Missile-target Engagement Research Articles

Matlab Class for Rapid Visualization of Missile-Target Engagement Scenarios

In this paper, the authorial Matlab Battlespace Visualization Class (MBVC) is proposed to plan, design, and compose the preliminary version of the desired computer animation, which can then be used both as a background for the discussion of the final composition and as an individual project for public presentation, providing a visual reference for missile-target engagement simulations. As a design tool, the MBVC allows us the combination of the advanced mathematical models of missile guidance loop elements (implemented in the discrete form as program scripts) with the capabilities offered by open, powerful, and flexible 3D graphical engine. As a visualization tool, the MBVC allows the designers to present their research findings in both an illustrative and informative way, providing a visual reference for the computer simulation. The class is freely available for scientific, engineering or educational use.

An annular event-triggered artificial time-delayed control-based guidance approach

This work proposes a resource efficient robust control scheme for missile-target engagement scenarios subjected to external disturbances. The robustness is achieved by using an annular event-triggered artificial time-delayed control (ET-TDC) methodology with input saturation. The ET-TDC philosophy uses the TDC strategy through a dynamic predefined triggering mechanism which overcomes the requirement to update the control periodically for every sampling instant, unlike conventional TDC and other robust control schemes. Thus the proposed methodology can tackle uncertainties with minimal a-priori knowledge while significantly reducing the over-utilisation of system resources. In addition, the adopted event-triggered mechanism facilitates further conservation of energy which might be crucial for mid-to-long range engagement scenarios. The closed-loop stability is derived analytically and the simulation results illustrate the efficacy of the proposed guidance framework in comparison with other state-of-art robust control methodologies.

Three-dimensional approximate cooperative integrated guidance and control with fixed-impact time and azimuth constraints

A novel three-dimensional (3D) approximate cooperative integrated guidance and control (ACIGC) scheme based on backstepping control (BC), sliding mode control (SMC), dynamic surface control (DSC), and a 3D reduced-order extended state observer (ESO) for multiple hypersonic skid-to-turn (STT) missiles simultaneously attacking ground-maneuver targets is proposed in this study, which considers a fixed-impact azimuth and time constraints. First, we established a novel integrated guidance and control (IGC) model that includes the missile-target relative distance and azimuth based on the missile-target engagement dynamics, attitude dynamics, and first-order delay dynamics of the rudder. It is a 3D fifth-order strict-feedback time-varying nonlinear model with mismatched uncertainties. Second, a 3D ACIGC scheme was designed, where a cooperative strategy was designed by transforming a fixed-impact time constraint into a nominal range-to-go constraint. The IGC model consists of seeker, guidance, angle-of-attack, attitude, and rudder subsystems based on the BC, and the SMC designs each subsystem. The DSC obtains the derivatives of virtual control commands, which solves the “differential explosion” caused by the BC. The unknown target acceleration, unmodeled parts of the system states, perturbations caused by time-varying parameters, and external disturbances are regarded as lumped disturbances, which are estimated and compensated for by the 3D reduced-order ESO to improve the robustness. Subsequently, the closed-loop system was proven to be stable, and the system states were ultimately uniformly bounded using Lyapunov theory. Finally, the simulation results of three missiles attacking a simultaneously ground-maneuvering target and Monte Carlo simulations demonstrated the effectiveness and robustness of the proposed ACIGC scheme.

State-Following-Kernel-Based Online Reinforcement Learning Guidance Law Against Maneuvering Target

In this article, a state-following-kernel-based reinforcement learning method with an extended disturbance observer is proposed, whose application to a missile-target interception system is considered. First, the missile-target engagement is formulated as a vertical planar pursuit–evasion problem. The target maneuver is then estimated by an extended disturbance observer in real time, which leads to an infinite-horizon optimal regulation problem. Next, utilizing the local state approximation ability of state-following kernels, the critic neural network (NN) and actor NN for synchronous iteration are constructed to calculate the approximate optimal guidance policy. The states and NN weights are proven to be uniformly ultimately bounded using the Lyapunov method. Finally, numerical simulations against different types of nonstationary targets are effectively tested, and the results highlight the role of state-following kernels in the value function and policy approximation.

Three Dimensional Nonlinear Guidance Law for Exact Impact Time Control

This paper presents a nonlinear guidance law for controlling the impact time of a missile-target engagement in three dimensions. The guidance law is initially formulated for a two-dimensional encounter before being extended to a three-dimensional scenario. The guidance law is constructed such that nonlinear kinematics are neither linearized nor approximated. The guidance law offers a precise closed-form expression for impact time, which is the principal contribution of this work. Choosing an integrable heading error profile is the central concept of this research for determining an accurate impact time. A two-step strategy is utilized to accomplish an interception at a predetermined time. Because the control parameter is related to the desired impact time with an exact expression, a simple and accurate control of impact time is attained. The method provides equations for calculating the minimum and maximum impact times, enabling the determination of the range of impact times that can be achieved. The proposed guidance law can ensure that the seeker field of view restriction is not violated, If the initial heading error is within this limit. The developed method is utilized in salvo attacks, in which multiple missiles simultaneously strike an enemy target, increasing the missiles’ effectiveness against the target’s self-defense mechanism. To validate the effectiveness of the proposed strategy, MATLAB-based numerical simulations of 2D and 3D engagements, including salvo attacks, are conducted.

An online data driven actor-critic-disturbance guidance law for missile-target interception with input constraints

In this article, we develop an online robust actor-critic-disturbance guidance law for a missile-target interception system with limited normal acceleration capability. Firstly, the missile-target engagement is formulated as a zero-sum pursuit-evasion game problem. The key is to seek the saddle point solution of the Hamilton Jacobi Isaacs (HJI) equation, which is generally intractable due to the nonlinearity of the problem. Then, based on the universal approximation capability of Neural Networks (NNs), we construct the critic NN, the actor NN and the disturbance NN, respectively. The Bellman error is adjusted by the normalized-least square method. The proposed scheme is proved to be Uniformly Ultimately Bounded (UUB) stable by Lyapunov method. Finally, the effectiveness and robustness of the developed method are illustrated through numerical simulations against different types of non-stationary targets and initial conditions.

Measurement Compensation for Time-Delay Seeker and Three-Dimensional Adaptive Guidance Law Design.

The time delay of seekers has grown to be a serious issue for tactical missile guidance with the development of flight vehicle technologies. To address the problem, a measurement compensation system for the seeker, with lags and delays based on predictive active disturbance rejection control, is proposed. In addition, to eliminate the effects of target maneuvers to the tactical missile guidance, an adaptive finite-time convergent sliding mode guidance law, based on super-twisting algorithm, is proposed in three-dimensional missile-target engagement kinematics. Specifically, the compensation system consists of a predictive tracking structure and an active disturbance rejection control system, which could follow a virtual measurement without lags and delays. The compensation system has advantages in disturbance rejection and model inaccuracy addressing, compared with existing compensation methods for seeker measurement. As for the sliding mode guidance law design, the proposed approach is based on an improved super-twisting algorithm with fast convergent adaptive gains, which has advantages in addressing unknown but bounded target maneuvers and avoiding chattering of the classical sliding mode control. As a result, the measurement compensation system and the adaptive sliding mode guidance law is verified robust and effective under the proposed constraints by the simulation examples.

Distributed target-encirclement guidance law for cooperative attack of multiple missiles

The target-encirclement guidance problem for many-to-one missile-target engagement scenario is studied, where the missiles evenly distribute on a target-centered circle during the homing guidance. The proposed distributed target-encirclement guidance law can achieve simultaneous attack of multiple missiles in different line-of-sight directions. Firstly, the decentralization protocols of desired line-of-sight angles are constructed based on the information of neighboring missiles. Secondly, a biased proportional navigation guidance law that can arbitrarily designate the impact angle is cited. The missiles can achieve all-aspect attack on the target in an encirclement manner by combining the biased proportional navigation guidance law and dynamic virtual targets strategy. Thirdly, the consensus protocol of simultaneous attack is designed, which can guarantee that all missiles’ time-to-go estimates achieve consensus asymptotically, and the convergence of the closed-loop system is proved strictly via the Lyapunov stability theory. Finally, numerical simulation results demonstrate the performance and feasibility of the proposed distributed target-encirclement guidance law in different engagement situations.

An Optimal Algorithm for Midcourse Guidance Law Under Wind Disturbance

The guidance laws are commonly designed to yield as small a miss distance as possible, harmonious with the missile’s acceleration capability. In recent decades, the concept of optimized guidance law is well understood in applications where information concerning the target range and line-of-sight angle is available. Researchers' efforts have been continually made to apply modern control theory to conventional and adaptive autopilot designs, even though the classical theory is still applicable to autopilots. It can be noted that it is desirable to perform a detailed computer-aided feasibility study within the context of a realistic missile-target engagement model. Development and evaluation of guidance and control laws for simplified missile-target engagement scenarios are extended and adapted to the air-to-air missile situation and implemented in a complete three-dimensional engagement model. Thus, this study proposed a computational method for constructing an optimal midcourse guidance law, which is based on the optimal control theory and initial boundary conditions. This proposed guidance law is derived from an optimal control theory with the boundary conditions such as allowed relative distance between missile and target at the final time, low line-of-sight rate. A numerical simulation verifies the performance of this guidance law with the impact of harmonic wind. The simulation results demonstrate that the quality of effectiveness as well as the applicability of this proposed algorithm.

Efficient and accurate online estimation algorithm for zero-effort-miss and time-to-go based on data driven method

This paper introduces a novel and efficient algorithm for online estimation of zero-effort-miss and time-to-go based on data driven method. Only missile-target separations are utilized to construct the estimation models, and a practical Fisher fusion algorithm is derived to acquire the estimates with high accuracy and computational efficiency. Further, the two parameters can be online estimated at a particular time. Meanwhile, the kinematics equations of the missile-target engagement are independent, and assumptions of the missile guidance system dynamics and behaviors of the missile and target are completely out of consideration. Moreover, the effectiveness and applicability are explicitly verified through various simulation scenarios.

Backstepping-based adaptive predictive optimal control of nonlinear systems with application to missile–target engagement

In this paper, an adaptive predictive optimal control scheme for a class of block strict-feedback nonlinear systems is proposed by integrating the adaptive dynamic programming (ADP) technique, predictive control and backstepping method. The basic idea is that designing the virtual and actual controls of backstepping is the optimized solutions of corresponding subsystems. Firstly, the virtual control input is derived for the subsystem by utilizing ADP technique, in which a critic neural network (NN) is constructed to approximate the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation. Then, to further reduce the computational complexity, the actual controller is given in an analytical form by using continuous-time predictive approach. Theoretical analysis guarantees the stability of the closed-loop system by Lyapunov method. Finally, the effectiveness of the proposed adaptive predictive optimal control scheme is validated through an application to missile–target engagement.

Designing an Optimal Control LQT for Controlling and Guidance of Missile

Missile has to be controlled and follow the commanded guidance in order to make its flight hit the target. Since missile has a nonlinear characteristic and coupled dynamic equation, controlling a missile has become more complex. Linear Quadratic Tracking (LQT) is one of optimal control theory where its objective is to make the output of a system tracks its reference as close as possible while minimize or maximize a desired performance index. In this paper, an autopilot for missile is designed which consists nonlinear state feedback decoupler and LQT controller. Pursuit Guidance is used for the guidance law. A missile-target engagement simulation is created using 2 kinds of target; static target and dynamic target. By using static target, the mean of the closest distance between missile and the target is 0.45 meters and by using dynamic target the mean of the closest distance between missile and the target is 2.562 meters.

The three dimensional guidance system design of terminal attack phase for exo-atmospheric kill vehicle

A novel terminal guidance system with a pulse-width-pulse-frequency (PWPF) modulator based on variable dead zone is designed for exo-atmospheric kill vehicle (EKV). At first, a three dimensional (3D) missile-target engagement kinematics is established on the line-of-sight (LOS) coordinate system, the guidance law is compensated by estimated maneuvering acceleration of target from nonlinear disturbance observer (DO). Secondly, a 3D terminal sliding mode guidance law with gradually increasing robustness is proposed for EKV, and the finite time stability of closed system is strictly proven. A PWPF modulator with variable dead zone is proposed to resist the sensitivity of LOS angle with relative distance decreasing, and the stability of modulator is proven by describing function technique. Finally, the guidance performances are assessed through a numerical simulation, the proposed guidance law is better attack precision than traditional guidance law, and the PWPF modulator with variable dead zone is more reasonable in fuel allocation and smaller on miss distance than traditional PWPF modulator.

Robust partial integrated guidance and control for missiles via extended state observer

A novel extended state observer (ESO) based control is proposed for a class of nonlinear systems subject to multiple uncertainties, and then applied to partial integrated guidance and control (PIGC) design for a missile. The proposed control strategy incorporates both an ESO and an adaptive sliding mode control law. The multiple uncertainties are treated as an extended state of the plant, and then estimate them using the ESO and compensate for them in the control action, in real time. Based on the output of the ESO, the resulting adaptive sliding mode control law is inherently continuous and differentiable. Strict proof is given to show that the estimation error of the ESO can be arbitrarily small in a finite time. In addition, the adaptive sliding mode control law can achieve finite time convergence to a neighborhood of the origin, and the accurate expression of the convergent region is given. Finally, simulations are conducted on the planar missile–target engagement geometry. The effectiveness of the proposed control strategy in enhanced interception performance and improved robustness against multiple uncertainties are demonstrated.

Design of a robust guidance law via active disturbance rejection control

Focusing on the three-dimensional guidance problem in case of target maneuvers and response delay of the autopilot, the missile guidance law utilizing active disturbance rejection control (ADRC) is proposed. Based on the nonlinear three-dimensional missile target engagement kinematics, the guidance model is established. The target acceleration is treated as a disturbance and the dynamics of the autopilot is considered by using a first-order model. A nonlinear continuous robust guidance law is designed by using a cascaded structure ADRC controller. In this method the disturbance is estimated by using the extended state observer (ESO) and compensated during each sampling period. Simulation results show that the proposed cascaded loop structure is a viable solution to the guidance law design and has strong robustness with respect to target maneuvers and response delay of the autopilot.

Geometrical Guidance Algorithm for Soft Landing on Lunar Surface

Abstract Augmented design of a guidance algorithm previously developed for intercepting target in a missile-target engagement scenario, but catering to powered descent soft landing on lunar surface is the main focus of this paper. When it comes to lunar soft landing guidance formulation, it is required that the Lander reach the desired position with terminal velocity constraints. An existing circular guidance law developed for missile guidance is modified to be applied for the fine braking phase of lunar powered descent. Presently in the algorithm, at the beginning of each guidance cycle, there will be an assumed varying circular path from missile to target and the guidance solution lies in finding the acceleration towards the centre of the circle so that the missile moves towards the target. The design augmentation proposed for lunar landing introduces a quadratic acceleration term opposite to the instantaneous tangential velocity vector to ensure terminal conditions. Coefficients of the quadratic acceleration profile are determined by the length of the circle as well as the magnitude of instantaneous tangential velocity. Finally a simple compensation scheme based on comparison of actual velocity from sensors and expected velocity from the algorithm is also proposed to take care of the variation in gravity and error in initial mass estimate.

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile–target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law.

A novel robust proportional navigation guidance law design for missile considering autopilot dynamic

In this paper, a novel robust proportional navigation guidance (RPNG) law is derived for missiles by integrating sliding mode control theory and proportional navigation guidance law in order to achieve robustness against target accelerations. A first-order autopilot dynamic is taken into account in the state space equations of the nonlinear missile-target engagement dynamic. The robustness of the designed guidance law against external disturbances is proved by the second method of Lyapunov. Some coefficients that appear in the proposed RPNG law are obtained using the genetic algorithm. Performance of the new designed guidance law is compared with the well known augmented proportional navigation guidance (APNG) law. Considering different types of target accelerations and several scenarios, numerical simulations are presented. Simulation results show that the proposed guidance law has much better robustness in comparison with the APNG law. Moreover, it is simple and easy to implement from the point of view of practical applications.

Particle Guidance: Applying POMDPs to the Optimization of Mid-Course Guidance Laws for Long-Range Missiles

During the mid-course phase of an air-to-air missile, choosing the optimal Guidance Point (GP) so as to maximize lock-on success and minimize intercept time is critical. Given low computational resources available on board and a very constrained maneuvering time frame, GP-based algorithms must be efficient. We suggest an innovative approach using Reinforcement Learning (RL) to produce finite state controllers that can be executed efficiently – using table lookup – to meet the strict time limits of a target engagement. Instead of hand-crafting a GP-picking algorithm for every combination of sensor and aircraft configuration, one promising alternative models a missile-target engagement as a Partially Observable Markov Decision Process (POMDP) and automatically generates a controller for picking the best GP by solving the POMDP model. Using a recently developed offline algorithm called Monte Carlo Value Iteration (MCVI) we constructed continuous-state POMDP models and solved them directly, without discretizing the entire state space.Invited session “Missile Guidance Navigation & Control” (pm846)

Time-varying line-of-sight rate estimator with a single modified tracking index for RF homing guidance

A practical time-varying line-of-sight (LOS) rate estimator is proposed for surface-to-air missile (SAM) guidance using an RF seeker. The range-dependant LOS rate dynamics and variances of boresight error (BSE) measurements constitute the Kalman filtering problem associated with the timevarying matrix differential Riccati equation (DRE). Since the conventional gain-scheduled steady-state Kalman filter derived by solving an algebraic Riccati equation (ARE) cannot fully consider the time-varying nature of LOS rate dynamics, it might not be appropriate for volatile missile-target engagement scenarios. This motivates us to investigate a pseudo-analytic solution to the time-varying Kalman filtering problem based on the algebraic transform of the given DRE. Apart from the previous works, the explicit form of time-varying Kalman gain is expressed in terms of a single filter design parameter, called modified tracking index. The proposed time-varying filter is not only able to effectively handle the time-varying LOS rate dynamics but is also affordable for real-time implementation. Adjoint analysis results for a homing guidance loop show that the proposed LOS rate estimator could improve guidance performance and be an excellent choice for SAM applications.