Optimization of a training program for an athlete is a difficult issue in sport science. It is a delicate trade-off between stimulating performance enhancement and allowing adequate recovery to prevent injury. The paper, presents a detailed structure of the offline optimization of training loads using the DQN architecture. The framework overcomes the simulation gap by applying a data-driven transition model as a digital twin, which can be used to find the optimal training policies without the ethical or safety concerns of conducting the experiment in real-time on athletes. This intelligent model, founded on comprehensive physiological and performance data collected from 25 athletes over a whole training season, has the capacity to dynamically provide ideal training prescriptions like increased intensity, increased volume, or active recovery. Considered data include parameters such as Heart Rate Variability (HRV), sleep quality, training loads, Acute to Chronic Workload Ratio (ACWR), and weekly performance. The proposed architecture uses a feedforward neural network as an estimator of the Q-value function. By optimizing the adaptive ε-Greedy policy and the Experience Replay Buffer, the stability and efficiency of the learning process are ensured. In addition, a dual reward function including performance reward and physiological state reward is designed. This function guides the agent towards policies that simultaneously lead to short-term performance improvement and long-term health maintenance of the athlete. The experimental results show that the model has successfully reduced the error rate and has tended to converge to near zero for the loss function. Also, the proposed method has shown a high ability in managing training load and controlling the risk of injury, in such a way that it has been able to dynamically and with high adaptability reduce the risk and always maintain the performance of athletes within the optimal range.

This study investigates vibration control strategies for flexible manipulators subject to human interaction. Since the original dynamic model consists of coupled ordinary and partial differential equations, singular perturbation technique is employed to separate it into slow and fast dynamics. Then, a transfer function model is introduced to model the human interaction behavior in the slow subsystem and an auxiliary feedback control law is proposed. Accordingly, the fast subsystem is controlled by an automation controller. Lyapunov-based analysis yields sufficient conditions for subsystem stability, with control gains determined via linear matrix inequalities. Furthermore, we also give the stability criterion for the full system to ensure the effectiveness of the designed controller. This work provides a basic research for the interaction between the human and flexible manipulator. Finally, simulation results are provided to demonstrate the feasibility of the proposed control method.

This paper addresses the prescribed-time cooperative guidance problem for striking a target under time-varying velocity, leveraging deep neural networks to enhance prediction accuracy. Unlike existing results, the proposed guidance law guarantees the stability of the guidance error system even under switching topologies. First, a 3-D vector-based cooperative guidance model is established, and the cooperative guidance objective is formulated. To achieve precise time-to-go estimation under time-varying velocity, a high-precision prediction algorithm based on deep neural networks is developed. Building on this, a practical prescribed-time cooperative guidance law accounting for time-varying velocity is designed, with rigorous stability analysis provided for the guidance error system under switching topologies. Furthermore, based on guidance trajectory analysis, 2-D results in both horizontal and vertical planes are provided. Finally, the proposed method is validated through numerical simulations and equivalent physical experiments.

This paper studies a multiplayer reach-avoid game with multiple goal subregions. The pursuers aim to defend these goal subregions against the evaders from reaching any one of them. Compared to the existing works for one goal subregion, protecting multiple goal subregions is more challenging, as the pursuers have no prior information about which goal subregion an evader tries to reach. The evaders can change the goal subregions to reach in real time, further complicating the synthesis of pursuit winning strategies. We propose a multiplayer multiple-goal-subregion safe-distance (MMS) pursuit strategy that can ensure an increasing lower bound of the number of guaranteed defeated evaders. This pursuit strategy adopts the divide-and-conquer approach via subgame outcomes for multiple pursuers against one evader. First, we introduce expanded Cartesian ovals and propose the Cartesian oval confinement pursuit strategy that can guarantee to confine the evader inside the initial expanded Cartesian ovals, showing that the Cartesian oval is sufficient for many reach-avoid games. We introduce the concept of safe distance and present the resulting Cartesian oval based pursuit winning conditions. Then, we propose two pursuit strategies when an evader can guarantee the evasion winning. The two pursuit strategies ensure that the minimum and weighted negative safe distances are non-decreasing, respectively. In each horizon, the task assignment is represented as two classes of matchings and generated via a maximum matching that fuses the subgame outcomes. Pruning methods are also proposed to eliminate some subgames from consideration without affecting the optimality. Numerical examples are presented to illustrate the results.

This article addresses the 3-D helical guidance problem for attacking a stationary target. Different from the existing works, a 3-D helical guidance law is developed to cater for impact time constraints. First, an analytical time-to-go estimation expression is proposed, and a vector guidance law is designed by using an inverse design method to ensure accurate time-to-go prediction. Furthermore, a helical term is incorporated to induce helical maneuvers, enhancing the system observability without compromising time-to-go estimation accuracy. To broaden applicability, a biased feedback command is augmented to accommodate diverse impact time constraints, with a rigorous convergence proof provided via Lyapunov theory. In addition, an unmanned aerial vehicle-based pure physical system and a fixed-wing hardware-in-the-loop system are introduced to provide experimental validation. Finally, the effectiveness and reliability of the proposed guidance law are confirmed through both numerical simulations and physical experiments.

This article investigates the time-varying formation tracking control problem for disturbed multiagent systems with a nonautonomous leader. The main challenge in solving this problem lies in dealing with the coupling among the formation tracking control object, leader’s unknown input, and unknown disturbances in followers’ dynamics. To overcome this challenge, a novel internal-model-based formation tracking controller is developed, which relies on a proposed distributed prescribed-time observer. First, a novel fully distributed adaptive observer is designed to estimate the leader’s state in the presence of unknown input within a prescribed time. Second, on the basis of the proposed adaptive observer, a kind of internal-model-based formation tracking controller is proposed under the influence of fully unknown disturbances. Based on Lyapunov stability theory, the stability of the system is rigorously proven. Finally, an experimental platform consisting of five autonomous aerial vehicles (AAVs) is established to verify the effectiveness of the proposed methods in formation tracking control, prescribed-time estimation, and disturbance rejection performance.

This article addresses an autonomous bipartite time-varying formation control problem for heterogeneous multiagent systems (MASs). Unlike traditional formation control methods, the proposed approach enables two antagonistic time-varying formations to emerge without requiring a common reference model or shared trajectory information. To tackle this problem, a novel dynamic update law and an adaptive formation control strategy, based solely on local output information, are proposed. The proposed controller allows agents to autonomously cooperate via a communication network to align with an implicit common reference trajectory and achieve the desired bipartite formation, independent of network topology. A rigorous Lyapunov-based analysis establishes the stability and convergence of the proposed fully distributed controller. The effectiveness of the approach is validated through both numerical simulations and real-world experiments on a platform consisting of six uncrewed ground vehicles (UGVs).

This paper investigates an event-triggered quantized consensus control method for strict-feedback multi-agent systems. The systems are subject to external disturbances. Only the first state is measurable. Extended state observers based controller is employed to estimate the other states and disturbances. To effectively conserve communication resources, an event-triggered strategy is adopted to dynamically regulate the timing of data transmission, significantly reducing the communication frequency. Moreover, a dynamic quantizer is employed to quantify the system’s states and an encoder–decoder structure is designed to transmit data, which reduces the communication word length to a finite number of bits. Theoretical analysis proves that the multi-agent system can reach consensus within a specified maximum quantization level while the communication graph contains a directed spanning tree. Simulations and experiments are conducted to validate the proposed method, demonstrating its ability to significantly reduce the amount of transmitted data.

This paper proposes an analytical Koopman-based linear model predictive control (MPC) method for real-time quadrotor trajectory tracking. While linear MPC offers computational efficiency, it sacrifices modeling fidelity; nonlinear MPC solved via sequential quadratic programming achieves high accuracy but requires multiple iterations at each control step. We develop a systematic procedure to derive Koopman observables that lift the dynamics into a quasi-linear model with state-dependent control matrix. An assumed state trajectory converts this to a linear time-varying system at each control period, enabling quadratic program formulation with guaranteed real-time solvability. An incremental nonlinear dynamic inversion (INDI)-based robust control allocation scheme is proposed, which requires no precise control effectiveness model. Simulation results demonstrate tracking performance comparable to nonlinear MPC with deterministic computation times. The proposed method requires no training data collection, making it straightforward to implement.

In this study, modeling based on game theory and strategic reasoning is employed to investigate a critical three-player conflict scenario involving active target defense engagement. In this scenario, a target aircraft deploys a defending missile to intercept an adversarial attacking missile that follows proportional navigation. Distinct from existing studies that primarily consider target evasive maneuvers or focus solely on the strategy of the defending missile, this study introduces a stationary virtual pinning point and proposes a cooperative pinning game (CPG) strategy, where the target aircraft actively maneuvers to geometrically constrain the trajectory of the attacking missile to pass through this point. This creates a predictable flight path for the attacking missile, enabling the defending missile to achieve head-on interception. First, an active target defense model is formulated, incorporating an attacking missile, a defending missile, a target aircraft, and a pinning point. Thereafter, a CPG strategy is proposed, where guidance laws for pinning and defense are jointly designed to meet the strategic requirements, and a feasible pinning point region is determined to ensure that the strategy can be practically implemented. Furthermore, a physical verification system is developed using multiple unmanned ground vehicles. Finally, numerical simulations and physical experiments are conducted to validate the effectiveness of the proposed strategy and its hardware adaptability.

The typical feature of an air-breathing hypersonic vehicle is the integrated design of the airframe and propulsion systems, which introduces a coupling challenge among aerodynamics, propulsion, control, and flight trajectory. In this study, an integrated aerodynamic-trajectory optimization method incorporating stability constraints is proposed to address this issue. The proposed method adopts a two-layer optimization framework. The outer-layer optimization focuses on configuration parameters, while the inner-layer optimization deals with flight trajectory. In the optimization process, static stability is taken into account as a constraint condition. This integrated method enables mission-level co-optimization of airframe geometry and flight trajectory, achieving synergistic improvements in overall system performance. Meanwhile, to validate this method, a Sa & uml;nger-type two-stage-to-orbit (TSTO) vehicle was investigated with the minimum climb-phase fuel consumption as the optimization objective. The key design variables included the parameters of the integrated forebody-inlet and aftbody-nozzle. Optimization results demonstrate a 13.6% reduction in fuel consumption of the climb phase compared to baseline configuration, which effectively improves the climbing performance of the vehicle and validates the optimization framework in this paper.

This paper investigates the impact time control guidance problem under field-of-view (FOV) constraints. Unlike existing results, the proposed method avoids control singularity, which enhances the reliability of the guidance system. First, a guidance model is formulated and the corresponding guidance objectives are explicitly defined. Then, a nominal guidance law is developed using an inverse-dynamics-based design method to enable accurate time-to-go prediction. Subsequently, by incorporating impact-time error feedback, a nonsingular impacttime guidance law with FOV constraints is proposed, and the stability of the impact-time error is rigorously proven. Finally, numerical simulations and equivalent physical experiments are conducted to comprehensively validate the effectiveness of the proposed method.

An Impact Time and Angle Control Guidance (ITACG) problem with constraints on maximum lateral acceleration is investigated in this paper. The goal for this problem is to achieve precise interception of a stationary target at the desired impact time and angle, while considering the maximum lateral acceleration constraint during the guidance process. The previous ITACG methods generally struggled to handle a large initial heading error, severely limiting the guidance law’s application scenarios. To tackle this problem and account for the maximum lateral acceleration constraint, an ITACG strategy is proposed from the perspectives of optimal guidance trajectory design and trajectory tracking in this paper. First, a guidance model is formulated, where Bézier curves are used to fit the guidance trajectory, and by parameterizing these curves and analyzing the trajectory constraints in detail, the optimal guidance trajectory design problem is transformed into an optimization problem of the control parameters. Then, a multi-layer zeroth-order Adam trajectory optimization algorithm is introduced to determine the control parameters without relying on gradient information. Subsequently, a hyperbolic tangent vector field trajectory tracking guidance algorithm is proposed to follow the pre-designed trajectory accurately. Finally, numerical simulations and equivalent physical experiments verify the effectiveness of the proposed guidance strategy.

This article addresses the problem of robust time-varying output formation tracking (TVOFT) in heterogeneous multiagent systems (MASs) having multiple heterogeneous leaders under a directed topology, where both followers and leaders may exhibit distinct dynamics and dimensional properties. The objective is for the followers to track a predefined convex combination of the leaders’ outputs while simultaneously achieving an expected time-varying formation. Current related approaches often assume that each follower is either well-informed (i.e., connected to all leaders) or uninformed. This work overcomes this constraint by introducing a novel approach that employs a fully distributed observer-based scheme. First, the proposed method utilizes neighboring information and local estimations to design an adaptive observer for each follower that can estimate multiple leaders’ states with unknown inputs. Besides, to further handle the unknown external disturbances, a novel neuro-adaptive learning algorithm is proposed. Moreover, the output regulation method and the Lyapunov stability theory are used to establish robust TVOFT criteria for the closed-loop system based on the proposed observer-based control protocol. The parameters of the control protocol are derived using a structured four-step algorithm. At last, a heterogeneous experimental platform consisting of three autonomous aerial vehicles and three autonomous ground vehicles is constructed to validate the theoretical results.

This article addresses a prescribed-time time-varying output formation tracking (TVOFT) problem for heterogeneous multiagent systems (MASs) under directed topologies. Formation tracking in heterogeneous linear MASs is critical for practical applications, such as cooperative robotics, autonomous transportation, and surveillance. However, many existing related designs often fail to guarantee convergence within a prescribed time. To overcome this limitation, a distributed prescribed-time TVOFT protocol associated with a corresponding design algorithm is presented. In the designed protocol, a distributed output-feedback observer is constructed for each follower to estimate the state of the leader within a prescribed time. Then, a local output-feedback controller is developed by incorporating a local state observer. It is proved that the heterogeneous MASs can achieve the desired TVOFT within the prescribed time. Furthermore, a heterogeneous experimental platform consisting of two autonomous aerial vehicles and three autonomous ground vehicles, is constructed to verify the effectiveness of the proposed prescribed-time TVOFT design. Comparative experiment results highlight the advantages of the proposed design over existing methods from the perspective of accurate prescribed-time convergence and practical feasibility.

This paper proposes a safe model predictive control (Safe-MPC) framework that integrates physics-informed neural networks (PINNs), model predictive control (MPC), and control barrier functions (CBFs), aiming to achieve safe trajectory tracking of nonlinear systems in complex environments with obstacles. The proposed approach leverages PINNs to learn system dynamics from limited data while preserving physical consistency. The learned model is then embedded into the rolling prediction module of MPC, enabling accurate and real-time solvable control strategies. In parallel, CBFs are incorporated in a soft-constraint formulation to enforce safety constraints on the system states, ensuring that they remain outside unsafe regions throughout the optimization process. Simulation results on a two-dimensional nonlinear system demonstrate that the proposed method can accurately track the reference trajectory and effectively avoid static obstacles. The system trajectory converges stably, validating the effectiveness and safety of the proposed method. Compared with traditional MPC methods based on explicit physical models, the proposed Safe-MPC framework exhibits superior performance in terms of modeling flexibility and tracking accuracy. Future work will extend the framework to higher-dimensional systems and validate its performance on real-world robotic platforms.

To enhance adaptability in practical applications, active disturbance rejection control is extended to uncertain nonaffine systems with input saturation, achieving practical prescribed-time tracking control that drives the error to a sufficiently small neighborhood within a user-defined settling time. Based on a time-varying function called time base generators (TBG), a more general practical prescribed-time (PPT) nonlinear extended state observer (NLESO) is designed to estimate unknown states and total uncertainties while effectively suppressing peaking phenomena. By utilizing the PPT NLESO outputs, a TBG-based saturation control law is constructed to achieve PPT output tracking and address the nonaffine-in-control problem. The local PPT convergence of the closed-loop system under low-level input saturation is proved in a new paradigm. The numerical simulation and semi-physical simulation on the F-16 aircraft demonstrate the efficacy and superiority of the proposed method.

Time-varying formation tracking (TVFT) control problem for multiple Euler-Lagrange (EL) systems with an uncertain leader is investigated in this article. The objective of this problem is for the followers' states to track the uncertain leader's output and achieve the desired formation. One of the major challenges in solving such a problem lies in estimating the information of the leader. In this article, an observer-based TVFT control framework is presented in this article, which does not require all or part of the follower agents to know the system dynamic knowledge of the leader agent directly in advance. First, two fully distributed adaptive observers are presented for estimating the uncertain leader's state, output, and the unknown system matrices under an IE condition, which relaxes the existing restrictive persistently exciting or cooperative finite-time excitation condition. Then, on the basis of the constructed adaptive observers, state and output variables of the leader, a fully distributed TVFT for EL systems with an uncertain leader is developed, which means the proposed formation tracking controller operates independently of the system dynamic knowledge of the leader agent; with the help of the Lyapunov stability theory, the TVFT criterion for the considered system is derived. Finally, in order to demonstrate the theoretical results derived in this article, a practical air-ground formation tracking platform, which consists of an unmanned aerial vehicle and four unmanned ground vehicles, is introduced, and physical experimental results are obtained.

Integrated guidance and decision-making (IGDM) problems are investigated. Unlike previous works, the expected angles are autonomously determined. Firstly, a fundamental angle-constrained optimal guidance law is proposed, and the properties of the fundamental guidance law are analyzed. Then, a spatiotemporal-constrained distributed prescribed time guidance law is derived, which ensures zero acceleration component at the prescribed time. Furthermore, the pay-off function favorable for rapid arrival is presented. The distributed optimization-based expected angle decision-making strategy is then developed, ultimately leading to the IGDM law and algorithm. Finally, the effectiveness of the theoretical results is validated through numerical simulation and experimental results.

For a class of uncertain nonlinear stochastic multiagent systems, a consensus control strategy is proposed with an adjustable-time-varying-gain-based event-triggered extended state observer (ATVG-ETESO) via dual-terminal event-triggered mechanism (DTETM). The ATVG-ETESO estimates internal uncertainties and external stochastic disturbances. Its adjustable time-varying gain avoids peaking phenomenon at the initial stage and accelerates estimation error convergence. A DTETM with an adaptive threshold reduce communication burdens on both the input and output channels of the ATVG-ETESO. Theoretically, both the ATVG-ETESO estimation errors and the state consensus errors are bounded. Finally, two illustrative simulation examples are given to illustrate the effectiveness of the control strategy.