This paper investigates the problem of fixed-time distributed Nash equilibrium seeking for constrained non-cooperative games with players governed by nonlinear Euler-Lagrange dynamics. A distributed Nash equilibrium seeking algorithm is proposed based on the leader-following consensus protocol, the sliding mode theory and the two-layer design framework. It is proven that the proposed distributed algorithm converges to the Nash equilibrium of the constrained game in a fixed time, which is independent of the initial conditions of the players, and the upper bound of the convergence time for the proposed Nash equilibrium seeking algorithm is explicitly given. The effectiveness of the proposed distributed algorithm is validated through two numerical experiments, including a network of two-link robot manipulators and a power generation game.

This paper studies the problem of distributed event-triggered coordinated tracking (DETCT) for heterogeneous multiagent systems (MASs) with unknown dynamics. Unknown dynamics of heterogeneous followers and un known input of the leader make the design of DETCT protocols much more difficult. To achieve leader-follower consensus, we design two different DETCT protocols. First, based on model reference adaptive control (MRAC) and state sampling measurements of neighboring nodes, a state-based DETCT protocol is proposed with dynamic event-triggered function for controllers. Compared with the existing coordinated tracking protocols, the proposed state-based DETCT protocol can solve cooperative tracking of heterogeneous followers with unknown dynamics and greatly reduce the consumption of network communication. Second, considering the scenario where the states are not measurable, an observer-based DETCT protocol is introduced which only needs output information. The validity of the above DETCT protocols is confirmed by excluding Zeno behavior within finite time. Finally, some simulations illustrate the theoretical results.

Accurate flood prediction is crucial for disaster mitigation. Addressing the limitations of existing deep learning methods-specifically in modeling long-range dependencies, leveraging the spatial heterogeneity of topographic features, and mitigating the optimization process's susceptibility to local optimathis paper proposes a novel Swin-UNet framework for flood prediction. The innovations of this work are the introduction of a feature fusion mechanism to adaptively focus on critical spatial regions and the proposal of an Adaptive Variable-Order Fractional Adam (AVOFAdam) optimizer, which leverages historical gradient information to enhance the “memory” of the optimization process.Experimental results demonstrate that the proposed framework significantly enhances prediction accuracy and generalization capability, particularly under unseen rainfall conditions.

This paper investigates the problem of distributed Nash equilibrium seeking with fixed-time convergence for players of high-order integrator dynamics. A novel distributed Nash equilibrium seeking algorithm with a two time-scale framework is proposed based on the leader-following consensus protocol and sliding mode theory. It is proved that the actions of the players under the proposed distributed algorithm converge to the Nash equilibrium in a fixed-time with its upper bound explicitly given. The effectiveness of the proposed distributed algorithm is demonstrated through a non-cooperative navigation example involving a heterogeneous swarm of unmanned vehicles of high-order integrator dynamics.

Due to the complex nonlinear control systems and the variability of driving tasks, intelligent vehicles face significant challenges in control. To address this problem, the theory of driving-by-targets is proposed to formalize basic driving tasks using mathematical models. Then, a driving-by-targets controller based on deep reinforcement learning (DRL) is designed to achieve coupled lateral–longitudinal control. Considering the driving task uncertainty, the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm trains the proposed controller. The state information is directly mapped to the steering angle and acceleration output, enabling control in a continuous action space. In addition, the reward function is constructed to facilitate policy learning. Experiments show the accuracy and real-time performance of the driving-by-targets controller.

This paper investigates the problem of distributed Nash equilibrium seeking with fixed-time convergence for constrained non-cooperative games over directed communication graphs. Distributed Nash equilibrium seeking algorithm is proposed based on a leader-following consensus protocol and the projection operator. It is proved that the proposed distributed algorithm converges to the Nash equilibrium in fixed-time, which is independent of the initial conditions of the players. Moreover, the upper bound of the convergence time for the proposed Nash equilibrium seeking algorithm is explicitly given. The effectiveness of the proposed distributed algorithm is validated through an example of a constrained energy consumption game.

Cellular mechanotransduction, mediated by specialized structures such as microvilli, regulates processes ranging from tissue homeostasis to disease progression. Existing tools for microvilli-specific biomechanical intervention suffer from limited spatiotemporal precision and non-physiological constraints, restricting mechanistic studies and targeted therapies. Here, we develop a magnetically driven gear-like metal-organic framework microrobot (MOFbot) for programmable mechanical manipulation of single-cell microvilli. MOFbots are fabricated through epitaxial growth of heterogeneous MOF structures followed by deposition of Ni/Au nanofilms. Under a rotating magnetic field, they perform rolling and obstacle negotiation. Their rotating gear structure entangles microvilli, exerting quantified pulling forces via Förster resonance energy transfer and traction force microscopy. This mechanical stimulation triggers intracellular calcium influx and enhanced focal adhesion kinase phosphorylation, indicating mechanotransduction pathway activation. Consequently, rotating MOFbots increase membrane permeability, enabling on-demand transmembrane delivery of therapeutics into targeted single cells. This work establishes a targeted cellular mechanomodulation strategy and informs future micro/nanorobotic biomedical designs.

Optical two-way time-frequency transfer (O-TWTFT), employing linear optical sampling and based on frequency combs, is a promising approach for future large-scale optical clock synchronization. It offers the dual benefits of high temporal resolution and an extensive unambiguous range. A critical challenge in establishing long-distance free-space optical links is enhancing detection sensitivity. Particularly at ultra-low received power levels, the error caused by time extraction algorithms for linear optical sampling becomes a significant hindrance to system sensitivity, surpassing the constraints imposed by quantum limitations. In this work, we introduce the Complex Least Squares (CLS) method to enhance both the accuracy and sensitivity of time extraction. Unlike most previous methods that relied solely on phase information, our scheme utilizes a maximum likelihood estimation technique incorporating both amplitude and phase data. Our experiments, conducted over a 113 km free-space link with an average link loss of up to 100 dB, achieved a record minimum received power of 0.1 nW, which is over ten times lower than previous benchmarks. The precision also approaches the quantum limitation.

This paper investigates the bipartite consensus problem of multi-agent systems (MASs) with matrix-weighted interactions, functioning on undirected signed graphs. To decrease communication loss, the event-triggered mechanism is incorporated into the proposed bipartite consensus protocol. To prove bipartite consensus, two auxiliary variables are introduced to make the proof simpler. The adaptive technique is utilized to reduce the impact of nonlinear factors, and Lyapunov theory is employed to establish the stability of error systems and verify their performance over time. The proposed controller allows the MASs to reach exponentially bipartite consensus. Furthermore, it can be demonstrated that the method prevents the occurrence of an infinite sequence within a finite time interval, ensuring that Zeno behavior is avoided. Finally, a series of simulations are presented to validate and reinforce these theoretical results.

For the jumping task of wheel-legged robots, this paper proposes a stage-wise reward shaping method based on the CMORL framework. In traditional reinforcement learning, the design of reward functions is complex, requiring the integration of multiple factors and facing difficulties in dynamic adjustment. Moreover, imitation learning demands massive amounts of data. This method divides the jumping task into five stages: standing, squatting, jumping, air, and landing, and defines independent reward and cost functions for each stage. It combines the CoMOPPO algorithm to optimize multi-objective rewards while satisfying constraints. A teacher-student network structure is adopted, where the teacher network uses privileged information for learning, and the student network imitates its behavior. Additionally, symmetry regularization is introduced to enhance stability. Experiments in both simulated and real environments verify that the robot can achieve stable jumping and effective Sim2Real transfer.

This paper proposes a control strategy for a 5-DOF vehicle active suspension system based on a fractional-order ultra-local model. The proposed approach integrates time delay estimation (TDE) with a Lyapunov-based adaptive sliding mode controller. By exploiting the memory-dependent properties of fractional-order dynamics, the method captures the inherent complexity and coupling characteristics of the suspension system more accurately. The TDE technique is utilized to estimate and compensate for unknown nonlinearities, uncertainties, and external disturbances in real time, transforming the uncertain nonlinear system into a tractable ultra-local fractional-order form with bounded estimation error. A robust adaptive sliding mode controller is then designed to ensure system stability and improve ride comfort. Lyapunov stability analysis guarantees the convergence of tracking errors under the designed control law. Simulation results conducted in MATLAB/Simulink on a nonlinear 5-DOF vehicle suspension model demonstrate that the proposed method significantly outperforms conventional integer-order and non-adaptive control schemes, effectively enhancing suspension performance and ride quality.

Magnetic suspension systems are widely used in engineering applications, such as maglev transportation and precision manufacturing, due to their frictionless and highly controllable characteristics. However, their inherent nonlinearity and fractional-order dynamics pose significant challenges in control design. This paper proposes an optimal position-tracking controller for the magnetic suspension system. As a complex nonlinear system with fractional-order components, the magnetic suspension system is modeled as a fractional-order ultra-local model. Via fractional-order time-delay estimation strategy, the lumped disturbances in the model are estimated and eliminated. Subsequently, an error convergence strategy based on fractional-order sliding mode and the Lyapunov equation is developed. Furthermore, to avoid brief oscillations of the system for discontinuous signals, an event-triggered mechanism is designed. Before the event-triggering condition being met, the system is controlled solely by the FO-PID. Finally, the optimal parameters of the controller are determined using the Hippopotamus Optimization algorithm. To validate the effectiveness of the proposed algorithm, the experiment is conducted on SolidWorks–MATLAB simulation platform. Under different types of inputs and noise disturbances, the proposed algorithm exhibits higher tracking accuracy and enhanced disturbance rejection capability compared to other methods.

Earthquakes threaten the security and stability of urban integrated energy systems. Enhancing system resilience improves the ability to withstand seismic hazards. This paper proposes a coordinated post-disaster restoration strategy for integrated electricity and natural gas systems (IENGSs) that exploits natural gas line pack under seismic conditions. First, a line pack model is developed to quantify its impact on IENGS resilience. Subsequently, leveraging the load-supporting capability of line pack, we investigate how distribution network reconfiguration influences IENGS load recovery. Accounting for cross-system fault propagation during earthquakes, we formulate a post-disaster repair strategy incorporating line pack flexibility. Case studies using the IEEE 33-bus power system and a 7-node natural gas system validate the proposed strategy’s effectiveness and feasibility in enhancing seismic resilience.

Magnetic anomaly detection (MAD) has been recognized as an effective method for detecting and positioning magnetic targets. To address the issue of scalar MAD being influenced by the magnetic moment orientation (MMO) and the challenge of estimating the vertical coordinates of the target, a three-dimensional (3D) target location method is developed in this article. The proposed method first employs the total vertical gradient of magnetic anomalies to characterize their spatial distribution and constructs a two-dimensional orthonormal basis functions (VG-2D-OBFs) model to represent these properties. Then, by employing a black-body model to decouple vertical and horizontal localization, this approach reduces the complexity of the solution while enhancing depth estimation accuracy. Ultimately, a 3D target localization framework is developed, utilizing a two-step strategy to enhance spatial accuracy. Simulations and field experiments demonstrate that the proposed method not only has good robustness and high positioning accuracy, but also is insensitive to the magnetic moment orientation, with the root mean square and standard deviation of the localization error for different MMOs reaching 0.149 m and 0.069 m, respectively. Therefore, as a post-processing method, it is of significant in the of detection.

Aiming at the problems of high randomness of search, slow convergence speed, and many redundant points of paths in the fast expanding random tree (RRT) algorithm. This paper proposes an improved RRT path planning algorithm. Firstly, through the probabilistic target bias combined with the dynamic sampling strategy of the artificial potential field method, the blindness of the random tree expansion is reduced; secondly, for the problem of poor obstacle avoidance ability of the random tree expansion, the dynamic variable step size expansion strategy is proposed; the work efficiency of the algorithm is improved. Finally, for the problems of many redundant points in the initial path as well as zigzagging paths, the greedy algorithm is used to eliminate the redundant points in the path as well as the cubic B-spline curve for path smoothing optimization. The results show that compared with the traditional RRT, RRT* and RRT-Connect algorithms, the algorithm in this paper reduces the path length, search time and the number of nodes to a certain extent, which effectively verifies the feasibility of the algorithm in the path planning of different environment maps.

The sequence-form representation has shown remarkable efficacy in computing Nash equilibria for two-player extensive-form games with perfect recall. Nonetheless, devising an efficient algorithm for n-player games using the sequence form remains a substantial challenge. To bridge this gap, we establish a necessary and sufficient condition, characterized by a polynomial system, for Nash equilibrium within the sequence-form framework. Building upon this, we develop a sequence-form differentiable path-following method for computing a Nash equilibrium. This method involves constructing an artificial logarithmic-barrier game in sequence form, where two functions of an auxiliary variable are introduced to incorporate logarithmic-barrier terms into the payoff functions and construct the strategy space. Afterward, we prove the existence of a smooth path determined by the artificial game, originating from an arbitrary totally mixed behavioral-strategy profile and converging to a Nash equilibrium of the original game as the auxiliary variable approaches zero. In addition, a convex-quadratic-penalty method and a variant of linear tracing procedure in sequence form are presented as two alternative techniques for computing a Nash equilibrium. Numerical comparisons further illuminate the effectiveness and efficiency of these methods.

The electricity spot market, a lack of electricity data disrupts the balance between supply and demand and makes it difficult to plan generation and supply. To solve this problem, this paper presents a tensor complementation algorithm that uses time series decomposition and considers the high dimensionality and significant fluctuations of electricity consumption data in the spot market. The method starts with the decomposition of time series data for individual users, followed by the construction of a Hankel tensor. A tensor regularization model based on parallel factorization is developed and solved using hierarchical alternating least squares (HALS) with gradient normalization to reduce computation time. The experiments were conducted using three different datasets. Using the relative recovery error as the evaluation metric, the results show a 12.7 % improvement in accuracy compared to tensor CP factorization for data with 60 consecutive missing entries, providing enhanced support for electricity spot trading decisions.

This paper investigates the fixed-time distributed optimization problem of first-order multi-agent systems with strongly convex local cost functions and consensus constraints. To address this problem, this paper designs a two-stage fixed-time optimization algorithm based on dynamic event-triggered strategy. Firstly, the first-stage algorithm is designed based on the gradient information of the local cost function, ensuring that the agent states converge to the local optimal values within a fixed time. Secondly, the second-stage algorithm is designed based on the dynamic event-triggered strategy and the Hessian matrix of the local cost function, achieving the convergence of agent states from the local optimal values to the global optimal value within a fixed time. The algorithm proposed in this paper solves the problem of excessive consumption of communication resources in the continuous communication optimization algorithm. It enables all agents to reach the global optimal state in fixed time, and the upper bound of the setting time does not depend on the initial values of the system. The numerical simulations validate the effectiveness of the algorithm.

This paper addresses the edge-consensus problem in a directed nodal network, where each edge is described by uncertain fractional-order dynamics subject to positivity constraints. To solve the issues of positivity and consensus in uncertain fractional-order networked systems (UFONSs) with the order 0 < q <= 1, a distributed control protocol by virtue of state feedback is designed. Some sufficient criteria are established to ensure positive edge-consensus of UFONSs. Subsequently, to handle scenarios with unmeasurable states in practical systems, an observer-based control protocol is proposed to achieve positive edge-consensus for UFONSs. Furthermore, by leveraging the fractional-order stability theory and the properties of positive systems, some sufficient positive edge-consensus conditions that depend only on the number of edges and nodes are formulated instead of the global information of the network. Finally, two simulation examples are shown to verify the feasibility of the proposed protocols.

Autonomous electric vehicles (AEVs) are equipped with numerous advanced control systems that rely on measurements of longitudinal velocity, yaw rate, lateral speed, and sideslip angle. However, one of the main challenges is that mass-produced vehicles cannot accommodate overly expensive sensors. This paper proposes a novel hybrid physics-data driven observer (HPDD-Observer) for vehicle dynamics state estimation (VDSE). HPDD-Observer aims to provide comprehensive and cost-effective information about the vehicle dynamics state using low-cost onboard sensors with high sampling frequency. This approach leverages the power of hybrid modeling. Firstly, it creates a linear relationship between the estimated states and the sensor vector using ridge regression. Secondly, it designs a Long Short-Term Memory (LSTM) network with dual stage attention mechanism as the data-driven component. Then, it integrates the output of ridge regression with the data-driven component, enhancing the accuracy and reliability of the deep learning model with the scientific knowledge of the physics model. Lastly, the proposed HPDD-Observer was validated through simulation tests using MATLAB/Simulink and CarSim software, followed by real-world vehicle testing. Experimental results validate that the proposed HPDD-Observer effectively combines the strengths of deep learning and physics models without any adverse effects.