In this paper, the problem of prescribed-time tracking control with unified prescribed performance is studied for multi-input multi-output (MIMO) nonlinear systems with mismatched nonvanishing disturbances, actuator faults, and time-varying control coefficients whose sign and magnitude are both unknown. On the one hand, a novel prescribed-time stability criterion using Nussbaum functions is proposed to deal with the issues raised by the presence of mismatched nonvanishing disturbances, actuator faults, and time-varying control coefficients. This criterion is of independent interest and can be used beyond the control problem addressed in this paper. On the other hand, based on the proposed stability criterion, a prescribed-time tracking control framework is developed so that the tracking error converges to zero within a prescribed time, in the presence of the aforementioned complicating factors. Compared with existing asymptotic stability results for uncertain MIMO nonlinear systems subject to unknown control coefficients, the proposed framework guarantees that the tracking error remains within the unified prescribed performance boundary, which is uniform with respect to different initial tracking errors, thereby eliminating the need for controller redesign and stability reanalysis. The proposed control method is verified via an electromechanical system and a robot manipulator system in numerical simulation.

In this article, we propose a self-triggered distributionally robust model predictive control algorithm for linear discrete systems with state chance constraints and unbounded stochastic disturbances. Assuming that only the first and second moments of the disturbance are accessible, we transform the objective function into a compact quadratic form and reformulate the state chance constraints into linear inequalities, which is more tractable when solving. In order to reduce communication and sampling times of the system, we propose a self-triggered update scheme, in which the state sampling and the control input sequence are updated when the control performance predicted based on the current sampling exceeds that of the periodic sampling scheme. We demonstrate that the optimization problem in the proposed self-triggered model predictive control (MPC) method is recursively feasible and stable. Numerical simulation results verify the effectiveness of the proposed algorithm.

To address the inadequate coverage of fixed-orbit constellations for emergent tasks, this paper proposes a Multi-Stage Integrated Optimization Framework (M-IOF) that couples discrete task assignment with continuous orbital maneuver planning. In this framework, candidate task chains generated by the scheduler are evaluated through inverse orbit design, and the corresponding feasibility information is fed back to the fitness function. Spatial-functional task clustering is first used to reduce the dimensionality of large-scale heterogeneous tasks. Then, a target-driven inverse orbit solving method maps spatio-temporal constraints into feasible resonant phasing conditions. By considering J2 perturbations, a one reconfiguration maneuver plan strategy is formulated, enabling satellites to sequentially observe multiple targets through passive drift after one initial maneuver. The scheduling model is solved using an adaptive genetic algorithm with feasibility penalties. Comparative simulations under three task-structure scenarios show that M-IOF improves target completion and task efficiency while reducing unnecessary maneuvering. The results demonstrate the effectiveness of the proposed framework for responsive constellation reconfiguration.

This paper investigates the problem of resilient satellite coordinate formation control considering two issues: a) the network may contain some Byzantine satellites, which update controls abnormally and can send arbitrarily different information to neighbors; b) the inter-satellite communication contains unknown but bounded noise. The former can drive the motion of normal satellites arbitrarily and deteriorate formation performances or even destroy the formation. Moreover, communication noises may be coupled with the erroneous information sent by adversaries and make normal satellites difficult to suppress the Byzantines' effects on formation control. Two formation scenarios are considered. In the first, each satellite can access its desired formation coordinate trajectory, while in the second, such information is only known by leaders and other satellites can access the desired relative positions with respect to neighbors. For each scenario, a novel consensus-based coordinate formation method is proposed guaranteeing that normal satellites are unaffected by the disruption of Byzantine satellites. By the proposed methods, normal satellites can communicate with neighbors periodically in discrete times and their states always evolve boundedly, and converge to be around the desired values. The conditions on the communication period and the graph connectivity that can ensure the achievement of resilient formations are characterized. The effectiveness of proposed methods are verified by numerical examples.

In this brief, we investigated an approximation-free event-triggered spacecraft formation flying (SFF) controller with prescribed performance. The parameter identification technique is not required in the control scheme, alleviating the computation burden. In addition, the communication burden can be reduced in terms of two aspects: by utilizing the model-free distributed control method, the position of neighbor spacecraft is the only information required to be transmitted; meanwhile, the control input needs to be updated only at the event-triggering instants by employing a event-triggered mechanism. Finally, a numerical example is conducted to illustrate the effectiveness of the proposed controller.

Distributed stochastic model predictive control (DSMPC) of linear systems with coupled chance constraints under disturbances is investigated in this paper. We consider a practical scenario where only the mean and covariance, but not the exact distribution, of the disturbance is available. A frozen technique is utilized to ensure the satisfaction of the coupled constraints, and a deterministic convex tight reformulation is used for handling the chance constraints based on the available information of the disturbance. Recursive feasibility and convergence of the proposed method are proved. Numerical simulations are given to demonstrate the effectiveness of the proposed algorithm.

This paper presents a distributed model predictive control (DMPC) method for multi-satellite cooperative encirclement. Based on the relative motion dynamics of the satellite, the cost function of cooperative encirclement control is designed. To ensure the smooth execution of the encirclement mission, constraints including control input saturation, limited communication range, and safety requirements are incorporated. By introducing the synchronous execution mechanism, each defense satellite can optimize its control strategy after information exchange, reaching the desired encirclement position. Finally, simulation results validate the presented control strategy's effectiveness in multi-satellite cooperative encirclement. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons,org/licenses/by-nc-nd/4.0/)

This paper proposes a UAV-assisted communication framework that jointly optimizes trajectory planning and motion control through weighted reinforcement learning. Unlike traditional methods that decouple trajectory design and tracking control, our approach integrates both processes in a unified learning architecture, effectively mitigating the accumulated errors and redundant computations inherent in sequential optimization. To resolve convergence difficulties in multi-task coordination, we propose a dynamic strategy that adjusts the priority between communication reliability and energy efficiency during different mission stages. Compared to methods with fixed weights, the proposed trajectory planning method achieves superior communication performance. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons,org/licenses/by-nc-nd/4,0/)

In this paper, we demonstrate a new model identification method for spacecraft rendezvous with few amounts of data and low computational burdens by utilizing sparse identification for nonlinear dynamical (SINDy). Besides, a control scheme composed of SINDy and Linear Quadratic Regulator (LQR) is demonstrated, which aims to enhance the robustness and optimality simultaneously. The numerical results show the effectiveness of the proposed control scheme for spacecraft rendezvous mission.

In this paper, we focus on the proximate orbital pursuit-evasion game of two spacecraft with magnitude-bounded continuous controls. Two scenarios are considered depending on whether the pursuer can access the control magnitude of the evader initially. When the pursuer accesses such information, we propose a fast numerical method for computing a sub-optimal control of the pursuer that guarantees the capture of the evader. The key to accelerating the solving is using a polynomial to approximate an important integration in the control computation, whose direct computing involves repeated calculations of matrices’ singular values. When the control magnitude of the evader is unavailable, we first propose a simple estimator for the evader’s control magnitude, by which the pursuer can estimate the maximal control effort of the evader disclosed over the history based on measured states. Based on the estimate, another fast method for computing the sub-optimal pursuing control is proposed based again on polynomial approximation. Then, considering practical measurements, we analyze how measurement noises influence the estimation of the control magnitude and the pursuing control computation. Finally, we present numerical examples to test the proposed computing methods and discuss the influence of noises.

In this paper we propose a stochastic model predictive control method for discrete linear unmanned aerial vehicle (UAV) guidance system with additive total disturbance. The velocity constraint is given in the form of two-sided joint chance constraint, while the acceleration constraint is a hard constraint. Based on the Boole's inequality and known probability distribution, we propose a deterministic convex transformation method for chance constraint. Subsequently, a stochastic model predictive control algorithm is derived. The effectiveness of the proposed algorithm is verified through a numerical simulation example.

This paper utilizes the distributed model predictive control (DMPC) method to investigate the formation control problem of unmanned aerial vehicles (UAVs) in the obstacle environment and establishes cooperative capability evaluation metrics of the swarm. Based on the DMPC approach, the formation cost function is constructed to adjust the relative positions and velocities of UAVs, ensuring the desired formation. Additionally, to address the obstacle avoidance problem in the formation, the obstacle avoidance function is designed to provide safe formation control in the obstacle environment. To evaluate the cooperative capability of UAVs, we design evaluation metrics from multiple dimensions to reflect the swarm’s cooperative capability. Finally, the simulation results show the effectiveness of the formation control method with obstacle avoidance and the applicability of the swarm’s cooperative capability evaluation metrics.

This paper focuses on simultaneous arrival multiple-to-one proximate pursuit-evasion games of spacecrafts with orbital maneuvering ability, where multiple pursuing spacecraft aim to catch one evading spacecraft with the same capture time, while the latter tries its best to avoid the capture. To achieve the objective, We first develop a decentralized control strategy with unknown control magnitude for each pursuing spacecraft based on the minimization of its zero-effort-miss (ZEM) to the evader, by assuming a global same but unknown time-to-go for all pursuers. To complete computing the pursing control, we then let the pursers cooperatively calculate the global time-to-go with local communication, as the maximization of the time-togo of each pursuer when reaching the evader using its maximal control magnitude. The actual control magnitude of each pursuer spacecraft is computed based on a simple algebraic equation constructing locally based on the spacecraft ZEM and the global time-to-go. Simulation shows that the proposed pursing control strategy can make the pursing spacecrafts reach the evading spacecraft at almost the same time.

This note presents our recent results on state estimation of multi-agent systems under homologous attacks. We first present a sufficient and necessary condition on agents’ dynamics such that agents states can be reconstructed under the considered attack with finite time measurements. Violating the condition prohibits the estimation of agents’ states, regardless of the length of time measurements collected. Then, assuming that agents states are reconstructable, we propose a fully distributed discrete-time estimation algorithm. This algorithm allows each agent to estimate its state and the attack signal through local information sharing. Unlike existing discrete-time estimation methods, agents need not to access global information of networks and agents dynamics by the proposed algorithm.

Line formation of migrating birds is well-accepted to be caused by birds exploiting wake benefits to save energy expenditure. A flying bird generates wingtip trailing vortices that stir the surrounding air upward and downward, and the following bird can get a free supportive lift when positioned at the upward airflow region. However, little to no attention has been paid to clarifying birds’ interests in energy saving, namely, do birds intend to reduce their individual energy consumption or the total energy of the flock? Here, by explicitly considering birds’ interests, we employ a modified fixed-wing wake model that includes the wake dissipation to numerically reexamine the energy saving mechanism in line formation. Surprisingly, our computations show that line formation cannot be explained simply by energy optimization. This remains true whether birds are selfish or cooperative. However, line formations may be explained by strategies optimizing energy cost and either avoiding collision or maintaining vision comfort. We also find that the total wake benefit of the formation attained by selfish birds does not differ much from that got by cooperative birds, the maximum that birds can attain. This implies that selfish birds are still able to fly in formation with very high efficiency of energy saving. In addition, we explore the hypothesis that birds are empathetic and would like to optimize their own energy cost and the neighbors’. Our analysis shows that if birds are more empathetic, the resulting line formation shape deviates more from a straight line, and the flock enjoys higher total wake benefit. Author summary Migratory birds can achieve remarkable performance and efficiency in energy exploitation during annual round-trip migration flight. Theoretical and experimental results have shown that this might be achieved because birds fly together in formation with specific shapes, e.g. the noticeable V formation, to utilize the aerodynamic benefits generated by their flock mates. However, it is still unclear whether energy-guided behavior indeed can lead to these formations. We show that the special formation adopted by migratory birds cannot be explained purely by the energy exploitation mechanism, and that birds’ vision performance and collision avoidance very likely also play important roles in the formation emergence. Our results imply that birds fly together in formation because of energy saving, but the specific shape of the formation depends on non-aerodynamic reasons. The research provides further understandings of the emergence of migratory formation and the energy saving mechanism of animal groups. It may also indicate that wing flapping, currently not considered, has an important effect on the way birds exploit aerodynamic benefits from others during the formation flight.

This article revisits the problem of secure state estimation of multiagent systems under homologous attacks in [1]. We first characterize the condition on agents dynamics such that agents states can be uniquely solved from the attacked measurements of agents outputs. This condition implies that the conclusion in [1] that the attack signal and agents states can be uniquely reconstructed by adding longer time-windowed measurements is incomplete. Based on this condition, when the communication graph of agents is undirected, we propose two different distributed secure state estimators by reformulating the state reconstruction as optimization problems. The first estimator does not need agents to exchange with others their dynamics information, which is used by the second, but requires updating and exchanging more variables. Both estimators are much simpler and easier to understand than that proposed in [1]. Moreover, when the communication graph is directed and strongly connected, we also proposed two distributed state estimators, adjusted from the estimators for undirected graphs. Both of them require no global information of communication graphs but the network size. At last, we verify all the theoretical results with simulation examples.

In this paper, we study spacecraft orbital pursuit–evasion games under J2 perturbations. We consider that situation where the thrust of each player is constrained and the control direction cannot deviate from the velocity more than a given angle. After characterizing the optimal control of players under direction constraints, we transfer the pursuit–evasion game into a two point boundary value problem, which is solved by the shooting method. Different with the classical research, the initial guess for the unknown initial adjoint variables and the game ending time are not generated by heuristic approaches, but from the solution of the orbital one-side interception problem with a non-maneuverable evader. We solve the one-side interception problem also by shooting, starting iteratively from multiple initial guesses. In each initial guess, the initial adjoint vector is chosen randomly small while the interception termination time is selected from contiguous feasible time subintervals. The simulations show that the shooting method for the one-side interception problem can converge even if the feasible interval of the termination time is partitioned into a small number of subintervals, and the whole method for solving the pursuit–evasion game can quickly find the saddle-point solution. The effect of the control direction constraint on the game ending time is also discussed.

This paper studies the resilient control of networked systems in the presence of cyber attacks. In particular, we consider the state feedback stabilization problem for nonlinear systems when the state measurement is sent to the controller via a communication channel that only has a finite transmitting rate and is moreover subject to cyber attacks in the form of Denial-of-Service (DoS). We use a dynamic quantization method to update the quantization range of the encoder/decoder and characterize the number of bits for quantization needed to stabilize the system under a given level of DoS attacks in terms of duration and frequency. Our theoretical result shows that under DoS attacks, the required data bits to stabilize nonlinear systems by state feedback control are larger than those without DoS since the communication interruption induced by DoS makes the quantization uncertainty expand more between two successful transmissions. Even so, in the simulation, we show that the actual quantization bits can be much smaller than the theoretical value.