Differential Game Guidance Law Research Articles

Deep Reinforcement Learning-Based Differential Game Guidance Law against Maneuvering Evaders

To achieve the intelligent interception of different types of maneuvering evaders, based on deep reinforcement learning, a novel intelligent differential game guidance law is proposed in the continuous action domain. Different from traditional guidance laws, the proposed guidance law can avoid tedious manual settings and save cost efforts. First, the interception problem is transformed into the pursuit–evasion game problem, which is solved by zero-sum differential game theory. Next, the Nash equilibrium strategy is obtained through the Markov game process. To implement the proposed intelligent differential game guidance law, an actor–critic neural network based on deep deterministic policy gradient is constructed to calculate the saddle point of the differential game guidance problem. Then, a reward function is designed, which includes the tradeoffs among guidance accuracy, energy consumption, and interception time. Finally, compared with traditional methods, the interception accuracy of the proposed intelligent differential game guidance law is 99.2%, energy consumption is reduced by 47%, and simulation time is shortened by 1.58 s. All results reveal that the proposed intelligent differential game guidance law has better intelligent decision-making ability.

Deep Reinforcement Learning-Based Differential Game Guidance Law against Maneuvering Evaders

To achieve the intelligent interception of different types of maneuvering evaders, based on deep reinforcement learning, a novel intelligent differential game guidance law is proposed in the continuous action domain. Different from traditional guidance laws, the proposed guidance law can avoid tedious manual settings and save cost efforts. First, the interception problem is transformed into the pursuit–evasion game problem, which is solved by zero-sum differential game theory. Next, the Nash equilibrium strategy is obtained through the Markov game process. To implement the proposed intelligent differential game guidance law, an actor–critic neural network based on deep deterministic policy gradient is constructed to calculate the saddle point of the differential game guidance problem. Then, a reward function is designed, which includes the tradeoffs among guidance accuracy, energy consumption, and interception time. Finally, compared with traditional methods, the interception accuracy of the proposed intelligent differential game guidance law is 99.2%, energy consumption is reduced by 47%, and simulation time is shortened by 1.58 s. All results reveal that the proposed intelligent differential game guidance law has better intelligent decision-making ability.

Data-Driven Finite-Time Three-Dimensional Differential Game Guidance Law against A Maneuvering Target with Input Constraints

Data-Driven Finite-Time Three-Dimensional Differential Game Guidance Law against A Maneuvering Target with Input Constraints

Zero-sum differential game guidance law for missile interception engagement via neuro-dynamic programming

In this paper, for solving the nonlinear control problem of the missile intercepting the maneuvering target, a novel nonlinear zero-sum differential game guidance law is proposed via the neuro-dynamic programming approach. First, the continuous-time nonlinear differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs (HJI) equation. Then, a critic neural network is designed to solve the corresponding nonlinear HJI equation. An adaptive weight tuning law for the critic weights is proposed, where an additional term is added to ensure the stability of the closed-loop nonlinear system. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic NN weights estimation error are proved with the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed differential game guidance law for nonlinear interception.

Cooperative guidance laws for interception of active maneuvering target under information symmetric and asymmetric conditions

This paper proposes novel cooperative guidance strategies with dynamic game properties for a group of interceptors to intercept an active intelligent maneuvering target under both information symmetric and asymmetric conditions. A novel differential game guidance law is proposed to intercept the target with an active maneuvering strategy based on relative distances, relative velocities, and remaining flight time under information symmetric conditions. In the case where the team of interceptors has information superiority, a reasonable evading strategy is designed for the target, and a cooperative optimal guidance law is proposed for interceptors taking the target's evading strategy into consideration. When neither side has the knowledge of the opponent's maneuvering strategy, a novel robust adaptive interception guidance law is designed based on the reduction of the surrounding area regarding the target's maneuver as unknown disturbances. Numerical simulations are carried out to illustrate the effectiveness and superiority of proposed cooperative guidance laws.

A Nonlinear Finite-Time Robust Differential Game Guidance Law.

In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs equation, a time-varying cost function is developed to reflect the fixed terminal time, and the robust guidance law is developed to compensate for the external disturbance. Then, a novel neural network identifier is designed to approximate the unknown nonlinear dynamics with online weight tuning. Subsequently, an online critic neural network approximator is presented to estimate the cost function, and time-varying activation functions are considered to deal with the fixed final time problem. An adaptive weight tuning law is given, where two additional terms are added to ensure the stability of the closed-loop nonlinear system and so as to meet the terminal cost at a fixed final time. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic neural network weights estimation error are proven based upon the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed robust differential game guidance law for nonlinear interception.

A Combined Linear–Quadratic/Bounded Control Differential Game Guidance Law

A new guidance law, based on the solution of a combined linear–quadratic and norm-bounded differential game, is proposed. It hinges on the insight that the hard constraints on the lateral acceleration are critical in the last part of the flight, and in contrast, at the early stages of the flight, it is important to avoid excessive speed loss due to induced drag. This yields a linear–quadratic differential game formulation for the initial stage and a norm-bounded differential game formulation for the last stage of the engagement. In an important particular case of players with ideal dynamics, the proposed guidance law is shown to be biased proportional navigation guidance with a deadzone. Due to its simple structure, the proposed guidance law is easy to implement in practice. The performance of the guidance law is illustrated using numerical simulations, and it is shown to perform better than comparable classical guidance laws.

Guidance strategies for interceptor against active defense spacecraft in two-on-two engagement

This paper investigates the guidance problem for interceptors against spacecraft with active defense in a two-on-two engagement. There are four adversaries in the engagement which are interceptor, protector, spacecraft and active defender. The interceptor is required to capture the spacecraft and evade the defender with the assist of the protector. Two classes of guidance laws are proposed based on norm differential game strategy and linear quadratic differential game strategy, respectively. Interceptor using norm differential game guidance laws is able to pursue the spacecraft without being intercepted by defender, even though the maneuverability of both interceptor and protector is lower than defender. Additionally, linear quadratic differential game guidance laws derived by numerical solution of Riccati differential equation take into account the control saturation, fuel cost and chattering phenomenon simultaneously. Finally, the effectiveness and performance of the developed guidance approaches are demonstrated by nonlinear numerical simulations.

Norm differential game guidance law for active defense aircraft

Norm differential game guidance law for active defense aircraft

Guidance laws for attacking defended target

In this paper, two new guidance laws based on differential game theory are proposed and investigated for the attacker in an attacker-defender-target scenario. The conditions for the attacker winning the game are analyzed when the target and defender using the differential game guidance law based on the linear model. The core ideas underlying the two guidance laws are the attacker evading to a critical safe boundary from the defender, and then maintaining a critical miss distance. The guidance law more appropriate for the attacker to win the game differs according to the initial parameters. Unlike other guidance laws, when using the derived guidance laws there is no need to know the target and the defender’s control efforts. The results of numerical simulations show that the attacker can evade the defender and hit the target successfully by using the proposed derived guidance laws.

Cooperative Differential Game Guidance Law for Two Pursuers and One Evader

For the nonlinear engagement between two pursuers and a single evader, in which small angle deviation assumption or other linearization conditions may not be applicable, a cooperative guidance law is analyzed and derived in the framework of a zero-sum two-person differential game. State-dependent Riccati-equation method is used to obtain the suboptimal solutions of the pursuit-evasion problem by choosing the line of sight angular rates as state variables, and closed-loop form guidance strategies that can be used online for the players are derived. Time-to-go estimations are not had to be taken into account to apply the guidance law proposed. Nonlinear two-dimensional simulations are carried out to validate the performance of the cooperative guidance law, and the comparison with a current cooperative linear quadratic differential game guidance law is made.

Integrated Estimation/Guidance Law against Exoatmospheric Maneuvering Targets

An integrated guidance integrated estimation/guidance law is designed for exoatmospheric interceptors equipped with divert thrusters and optical seekers to intercept maneuvering targets. This paper considers an angles-only guidance problem for exoatmospheric maneuvering targets. A bounded differential game-based guidance law is derived against maneuvering targets using zero-effort-miss (ZEM). Estimators based the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) are designed to estimate LOS rates that are contaminated by noise and target maneuver. Furthermore, to improve the observability of the range, an observability enhancement differential game guidance law is derived. The guidance law and the estimator are integrated together in the guidance loop. The proposed integrated estimation/guidance law has been tested in several three-dimensional nonlinear interception scenarios. Numerical simulations on a set of Monte-Carlo simulations prove the validity and superiority of the proposed guidance law in hit-to-kill interception.

Guidance of Seekerless Interceptors Using Innovation Covariance Based Tuning of Kalman Filters

In this paper, an integrated estimation/guidance algorithm that combines Kalman-filter-based interactive multiple-model estimators with a modified differential game guidance law is developed for seekerless interceptors in three-dimensional space. The target is assumed to perform various types of maneuvers, while the sensor has noisy measurements and the interceptor is subject to acceleration bound. To handle these, the Kalman filters used in the interactive multiple model are pretuned using two recently developed metrics based on innovation covariance. To determine the filter tuning parameters, the metrics are evaluated offline for the Kalman filter using different process models, and the tuned values of the process noise covariance are selected in each case. These tuned Kalman filters are then used in the interactive multiple-model configuration to cater to various maneuvers that are expected during the end game. A numerical study compares the performances of these, and a previously reported interactive multiple-model technique demonstrates significant improvements in performance.

Robust differential game guidance laws design for uncertain interceptor-target engagement via adaptive dynamic programming

ABSTRACTIn this paper, the problem of intercepting a maneuvering target is formulated as a two-player zero-sum differential game framework affected by matched uncertainties. By introducing an appropriate cost function that reflects the uncertainties, the robust control is transformed into a two-player zero-sum differential game control problem and therefore ensures the compensation of the matched uncertainties. Additionally, the corresponding Hamilton--Jacobi--Isaacs (HJI) equation is solved by constructing a critic neural network (NN). The closed-loop system and the critic NN weight estimation error are proved to be uniform ultimate boundedness (UUB) by utilising Lyapunov approach. Finally, the effectiveness of the proposed robust guidance law is demonstrated by using a nonlinear two-dimensional kinematics, assuming first-order dynamics for the interceptor and the target.

Differential game guidance law for dual and bounded controlled missiles

Differential game guidance law for dual and bounded controlled missiles

Retraction notice

At the request of the Editor(s) and the Publisher and author(s), the following article “Differential Game Guidance Law for a Kinetic Kill Vehicle and Its Simulation” by Xing-Yuan Xu, Xiao-Na Song and Yuan-Li Cai. Simulation, first published June 10, 2015, DOI 10.1177/0037549715588839 . has been retracted. The Editor has judged that the paper plagiarized the following article, and the authors have agreed to their paper being retracted: “Linear Quadratic Guidance Laws for Imposing a Terminal Intercept Angle” by Vitaly Shaferman and Tal Shima, Journal of Guidance, Control, and Dynamics, Vol. 31, No. 5, DOI 10.2514/1.32836.

RETRACTED: Differential game guidance law for a kinetic kill vehicle and its simulation

As the maneuverability of targets has been further increased in recent years, it is highly desirable to improve the performance of an interceptor’s guidance law. The ‘‘hit-to-kill’’ scenarios of a kinetic kill vehicle (KKV) require a centimeter-level miss distance, and control of impact angle can considerably increase the KKV’s lethality. Two forms of linear quadratic differential game (LQDG) guidance laws for the KKV are proposed in this paper. The first can achieve only zero terminal miss distance, and the second can achieve a specified impact angle as well as zero terminal miss distance. The LQDG guidance laws are obtained by solving a two-sided linear quadratic optimization problem. In game theory, the adversaries are considered as two independent controlled objects. A major advantage is that the LQDG guidance laws make no assumption of the target’s future maneuver strategy. Simulation results show that the two guidance laws can meet the requirements of the KKV and that the centimeter-level miss distance does not lead to a large guidance command near the terminal time.

An integrated estimation/guidance approach for seeker-less interceptors

This paper addresses the problem of intercepting highly maneuverable threats using seeker-less interceptors that operate in the command guidance mode. These systems are more prone to estimation errors than standard seeker-based systems. In this paper, an integrated estimation/guidance (IEG) algorithm, which combines interactive multiple model (IMM) estimator with differential game guidance law (DGL), is proposed for seeker-less interception. In this interception scenario, the target performs an evasive bang–bang maneuver, while the sensor has noisy measurements and the interceptor is subject to acceleration bound. The IMM serves as a basis for the synthesis of efficient filters for tracking maneuvering targets and reducing estimation errors. The proposed game-based guidance law for two-dimensional interception, later extended to three-dimensional interception scenarios, is used to improve the endgame performance of the command-guided seeker-less interceptor. The IMM scheme and an optimal selection of filters, to cater to various maneuvers that are expected during the endgame, are also described. Furthermore, a chatter removal algorithm is introduced, thus modifying the differential game guidance law (modified DGL). A comparison between modified DGL guidance law and conventional proportional navigation guidance law demonstrates significant improvement in miss distance in a pursuer-evader scenario. Simulation results are also presented for varying flight path angle errors. A numerical study is provided which demonstrates the performance of the combined interactive multiple model with game-based guidance law (IMM/DGL). Simulation study is also carried out for combined IMM and modified DGL (IMM/modified DGL) which exhibits the superior performance and viability of the algorithm reducing the chattering phenomenon. The results are illustrated by an extensive Monte Carlo simulation study in the presence of estimation errors.

An Adaptive Weighted Differential Game Guidance Law

For intercepting modern high maneuverable targets, a novel adaptive weighted differential game guidance law based on the game theory of mixed strategy is proposed, combining two guidance laws which are derived from the perfect and imperfect information pattern, respectively. The weights vary according to the estimated error of the target's acceleration, the guidance law is generated by directly using the estimation of target's acceleration when the estimated error is small, and a differential game guidance law with adaptive penalty coefficient is implemented when the estimated error is large. The adaptive penalty coefficients are not constants and they can be adjusted with current target maneuverability. The superior homing performance of the new guidance law is verified by computer simulations.

Differential Game Guidance Law Against High Maneuver Target with Different Information Patterns

Differential Game Guidance Law Against High Maneuver Target with Different Information Patterns