The concept of the spacecraft Reachable Domain(RD)has garnered significant scholarly attention due to its crucial role in space situational awareness and on-orbit service applications.While the existing research has l...The concept of the spacecraft Reachable Domain(RD)has garnered significant scholarly attention due to its crucial role in space situational awareness and on-orbit service applications.While the existing research has largely focused on single-impulse RD analysis,the challenge of Multi-Impulse RD(MIRD)remains a key area of interest.This study introduces a methodology for the precise calculation of spacecraft MIRD.The reachability constraints specific to MIRD are first formulated through coordinate transformations.Two restricted maneuvering strategies are examined.The derivation of two extremum conditions allows for determining the accessible orientation range and the nodes encompassing the MIRD.Subsequently,four nonlinear programming models are developed to address two types of MIRD by skillfully relaxing constraints using scale factors.Numerical results validate the robustness and effectiveness of the proposed approach,showing substantial agreement with Monte Carlo simulations and confirming its applicability to spacecraft on various elliptical orbits.展开更多
Task allocation for munition swarms is constrained by reachable region limitations and real-time requirements.This paper proposes a reachable region guided distributed coalition formation game(RRGDCF)method to address...Task allocation for munition swarms is constrained by reachable region limitations and real-time requirements.This paper proposes a reachable region guided distributed coalition formation game(RRGDCF)method to address these issues.To enable efficient online task allocation,a reachable region prediction strategy based on fully connected neural networks(FCNNs)is developed.This strategy integrates high-fidelity data generated from the golden section method and low-fidelity data from geometric approximation in an optimal mixing ratio to form multi-fidelity samples,significantly enhancing prediction accuracy and efficiency under limited high-fidelity samples.These predictions are then incorporated into the coalition formation game framework.A tabu search mechanism guided by the reachable region center directs munitions to execute tasks within their respective reachable regions,mitigating redundant operations on ineffective coalition structures.Furthermore,an adaptive guidance coalition formation strategy optimizes allocation plans by leveraging the hit probabilities of munitions,replacing traditional random coalition formation methods.Simulation results demonstrate that RRGDCF surpasses the contract network protocol and traditional coalition formation game algorithms in optimality and computational efficiency.Hardware experiments further validate the method's practicality in dynamic scenarios.展开更多
It is important to calculate the reachable domain(RD)of the manned lunar mission to evaluate whether a lunar landing site could be reached by the spacecraft. In this paper, the RD of free return orbits is quickly eval...It is important to calculate the reachable domain(RD)of the manned lunar mission to evaluate whether a lunar landing site could be reached by the spacecraft. In this paper, the RD of free return orbits is quickly evaluated and calculated via the classification and regression neural networks. An efficient databasegeneration method is developed for obtaining eight types of free return orbits and then the RD is defined by the orbit’s inclination and right ascension of ascending node(RAAN) at the perilune. A classify neural network and a regression network are trained respectively. The former is built for classifying the type of the RD, and the latter is built for calculating the inclination and RAAN of the RD. The simulation results show that two neural networks are well trained. The classification model has an accuracy of more than 99% and the mean square error of the regression model is less than 0.01°on the test set. Moreover, a serial strategy is proposed to combine the two surrogate models and a recognition tool is built to evaluate whether a lunar site could be reached. The proposed deep learning method shows the superiority in computation efficiency compared with the traditional double two-body model.展开更多
For spacecraft formation flight,the information of relative motion reachable set is very important,which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft...For spacecraft formation flight,the information of relative motion reachable set is very important,which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft operation.In this paper,we aim at developing a numerical method to approximate the reachable set for spacecraft relative motion.In particular,we focus on the quality of the approximation and the computational cost.Based on the bang-bang control principle,a polyhedral approximation algorithm is proposed to compute the reachable set of a relative motion spacecraft system.An inner approximation and an outer approximation of the reachable set for the system can be obtained.We prove that the approximation quality measured in Hausdorff distance can be guaranteed.The method is easy to implement and has low computational cost.Finally,the effectiveness of the algorithm is demonstrated by experimental simulation.展开更多
A novel reachable set（RS） model is developed within a framework of exoatmospheric interceptor engagement analysis. The boost phase steering scheme and trajectory distortion mechanism of the interceptor are firstly e...A novel reachable set（RS） model is developed within a framework of exoatmospheric interceptor engagement analysis. The boost phase steering scheme and trajectory distortion mechanism of the interceptor are firstly explored. A mathematical model of the distorted RS is then formulated through a dimension–reduction analysis. By treating the outer boundary of the RS on sphere surface as a spherical convex hull, two relevant theorems are proposed and the RS envelope is depicted by the computational geometry theory. Based on RS model, the algorithms of intercept window analysis and launch parameters determination are proposed, and numerical simulations are carried out for interceptors with different energy or launch points. Results show that the proposed method can avoid intensive on-line computation and provide an accurate and effective approach for interceptor engagement analysis. The suggested RS model also serves as a ready reference to other related problems such as interceptor effectiveness evaluation and platform disposition.展开更多
In this paper,the reachable set estimation problem is studied for a class of dynamic neural networks subject to polytopic uncertainties.The problem addressed here is to find a set as small as possible to bound the sta...In this paper,the reachable set estimation problem is studied for a class of dynamic neural networks subject to polytopic uncertainties.The problem addressed here is to find a set as small as possible to bound the states starting from the origin by inputs with peak values.The maximal Lyapunov functional is proposed to derive a sufficient condition for the existence of a non-ellipsoidal bound to estimate the states of neural networks.It is theoretically shown that this method is superior to the traditional one based on the common Lyapunov function.Finally,two examples illustrate the advantages of our proposed result.展开更多
This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration...This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.展开更多
This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clock...This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.展开更多
This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism...This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism of these systems.To fully exploit the unified uncertain transition probabilities,an equivalent transformation technique is introduced as an alternative to traditional estimation methods,effectively utilizing the information of transition probabilities.Furthermore,a vector Wirtinger-based summation inequality is proposed,which captures more system information compared to existing ones.Building upon these components,a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities.A numerical example is illustrated to demonstrate the superiority of the approaches.展开更多
The set SF(x0;T) of states y reachable from a given state x0 at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x0 at T...The set SF(x0;T) of states y reachable from a given state x0 at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x0 at T in reverse time of the target {x0} while remaining in K. In dimension up to three, Saint-Pierre’s viability algorithm is well-adapted;for higher dimensions, Bonneuil’s viability algorithm is better suited. It is used on a large-dimensional example.展开更多
This paper proposes an event-triggered stochastic model predictive control for discrete-time linear time-invariant(LTI)systems under additive stochastic disturbances.It first constructs a probabilistic invariant set a...This paper proposes an event-triggered stochastic model predictive control for discrete-time linear time-invariant(LTI)systems under additive stochastic disturbances.It first constructs a probabilistic invariant set and a probabilistic reachable set based on the priori knowledge of system uncertainties.Assisted with enhanced robust tubes,the chance constraints are then formulated into a deterministic form.To alleviate the online computational burden,a novel event-triggered stochastic model predictive control is developed,where the triggering condition is designed based on the past and future optimal trajectory tracking errors in order to achieve a good trade-off between system resource utilization and control performance.Two triggering parametersσandγare used to adjust the frequency of solving the optimization problem.The probabilistic feasibility and stability of the system under the event-triggered mechanism are also examined.Finally,numerical studies on the control of a heating,ventilation,and air conditioning(HVAC)system confirm the efficacy of the proposed control.展开更多
ABSTRACT Satellite encounters during close operations,such as rendezvous,formation,and cluster flights,are typical long-term encounters.The collision probability in such an encounter is a primary safety concern.In thi...ABSTRACT Satellite encounters during close operations,such as rendezvous,formation,and cluster flights,are typical long-term encounters.The collision probability in such an encounter is a primary safety concern.In this study,a parametric method is proposed to compute the long-term collision probability for close satellite operations with initial state uncertainty.Random relative state errors resulting from system uncertainty lead to possible deviated trajectories with respect to the nominal one.To describe such a random event meaningfully,each deviated trajectory sample should be mapped to a unique and time-independent element in a random variable(RV)space.In this study,the RV space was identified as the transformed state space at a fixed initial time.The physical dimensions of both satellites were characterized by a combined hard-body sphere.Transforming the combined hard-body sphere into the RV space yielded a derived ellipsoid,which evolved over time and swept out a derived collision volume.The derived collision volume was solved using the reachable domain method.Finally,the collision probability was computed by integrating a probability density function over the derived collision volume.The results of the proposed method were compared with those of a nonparametric computation-intensive Monte Carlo method.The relative difference between the two results was found to be<0.6%,verifying the accuracy of the proposed method.展开更多
In the last decade, as an emerging transaction measure driven by computer and internet technology, e-commerce experienced explosive growth in many areas. It has greatly broken down the limitations of space and time to...In the last decade, as an emerging transaction measure driven by computer and internet technology, e-commerce experienced explosive growth in many areas. It has greatly broken down the limitations of space and time to economic activities, thus changing the rules of business fundamentally. Significant work has been done to understand the laws of e-commerce from multiple dimensions, but the question of how e-commerce shapes firms＇ specialization and market structure from the perspective of spatial factors remains obscure. In this paper, we propose a simple and symmetric firm resource allocation model with a specialized-economy production function and market size constraint, to investigate how individual firms adjust resource allocation with reachable transaction scope expanded. It is shown that with the expansion of reachable transaction scope, individual firms discretely take back one unit resource from a low-investment direction and, instead, channel it to a ＂specialized direction＂. Meanwhile, at the macro level, an optimal division network evolves from a static self-sufficient stage to a diverse semi-specialized stage, and finally to a highly integrated completely specialized stage. Ergo, a Complex Adaptive System （CAS） based simulation framework is constructed. Designed simulation experiments are carried out and confirm to the analysis result of our proposed model.展开更多
Conventional reachable domain(RD)problem with an admissible velocity increment,Δv,in an isotropic distribution,was extended to the general case withΔv in an anisotropic ellipsoidal distribution.Such an extension ena...Conventional reachable domain(RD)problem with an admissible velocity increment,Δv,in an isotropic distribution,was extended to the general case withΔv in an anisotropic ellipsoidal distribution.Such an extension enables RD to describe the effect of initial velocity uncertainty because a Gaussian form of velocity uncertainty can be regarded as possible velocity deviations that are confined within an error ellipsoid.To specify RD in space,the boundary surface of RD,also known as the envelope,should be determined.In this study,the envelope is divided into two parts:inner and outer envelopes.Thus,the problem of solving the RD envelope is formulated into an optimization problem.The inner and outer reachable boundaries that are closest to and farthest away from the center of the Earth,respectively,were found in each direction.An optimal control policy is then formulated by using the necessary condition for an optimum;that is,the first-order derivative of the performance function with respect to the control variable becomes zero.Mathematical properties regarding the optimal control policy is discussed.Finally,an algorithm to solve the RD envelope is proposed.In general,the proposed algorithm does not require any iteration,and therefore benefits from quick computation.Numerical examples,including two coplanar cases and two 3D cases,are provided,which demonstrate that the proposed algorithm works efficiently.展开更多
In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are addressed.First,an iterative sums of squares(SOS)programming approach ...In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are addressed.First,an iterative sums of squares(SOS)programming approach is developed for reachable set estimation.It characterizes the over-approximations of the forward reachable sets by sub-level sets of time-varying Lyapunovlike functions that satisfy an invariance condition,and formulates the problem of searching for the Lyapunov-like functions as a bilinear SOS program,which can be solved via an iterative algorithm.To make the over-approximation tight,the proposed approach seeks to minimize the volume of the overapproximation set with a desired shape.Then,the reachable set estimation approach is extended for safety verification,via explicitly encoding the safety constraint such that the Lyapunov-like functions guarantee both reaching and avoidance.The efficiency of the presented method is illustrated by some numerical examples.展开更多
A situation maintenance-based cooperative guidance strategy is proposed to intercept a high-speed and high-maneuverability target via inferior missiles.Reachability and relative motion analyses are conducted to develo...A situation maintenance-based cooperative guidance strategy is proposed to intercept a high-speed and high-maneuverability target via inferior missiles.Reachability and relative motion analyses are conducted to develop and pursue virtual targets,respectively.A two-stage guidance strategy under nonlinear kinematics is developed on the basis of virtual targets.The first stage optimizes the coverage and collision situation by pursuing virtual targets under specific angular constraints.The second stage subsequently intercepts the superior target based on the handover condition optimized by the first stage.Numerical simulation results are provided to compare the effectiveness and superiority of the proposed strategy with those of the reachability-based cooperative strategy(RCS),coverage-based cooperative guidance(CBCG)and augmented proportional navigation(APN)under various maneuvering modes.展开更多
To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles(RGVs),new analytical solutions are developed for calculating their coverage perfor-mance.Specifically,a new coverage m...To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles(RGVs),new analytical solutions are developed for calculating their coverage perfor-mance.Specifically,a new coverage model is established by approximating the Reentry Reachable Domain(RRD).However,the computation of real-time relative distances between satellites and targets,which is essential for coverage analysis based on this model,imposes a significant compu-tational burden.To address this challenge,a coverage analysis method based on two-dimensional map theory is proposed.This method represents the coverage conditions of a target as a fixed area on a two-dimensional map and transforms the satellite trajectory into a series of parallel lines.By determining the intersection points between these lines and the area boundaries,the coverage ana-lytical solutions for a target point are derived.On this basis,coverage theorems are presented for rapid calculation of the constellation coverage performance for an area.Simulation results demon-strate the effectiveness and high precision of the proposed analytical solutions.展开更多
Aircraft icing poses a great threat to flight safety.In response to the characteristics of high-power consumption,large volume,and heavy weight of traditional anti-/de-icing technologies,the concept of ice shape modul...Aircraft icing poses a great threat to flight safety.In response to the characteristics of high-power consumption,large volume,and heavy weight of traditional anti-/de-icing technologies,the concept of ice shape modulation is proposed,which is called ice tolerant flight.Firstly,the flight performance of Unmanned Aerial Vehicle(UAV)was compared in three states:no ice,full ice,and modulated ice through flight tests.It was found that ice shape modulation has a significant improvement effect on the aerodynamic performance of aircraft under icing conditions.Under the three modulated ice shape conditions in this experiment,the lift coefficient of the UAV under different ice shape modulation conditions increased by 18%–33%,and the stalling angle was delayed by 3°-5°.Subsequently,the pressure distribution,streamlines in the flow field,and detached vortex distribution of the UAV model in these three states were obtained through numerical simulation,to study the mechanism of ice shape modulation on the aerodynamic performance of aircraft.The simulation found that the reason for the improvement of the wings effect after ice shape modulation is that the modulated area forms a leading-edge protrusion structure similar to a vortex generator.This structure prolongs the mixed flow region on the wings surface and reduces the trend of flow separation,which plays a role in increasing lift and reducing drag for UAVs under icing conditions.Finally,a reverse reachable set that can be used for unexpected state recovery is used as the definition of flight safety boundaries,and an aircraft dynamics model is established to obtain flight safety boundaries for different states.Research has found that the flight safety boundary of the UAV in a no ice state is greater than that in a modulated ice state,and the safety boundary in a modulated ice state is greater than that in a full ice state.Compared with the full ice state,the flight safety boundary after modulation has expanded by 27.0%.The scheme of ice shape modulation can provide a basis for the flight safety of aircraft under icing conditions.展开更多
Qualitative spacecraft pursuit-evasion problem which focuses on feasibility is rarely studied because of high-dimensional dynamics,intractable terminal constraints and heavy computational cost.In this paper,A physics-...Qualitative spacecraft pursuit-evasion problem which focuses on feasibility is rarely studied because of high-dimensional dynamics,intractable terminal constraints and heavy computational cost.In this paper,A physics-informed framework is proposed for the problem,providing an intuitive method for spacecraft threat relationship determination,situation assessment,mission feasibility analysis and orbital game rules summarization.For the first time,situation adjustment suggestions can be provided for the weak player in orbital game.First,a dimension-reduction dynamics is derived in the line-of-sight rotation coordinate system and the qualitative model is determined,reducing complexity and avoiding the difficulty of target set presentation caused by individual modeling.Second,the Backwards Reachable Set(BRS)of the target set is used for state space partition and capture zone presentation.Reverse-time analysis can eliminate the influence of changeable initial state and enable the proposed framework to analyze plural situations simultaneously.Third,a time-dependent Hamilton-Jacobi-Isaacs(HJI)Partial Differential Equation(PDE)is established to describe BRS evolution driven by dimension-reduction dynamics,based on level set method.Then,Physics-Informed Neural Networks(PINNs)are extended to HJI PDE final value problem,supporting orbital game rules summarization through capture zone evolution analysis.Finally,numerical results demonstrate the feasibility and efficiency of the proposed framework.展开更多
For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system...For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system state together with the time-delay term and measurement noise is augmented as a new state, and a singular system is then constructed. Subsequently, a kind of decoupling technique is employed to eliminate the effect of external disturbance, and an observer is designed to simultaneously estimate the system state and measurement noise. Based on the estimated state and measurement noise, the interval estimations of system state and measurement noise are obtained by reachability analysis technique. Finally, the effectiveness of the proposed method is verified by a four-tank liquid level system.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12372052,12125207)the Young Elite Scientists Sponsorship Program,China(No.2021JCJQ-QT-047)+1 种基金the Natural Science Foundation of Hunan Province,China(No.2023JJ20047)the Technology Innovation Team of Manned Space Engineering,China。
文摘The concept of the spacecraft Reachable Domain(RD)has garnered significant scholarly attention due to its crucial role in space situational awareness and on-orbit service applications.While the existing research has largely focused on single-impulse RD analysis,the challenge of Multi-Impulse RD(MIRD)remains a key area of interest.This study introduces a methodology for the precise calculation of spacecraft MIRD.The reachability constraints specific to MIRD are first formulated through coordinate transformations.Two restricted maneuvering strategies are examined.The derivation of two extremum conditions allows for determining the accessible orientation range and the nodes encompassing the MIRD.Subsequently,four nonlinear programming models are developed to address two types of MIRD by skillfully relaxing constraints using scale factors.Numerical results validate the robustness and effectiveness of the proposed approach,showing substantial agreement with Monte Carlo simulations and confirming its applicability to spacecraft on various elliptical orbits.
基金supported by the National Natural Science Foundation of China(Grant 52372347,52425211,52272360)。
文摘Task allocation for munition swarms is constrained by reachable region limitations and real-time requirements.This paper proposes a reachable region guided distributed coalition formation game(RRGDCF)method to address these issues.To enable efficient online task allocation,a reachable region prediction strategy based on fully connected neural networks(FCNNs)is developed.This strategy integrates high-fidelity data generated from the golden section method and low-fidelity data from geometric approximation in an optimal mixing ratio to form multi-fidelity samples,significantly enhancing prediction accuracy and efficiency under limited high-fidelity samples.These predictions are then incorporated into the coalition formation game framework.A tabu search mechanism guided by the reachable region center directs munitions to execute tasks within their respective reachable regions,mitigating redundant operations on ineffective coalition structures.Furthermore,an adaptive guidance coalition formation strategy optimizes allocation plans by leveraging the hit probabilities of munitions,replacing traditional random coalition formation methods.Simulation results demonstrate that RRGDCF surpasses the contract network protocol and traditional coalition formation game algorithms in optimality and computational efficiency.Hardware experiments further validate the method's practicality in dynamic scenarios.
基金supported by the National Natural Science Foundation of China (12072365)the Natural Science Foundation of Hunan Province of China (2020JJ4657)。
文摘It is important to calculate the reachable domain(RD)of the manned lunar mission to evaluate whether a lunar landing site could be reached by the spacecraft. In this paper, the RD of free return orbits is quickly evaluated and calculated via the classification and regression neural networks. An efficient databasegeneration method is developed for obtaining eight types of free return orbits and then the RD is defined by the orbit’s inclination and right ascension of ascending node(RAAN) at the perilune. A classify neural network and a regression network are trained respectively. The former is built for classifying the type of the RD, and the latter is built for calculating the inclination and RAAN of the RD. The simulation results show that two neural networks are well trained. The classification model has an accuracy of more than 99% and the mean square error of the regression model is less than 0.01°on the test set. Moreover, a serial strategy is proposed to combine the two surrogate models and a recognition tool is built to evaluate whether a lunar site could be reached. The proposed deep learning method shows the superiority in computation efficiency compared with the traditional double two-body model.
基金partially supported by the National Natural Science Foundation of China(No.12071025)the Natural Science Foundation of Guangdong Province,China(No.2022A1515011172)+1 种基金the Science and Technology on Space Intelligent Control Laboratory for National Defense,China(No.KGJZDSYS-2018-13)the Scientific and Technological Innovation of Shunde Graduate School of University of Science and Technology Beijing,China(No.BK20AE004)。
文摘For spacecraft formation flight,the information of relative motion reachable set is very important,which can be used to predict the operating boundary of adjacent spacecraft and thus to ensure the safety of spacecraft operation.In this paper,we aim at developing a numerical method to approximate the reachable set for spacecraft relative motion.In particular,we focus on the quality of the approximation and the computational cost.Based on the bang-bang control principle,a polyhedral approximation algorithm is proposed to compute the reachable set of a relative motion spacecraft system.An inner approximation and an outer approximation of the reachable set for the system can be obtained.We prove that the approximation quality measured in Hausdorff distance can be guaranteed.The method is easy to implement and has low computational cost.Finally,the effectiveness of the algorithm is demonstrated by experimental simulation.
基金co-supported by the National Natural Science Foundation of China (No. 11272346)the National Basic Research Program of China (No. 2013CB733100)
文摘A novel reachable set（RS） model is developed within a framework of exoatmospheric interceptor engagement analysis. The boost phase steering scheme and trajectory distortion mechanism of the interceptor are firstly explored. A mathematical model of the distorted RS is then formulated through a dimension–reduction analysis. By treating the outer boundary of the RS on sphere surface as a spherical convex hull, two relevant theorems are proposed and the RS envelope is depicted by the computational geometry theory. Based on RS model, the algorithms of intercept window analysis and launch parameters determination are proposed, and numerical simulations are carried out for interceptors with different energy or launch points. Results show that the proposed method can avoid intensive on-line computation and provide an accurate and effective approach for interceptor engagement analysis. The suggested RS model also serves as a ready reference to other related problems such as interceptor effectiveness evaluation and platform disposition.
基金Supported by the National Natural Science Foundation of China under Grant Nos.60774039,60974024,61074089,61174129Program for New Century Excellent Talents in University under Grant No.NCET-11-0379the Independent Innovation Foundation of Tianjin University
文摘In this paper,the reachable set estimation problem is studied for a class of dynamic neural networks subject to polytopic uncertainties.The problem addressed here is to find a set as small as possible to bound the states starting from the origin by inputs with peak values.The maximal Lyapunov functional is proposed to derive a sufficient condition for the existence of a non-ellipsoidal bound to estimate the states of neural networks.It is theoretically shown that this method is superior to the traditional one based on the common Lyapunov function.Finally,two examples illustrate the advantages of our proposed result.
文摘This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC).
文摘This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.
基金funded by National Key Research and Development Program of China under Grant 2022YFE0107300the Chongqing Technology Innovation and Application Development Special Key Project under Grant CSTB2022TIAD-KPX0162+3 种基金the National Natural Science Foundation of China under Grant U22A20101the Chongqing Technology Innovation and Application Development Special Key Project under Grant CSTB2022TIAD-CUX0015the Chongqing postdoctoral innovativetalents support program under Grant CQBX202205the China Postdoctoral Science Foundation under Grant 2023M730411.
文摘This paper focuses on the reachable set estimation for Markovian jump neural networks with time delay.By allowing uncertainty in the transition probabilities,a framework unifies and enhances the generality and realism of these systems.To fully exploit the unified uncertain transition probabilities,an equivalent transformation technique is introduced as an alternative to traditional estimation methods,effectively utilizing the information of transition probabilities.Furthermore,a vector Wirtinger-based summation inequality is proposed,which captures more system information compared to existing ones.Building upon these components,a novel condition that guarantees a reachable set estimation is presented for Markovian jump neural networks with unified uncertain transition probabilities.A numerical example is illustrated to demonstrate the superiority of the approaches.
文摘The set SF(x0;T) of states y reachable from a given state x0 at time T under a set-valued dynamic x’(t)∈F(x (t)) and under constraints x(t)∈K where K is a closed set, is also the capture-viability kernel of x0 at T in reverse time of the target {x0} while remaining in K. In dimension up to three, Saint-Pierre’s viability algorithm is well-adapted;for higher dimensions, Bonneuil’s viability algorithm is better suited. It is used on a large-dimensional example.
基金supported by the National Nature Science Foundation of China(62073194)the Natural Science Foundation of Shandong Province of China(ZR2023MF028)the Taishan Scholars Program of Shandong Province(tsqn202312008)
文摘This paper proposes an event-triggered stochastic model predictive control for discrete-time linear time-invariant(LTI)systems under additive stochastic disturbances.It first constructs a probabilistic invariant set and a probabilistic reachable set based on the priori knowledge of system uncertainties.Assisted with enhanced robust tubes,the chance constraints are then formulated into a deterministic form.To alleviate the online computational burden,a novel event-triggered stochastic model predictive control is developed,where the triggering condition is designed based on the past and future optimal trajectory tracking errors in order to achieve a good trade-off between system resource utilization and control performance.Two triggering parametersσandγare used to adjust the frequency of solving the optimization problem.The probabilistic feasibility and stability of the system under the event-triggered mechanism are also examined.Finally,numerical studies on the control of a heating,ventilation,and air conditioning(HVAC)system confirm the efficacy of the proposed control.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11702293).
文摘ABSTRACT Satellite encounters during close operations,such as rendezvous,formation,and cluster flights,are typical long-term encounters.The collision probability in such an encounter is a primary safety concern.In this study,a parametric method is proposed to compute the long-term collision probability for close satellite operations with initial state uncertainty.Random relative state errors resulting from system uncertainty lead to possible deviated trajectories with respect to the nominal one.To describe such a random event meaningfully,each deviated trajectory sample should be mapped to a unique and time-independent element in a random variable(RV)space.In this study,the RV space was identified as the transformed state space at a fixed initial time.The physical dimensions of both satellites were characterized by a combined hard-body sphere.Transforming the combined hard-body sphere into the RV space yielded a derived ellipsoid,which evolved over time and swept out a derived collision volume.The derived collision volume was solved using the reachable domain method.Finally,the collision probability was computed by integrating a probability density function over the derived collision volume.The results of the proposed method were compared with those of a nonparametric computation-intensive Monte Carlo method.The relative difference between the two results was found to be<0.6%,verifying the accuracy of the proposed method.
基金supported by the National Key Technology Research and Development Program (No. 2015BAH18F04)
文摘In the last decade, as an emerging transaction measure driven by computer and internet technology, e-commerce experienced explosive growth in many areas. It has greatly broken down the limitations of space and time to economic activities, thus changing the rules of business fundamentally. Significant work has been done to understand the laws of e-commerce from multiple dimensions, but the question of how e-commerce shapes firms＇ specialization and market structure from the perspective of spatial factors remains obscure. In this paper, we propose a simple and symmetric firm resource allocation model with a specialized-economy production function and market size constraint, to investigate how individual firms adjust resource allocation with reachable transaction scope expanded. It is shown that with the expansion of reachable transaction scope, individual firms discretely take back one unit resource from a low-investment direction and, instead, channel it to a ＂specialized direction＂. Meanwhile, at the macro level, an optimal division network evolves from a static self-sufficient stage to a diverse semi-specialized stage, and finally to a highly integrated completely specialized stage. Ergo, a Complex Adaptive System （CAS） based simulation framework is constructed. Designed simulation experiments are carried out and confirm to the analysis result of our proposed model.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11702293).
文摘Conventional reachable domain(RD)problem with an admissible velocity increment,Δv,in an isotropic distribution,was extended to the general case withΔv in an anisotropic ellipsoidal distribution.Such an extension enables RD to describe the effect of initial velocity uncertainty because a Gaussian form of velocity uncertainty can be regarded as possible velocity deviations that are confined within an error ellipsoid.To specify RD in space,the boundary surface of RD,also known as the envelope,should be determined.In this study,the envelope is divided into two parts:inner and outer envelopes.Thus,the problem of solving the RD envelope is formulated into an optimization problem.The inner and outer reachable boundaries that are closest to and farthest away from the center of the Earth,respectively,were found in each direction.An optimal control policy is then formulated by using the necessary condition for an optimum;that is,the first-order derivative of the performance function with respect to the control variable becomes zero.Mathematical properties regarding the optimal control policy is discussed.Finally,an algorithm to solve the RD envelope is proposed.In general,the proposed algorithm does not require any iteration,and therefore benefits from quick computation.Numerical examples,including two coplanar cases and two 3D cases,are provided,which demonstrate that the proposed algorithm works efficiently.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.12171159 and 61772203in part by the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY20F020020。
文摘In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are addressed.First,an iterative sums of squares(SOS)programming approach is developed for reachable set estimation.It characterizes the over-approximations of the forward reachable sets by sub-level sets of time-varying Lyapunovlike functions that satisfy an invariance condition,and formulates the problem of searching for the Lyapunov-like functions as a bilinear SOS program,which can be solved via an iterative algorithm.To make the over-approximation tight,the proposed approach seeks to minimize the volume of the overapproximation set with a desired shape.Then,the reachable set estimation approach is extended for safety verification,via explicitly encoding the safety constraint such that the Lyapunov-like functions guarantee both reaching and avoidance.The efficiency of the presented method is illustrated by some numerical examples.
基金supported by the National Natural Science Foundation of China(Grant No.62203362)the Natural Science Basic Research Program of Shaanxi(Grant No.2023-JC-QN-0569)。
文摘A situation maintenance-based cooperative guidance strategy is proposed to intercept a high-speed and high-maneuverability target via inferior missiles.Reachability and relative motion analyses are conducted to develop and pursue virtual targets,respectively.A two-stage guidance strategy under nonlinear kinematics is developed on the basis of virtual targets.The first stage optimizes the coverage and collision situation by pursuing virtual targets under specific angular constraints.The second stage subsequently intercepts the superior target based on the handover condition optimized by the first stage.Numerical simulation results are provided to compare the effectiveness and superiority of the proposed strategy with those of the reachability-based cooperative strategy(RCS),coverage-based cooperative guidance(CBCG)and augmented proportional navigation(APN)under various maneuvering modes.
基金supported by the National Natural Science Foundation of China (No.62273119).
文摘To efficiently and accurately design satellite constellations equipped with Reentry Glide Vehicles(RGVs),new analytical solutions are developed for calculating their coverage perfor-mance.Specifically,a new coverage model is established by approximating the Reentry Reachable Domain(RRD).However,the computation of real-time relative distances between satellites and targets,which is essential for coverage analysis based on this model,imposes a significant compu-tational burden.To address this challenge,a coverage analysis method based on two-dimensional map theory is proposed.This method represents the coverage conditions of a target as a fixed area on a two-dimensional map and transforms the satellite trajectory into a series of parallel lines.By determining the intersection points between these lines and the area boundaries,the coverage ana-lytical solutions for a target point are derived.On this basis,coverage theorems are presented for rapid calculation of the constellation coverage performance for an area.Simulation results demon-strate the effectiveness and high precision of the proposed analytical solutions.
基金financially supported by the National Natural Science Foundation of China(No.12002384)National Natural Science Foundation of China Youth Fund(No.62003368).
文摘Aircraft icing poses a great threat to flight safety.In response to the characteristics of high-power consumption,large volume,and heavy weight of traditional anti-/de-icing technologies,the concept of ice shape modulation is proposed,which is called ice tolerant flight.Firstly,the flight performance of Unmanned Aerial Vehicle(UAV)was compared in three states:no ice,full ice,and modulated ice through flight tests.It was found that ice shape modulation has a significant improvement effect on the aerodynamic performance of aircraft under icing conditions.Under the three modulated ice shape conditions in this experiment,the lift coefficient of the UAV under different ice shape modulation conditions increased by 18%–33%,and the stalling angle was delayed by 3°-5°.Subsequently,the pressure distribution,streamlines in the flow field,and detached vortex distribution of the UAV model in these three states were obtained through numerical simulation,to study the mechanism of ice shape modulation on the aerodynamic performance of aircraft.The simulation found that the reason for the improvement of the wings effect after ice shape modulation is that the modulated area forms a leading-edge protrusion structure similar to a vortex generator.This structure prolongs the mixed flow region on the wings surface and reduces the trend of flow separation,which plays a role in increasing lift and reducing drag for UAVs under icing conditions.Finally,a reverse reachable set that can be used for unexpected state recovery is used as the definition of flight safety boundaries,and an aircraft dynamics model is established to obtain flight safety boundaries for different states.Research has found that the flight safety boundary of the UAV in a no ice state is greater than that in a modulated ice state,and the safety boundary in a modulated ice state is greater than that in a full ice state.Compared with the full ice state,the flight safety boundary after modulation has expanded by 27.0%.The scheme of ice shape modulation can provide a basis for the flight safety of aircraft under icing conditions.
基金This study was supported by the Independent Innovation Science Foundation Project of National University of Defense Technology,China(No.22-ZZCX-083).
文摘Qualitative spacecraft pursuit-evasion problem which focuses on feasibility is rarely studied because of high-dimensional dynamics,intractable terminal constraints and heavy computational cost.In this paper,A physics-informed framework is proposed for the problem,providing an intuitive method for spacecraft threat relationship determination,situation assessment,mission feasibility analysis and orbital game rules summarization.For the first time,situation adjustment suggestions can be provided for the weak player in orbital game.First,a dimension-reduction dynamics is derived in the line-of-sight rotation coordinate system and the qualitative model is determined,reducing complexity and avoiding the difficulty of target set presentation caused by individual modeling.Second,the Backwards Reachable Set(BRS)of the target set is used for state space partition and capture zone presentation.Reverse-time analysis can eliminate the influence of changeable initial state and enable the proposed framework to analyze plural situations simultaneously.Third,a time-dependent Hamilton-Jacobi-Isaacs(HJI)Partial Differential Equation(PDE)is established to describe BRS evolution driven by dimension-reduction dynamics,based on level set method.Then,Physics-Informed Neural Networks(PINNs)are extended to HJI PDE final value problem,supporting orbital game rules summarization through capture zone evolution analysis.Finally,numerical results demonstrate the feasibility and efficiency of the proposed framework.
基金supported in part by the National Nature Science Foundation of China(No.61973105)the Natural Science Foundation of Henan Province(No.232300420147)the Fundamental Research Funds for the Universities of Henan Province(No.NSFRF180335).
文摘For a class of time-delay discrete-time linear systems with external disturbance and measurement noise, the interval estimation problems of state and measurement noise are investigated in this paper. First, the system state together with the time-delay term and measurement noise is augmented as a new state, and a singular system is then constructed. Subsequently, a kind of decoupling technique is employed to eliminate the effect of external disturbance, and an observer is designed to simultaneously estimate the system state and measurement noise. Based on the estimated state and measurement noise, the interval estimations of system state and measurement noise are obtained by reachability analysis technique. Finally, the effectiveness of the proposed method is verified by a four-tank liquid level system.
