superiority of the proposed algorithm is verified by two applications of image reconstruction and elastic net logistic regression.

This paper proposes three gradient-based neurodynamic optimization approaches for Nash equilibrium seeking in non-cooperative games. The decoupled-gradient and coupled-gradient neurodynamic optimization approaches achieve Nash equilibrium with different fixed-time convergence upper bounds, which are invariant to initial conditions, while the proposed mixed-gradient neurodynamic approach exponentially converges to the Nash equilibrium. The robustness of the proposed fixed-time neurodynamic approaches under vanishing disturbances is also investigated. In addition, three novel analog circuit frameworks are introduced, where the actions of neurons are simulated through a feedback loop composed of multipliers, operational amplifiers, resistors, capacitors, and other basic operation models. The circuits demonstrate that the stable output voltages correspond to the Nash equilibrium. Finally, an example is simulated on Multisim 14.3 to validate the superiority and practicality of the proposed analog circuits.

This article investigates a class of systems of nonlinear equations (SNEs). Three distributed neurodynamic models (DNMs), namely a two-layer model (DNM-I) and two single-layer models (DNM-II and DNM-III), are proposed to search for such a system's exact solution or a solution in the sense of least-squares. Combining a dynamic positive definite matrix with the primal-dual method, DNM-I is designed and it is proved to be globally convergent. To obtain a concise model, based on the dynamic positive definite matrix, time-varying gain, and activation function, DNM-II is developed and it enjoys global convergence. To inherit DNM-II's concise structure and improved convergence, DNM-III is proposed with the aid of time-varying gain and activation function, and this model possesses global fixed-time consensus and convergence. For the smooth case, DNM-III's globally exponential convergence is demonstrated under the Polyak-Łojasiewicz (PL) condition. Moreover, for the nonsmooth case, DNM-III's globally finite-time convergence is proved under the Kurdyka-Łojasiewicz (KL) condition. Finally, the proposed DNMs are applied to tackle quadratic programming (QP), and some numerical examples are provided to illustrate the effectiveness and advantages of the proposed models.

This article presents a novel proximal gradient neurodynamic network (PGNN) for solving composite optimization problems (COPs). The proposed PGNN with time-varying coefficients can be flexibly chosen to accelerate the network convergence. Based on PGNN and sliding mode control technique, the proposed time-varying fixed-time proximal gradient neurodynamic network (TVFxPGNN) has fixed-time stability and a settling time independent of the initial value. It is further shown that fixed-time convergence can be achieved by relaxing the strict convexity condition via the Polyak-Lojasiewicz condition. In addition, the proposed TVFxPGNN is being applied to solve the sparse optimization problems with the log-sum function. Furthermore, the field-programmable gate array (FPGA) circuit framework for time-varying fixed-time PGNN is implemented, and the practicality of the proposed FPGA circuit is verified through an example simulation in Vivado 2019.1. Simulation and signal recovery experimental results demonstrate the effectiveness and superiority of the proposed PGNN.

This article proposes two novel projection neural networks (PNNs) with fixed-time ( ) convergence to deal with variational inequality problems (VIPs). The remarkable features of the proposed PNNs are convergence and more accurate upper bounds for arbitrary initial conditions. The robustness of the proposed PNNs under bounded noises is further studied. In addition, the proposed PNNs are applied to deal with absolute value equations (AVEs), noncooperative games, and sparse signal reconstruction problems (SSRPs). The upper bounds of the settling time for the proposed PNNs are tighter than the bounds in the existing neural networks. The effectiveness and advantages of the proposed PNNs are confirmed by numerical examples.

In this article, several novel time-varying momentum-like neurodynamic optimization approaches are proposed for Nash equilibrium (NE) seeking of noncooperative games. It is shown that the dynamics trajectories converge to NE within fixed-time from arbitrary initial conditions, achieving a quicker convergence rate through the selection of distinct time-varying coefficients. Moreover, the upper bounds of the settling time for the proposed NE seeking neurodynamic approaches are explicitly provided. In addition, the study investigates the robustness of the designed neurodynamic approaches in the presence of bounded noises. The superior convergence properties and practicability of our approaches are demonstrated through a simulation example involving energy consumption games.

In this article, several fixed-time (FT) neurodynamic algorithms with time-varying coefficients are introduced for composite optimization problems. The remarkable features of neurodynamic algorithms are FT convergence from arbitrary initial conditions with faster convergence rate by choosing different time-varying coefficients. The FT convergence of neurodynamic algorithms can be proved by the Polyak-${\L}$ojasiewicz condition, which is beyond strong convexity condition. The upper bounds of the settling time for time-varying neurodynamic algorithms are explicitly given. The robustness of neurodynamic algorithms under bounded noises are further studied. In addition, the proposed neurodynamic algorithms are also utilized for dealing with absolute value equations and sparse signal reconstruction problems. The circuit framework for FT neurodynamic algorithms is subsequently introduced, and an example simulated in Multisim 14.3 is provided to verify the practicability of the proposed analog circuits. Numerical experiments on image recovery and sparse logistic regression are conducted to validate the superiority of the proposed algorithms.

This article proposes a novel fixed-time converging proximal neurodynamic network (FXPNN) via a proximal operator to deal with equilibrium problems (EPs). A distinctive feature of the proposed FXPNN is its better transient performance in comparison to most existing proximal neurodynamic networks. It is shown that the FXPNN converges to the solution of the corresponding EP in fixed-time under some mild conditions. It is also shown that the settling time of the FXPNN is independent of initial conditions and the fixed-time interval can be prescribed, unlike existing results with asymptotical or exponential convergence. Moreover, the proposed FXPNN is applied to solve composition optimization problems (COPs),$l_{1}$-regularized least-squares problems, mixed variational inequalities (MVIs), and variational inequalities (VIs). It is further shown, in the case of solving COPs, that the fixed-time convergence can be established via the Polyak–Lojasiewicz condition, which is a relaxation of the more demanding convexity condition. Finally, numerical examples are presented to validate the effectiveness and advantages of the proposed neurodynamic network.

This article proposes a novel fixed-time converging forward-backward-forward neurodynamic network (FXFNN) to deal with mixed variational inequalities (MVIs). A distinctive feature of the FXFNN is its fast and fixed-time convergence, in contrast to conventional forward-backward-forward neurodynamic network and projected neurodynamic network. It is shown that the solution of the proposed FXFNN exists uniquely and converges to the unique solution of the corresponding MVIs in fixed time under some mild conditions. It is also shown that the fixed-time convergence result obtained for the FXFNN is independent of initial conditions, unlike most of the existing asymptotical and exponential convergence results. Furthermore, the proposed FXFNN is applied in solving sparse recovery problems, variational inequalities, nonlinear complementarity problems, and min-max problems. Finally, numerical and experimental examples are presented to validate the effectiveness of the proposed neurodynamic network.