Jiong Li

To address the difficulty of simultaneously satisfying terminal state constraints and time cooperation in cooperative missions of multiple cross-domain unmanned aerial vehicles, a cooperative trajectory optimization method based on improved generalized quasi-spectral model predictive static programming (GS-MPSP) is proposed. First, to overcome the local control information coupling and the insufficient accuracy of terminal constraint satisfaction that arise when the conventional (original) GS-MPSP updates the control variables in the spectral coefficient space, the spectral coefficient update scheme is abandoned and the control variables are optimized directly in the Legendre–Gauss–Lobatto (LGL) node space. The node control variables are mapped onto a fine grid by the Legendre orthogonal projection method for trajectory integration so that the control adjustment at each node can respond independently to the terminal constraint requirements. Second, an aerodynamic-drag energy term is introduced into the performance index, and penalty terms for the dynamic pressure, heat flux, and overload constraints are constructed, thereby achieving trajectory design that accounts for both energy optimization and path constraint satisfaction. Furthermore, the improved GS-MPSP algorithm is nested with a time consensus protocol to construct two multi-vehicle cooperation architectures, namely distributed and decentralized ones. Simulation results show that, compared with the conventional (original) GS-MPSP, the proposed method reduces the terminal position error by 83.8% (distributed) and 87.6% (decentralized) on average; that is, the accuracy is improved by a factor of 6.2 and 8.1 (up to 11.1), the time-consensus error is reduced by approximately 20%, and the total energy loss of the three vehicles is reduced by 3.5–4.2%; compared with the Gauss pseudospectral method (GPM), the terminal position error is reduced by 94.5–94.7% and the computation time is shortened by about two orders of magnitude; compared with the trajectory shaping guidance law (TSGL) method, the terminal position error is lower by about five orders of magnitude and the energy loss is lower by 24.9–27.5%. In 300 Monte Carlo simulations, the cooperative mission completion rates are 94.33% and 96.67%, the time-consensus convergence rates are 100% and 97.56%, and all process constraints are satisfied throughout. The proposed method can provide an effective solution for multi-vehicle cooperative trajectory planning in complex autonomous flight missions.

Traditional parameter estimation-based trajectory prediction algorithms for Reentry Glide Vehicles (RGVs) typically suffer from limitations, as they neglect the influence of state variables and rely heavily on high-dimensional motion information. To address these issues, this paper proposes an intelligent trajectory prediction algorithm for RGV via physics-informed constraints and state predictive control. First, based on linear system theory, we derived an analytical expression for the prediction error in parameter estimation methods and demonstrated the superiority of these methods through simulations. Second, the Transformer network based on parallel generative decoding pioneers a parameter estimation method of state predictive control, effectively enhancing the accuracy of medium-to-long-term trajectory prediction for RGVs and resolving the dependency of such methods on high-precision parameter estimation information. Finally, by incorporating physics-informed loss during network training based on the dynamic constraints between state variables and control inputs, the network is transformed into a knowledge-data dual-driven model. Simulation results demonstrate that compared to traditional parameter estimation methods, the proposed method exhibits higher prediction accuracy and improved robustness, offering significant engineering application value. Specifically, for prediction durations ranging from 50 to 200 s, this method keeps the average prediction error and the maximum prediction error within 1.4 km and 3.4 km, respectively.

To address the challenges of strong nonlinearity, stringent terminal constraints, and the trade-off between computational efficiency and accuracy in the midcourse guidance trajectory optimization problem of aerodynamically controlled interceptors, this paper proposes a variable-discrete-scale sequential convex programming (SCP) method. Firstly, a dynamic model is established by introducing the range domain to replace the traditional time domain, thereby reducing the approximation error of the planned trajectory. Second, to overcome the critical issues of solution space restriction and trajectory divergence caused by terminal equality constraints, a terminal error-proportional relaxation approach is proposed. Subsequently, an improved second-order cone programming (SOCP) formulation is developed through systematic integration of three key techniques: terminal error-proportional relaxation, variable trust region, and path normalization. Finally, an initial trajectory generation algorithm is proposed, upon which a variable-discrete-scale optimization framework is constructed. This framework incorporates a residual-driven discrete-scale adaptation mechanism, which balances discretization errors and computational load. Numerical simulation results indicate that under large discretization scales, the computation time required by the improved SOCP is only about 5.4% of that of GPOPS-II. For small-discretization-scale optimization, the SCP method with the variable discretization framework demonstrates high efficiency, achieving comparable accuracy to GPOPS-II while reducing the computation time to approximately 7.4% of that required by GPOPS-II.

To address the key issues in cooperative collision avoidance of multiple aircraft, such as unknown dynamics, external disturbances, and limited communication resources, this paper proposes a reference correction method based on the Artificial Potential Field-Control Barrier Function (APF-CBF) and combines it with a dynamic event-triggered mechanism to achieve efficient cooperative control. This paper adopts a Fuzzy Wavelet Neural Network (FWNN) to design a finite-time disturbance observer. By leveraging the advantages of FWNN, which integrates fuzzy logic reasoning and the time-frequency locality of wavelet basis functions, this observer can synchronously estimate system states and unknown disturbances, to ensure the finite-time uniformly ultimate boundedness of errors and break through the limitation of insufficient robustness in traditional observers. Meanwhile, the APF is embedded in the CBF framework. On the one hand, APF is utilized to intuitively describe spatial interaction relationships, thereby reducing reliance on prior knowledge of obstacles; on the other hand, CBF is used to strictly construct safety constraints to overcome the local minimum problem existing in APF. Additionally, the reference correction mechanism is combined to optimize trajectory tracking performance. In addition, this paper introduces a dynamic event-triggered mechanism, which adjusts the triggering threshold by real-time adaptation to error trends and mission phases, realizing “communication on demand”. This mechanism can reduce communication resource consumption by 49.8% to 69.8% while avoiding Zeno behavior. Theoretical analysis and simulation experiments show that the proposed method can ensure the uniformly ultimate boundedness of system states and effectively achieve safe collision avoidance and efficient formation tracking of multiple aircraft.

This paper proposes a hierarchical cooperative tracking control method for multi-missile formations under dynamic event-triggered mechanisms, addressing parameter uncertainties and saturated overload constraints. The proposed hierarchical structure consists of a reference-trajectory generator and a trajectory-tracking controller. The reference-trajectory generator considers communication and collaboration among multiple interceptors, imposes saturation constraints on virtual control inputs, and generates reference trajectories for each receptor, effectively suppressing aggressive motions caused by overload saturation. On this basis, a radial basis function neural network (RBFNN) combined with a sliding-mode disturbance observer is adopted to estimate unknown external disturbances and unmodeled dynamics, and the finite-time convergence of the disturbance observer is proved. A tracking controller is then designed to ensure precise tracking of the reference trajectory by missile. This approach not only reduces communication and computational burdens but also effectively avoids Zeno behavior, enhancing the practical feasibility and robustness of the proposed method in engineering applications. The simulation results verify the effectiveness and superiority of the proposed method.

In midcourse guidance, strong constraints and dual-channel control coupling pose major challenges for trajectory optimization. To address this, this paper proposes an optimal guidance method based on terminal relaxation and range convex programming. The study first derived a range-domain dynamics model with the angle of attack and bank angle as dual control inputs, augmented with path constraints including heat flux limitations, to formulate the midcourse guidance optimization problem. A terminal relaxation strategy was then proposed to mitigate numerical infeasibility induced by rigid terminal constraints, thereby guaranteeing the solvability of successive subproblems. Through the integration of affine variable transformations and successive linearization techniques, the original nonconvex problem was systematically converted into a second-order cone programming (SOCP) formulation, with theoretical equivalence between the relaxed and original problems established under well-justified assumptions. Furthermore, a heuristic initial trajectory generation scheme was devised, and the solution was obtained via a sequential convex programming (SCP) algorithm. Numerical simulation results demonstrated that the proposed method effectively satisfies strict path constraints, successfully generates feasible midcourse guidance trajectories, and exhibits strong computational efficiency and robustness. Additionally, a systematic comparison was conducted to evaluate the impact of different interpolation methods and discretization point quantities on algorithm performance.

This paper proposes a hierarchical cooperative tracking control method for multi-missile formations under dynamic event-triggered mechanisms, addressing parameter uncer-tainties and saturated overload constraints. The proposed hierarchical structure consists of a reference trajectory generator and a trajectory tracking controller. The reference tra-jectory generator considers communication and collaboration among multiple intercep-tors, imposes saturation constraints on virtual control inputs, and generates reference trajectories for each receptor, effectively suppressing aggressive motions caused by overload saturation. On this basis, a Radial Basis Function Neural Network (RBFNN) combined with a sliding mode disturbance observer is adopted to estimate unknown external disturbances and unmodeled dynamics, and the finite-time convergence of the disturbance observer is proved. A tracking controller is then designed to ensure precise tracking of the reference trajectory by missile. This approach not only reduces commu-nication and computational burdens but also effectively avoids Zeno behavior, enhancing the practical feasibility and robustness of the proposed method in engineering applica-tions. Simulation results verify the effectiveness and superiority of the proposed method.

This paper proposes a trajectory prediction method via the adaptive cost function to address the difficulties in inferring the attack intention and maneuver mode, as well as the accumulation of prediction error during the trajectory prediction of reentry glide vehicles. Firstly, the vehicle guidance task is divided into two distinct categories: conventional guidance and no-fly zone avoidance guidance. A task-matched time-varying parameter prediction model set is then constructed. Secondly, taking into account the maneuverability, guidance intent, and battlefield situation of the vehicle, an adaptive intent cost function adapted to the guidance task is proposed, which avoids the estimation failure problem caused by manually setting cost coefficients in traditional methods. Finally, long-term trajectory prediction of vehicles is achieved using Bayesian theory to infer the attack intent and parametric model with the maximum a posteriori probability. The results of the simulations demonstrate that the proposed prediction method is capable of accurately inferring the vehicle’s attack intention and parameter model, and of effectively reducing the accumulation of prediction errors and the time required for the algorithmic process compared to existing methods.

To address the problem of low accuracy and efficiency in trajectory planning algorithms for interceptors facing multiple constraints during the midcourse guidance phase, an improved trajectory convex programming method based on the lateral distance domain is proposed. This algorithm can achieve fast trajectory planning, reduce the approximation error of the planned trajectory, and improve the accuracy of trajectory guidance. First, the concept of lateral distance domain is proposed, and the motion model of the midcourse guidance segment in the interceptor is converted from the time domain to the lateral distance domain. Second, the motion model and multiple constraints are convexly and discretely transformed, and the discrete trajectory convex model is established in the lateral distance domain. Third, the deep reinforcement learning algorithm is used to learn and train the initial solution of trajectory convex programming, and a high-quality initial solution trajectory is obtained. Finally, a dynamic adjustment method based on the distribution of approximate solution errors is designed to achieve efficient dynamic adjustment of grid points in iterative solving. The simulation experiments show that the improved trajectory convex programming algorithm proposed in this paper not only improves the accuracy and efficiency of the algorithm but also has good optimization performance.

Concerned with the problem of interceptor midcourse guidance trajectory online planning satisfying multiple constraints, an online midcourse guidance trajectory planning method based on deep reinforcement learning (DRL) is proposed. The Markov decision process (MDP) corresponding to the background of a trajectory planning problem is designed, and the key reward function is composed of the final reward and the negative step feedback reward, which lays the foundation for the interceptor training trajectory planning method in the interactive data of a simulation environment; at the same time, concerned with the problems of unstable learning and training efficiency, a trajectory planning training strategy combined with course learning (CL) and deep deterministic policy gradient (DDPG) is proposed to realize the progressive progression of trajectory planning learning and training from satisfying simple objectives to complex objectives, and improve the convergence of the algorithm. The simulation results show that our method can not only generate the optimal trajectory with good results, but its trajectory generation speed is also more than 10 times faster than the hp pseudo spectral convex method (PSC), and can also resist the error influence mainly caused by random wind interference, which has certain application value and good research prospects.