Robust Guidance Law Research Articles

Observer-based robust impact angle control three-dimensional guidance laws with autopilot lag

Considering an air-based missile intercepting maneuvering target with desired impact angles, robust guidance laws with autopilot lag in three-dimensional coupling space are presented in this paper. First, combining the fixed-time stability theory and adaptive sliding mode control technique, a novel dual-layer adaptive fixed-time sliding mode disturbance observer is proposed to estimate the unknown target maneuver. The proposed disturbance observer releases the requirement of information on either the target maneuver or its derivative. To achieve interception with the desired impact angles, a novel guidance law based on the nonsingular terminal sliding mode (NTSM) with an exponent coefficient is provided. The proposed control framework prevents singular problems and ensures the fixed-time stability of the guidance system. In addition, autopilot dynamics are taken into consideration, and the dynamics surface control (DSC) method is used to address the nonlinear static feedback system. Meanwhile, the improved fixed-time differentiator is used to acquire the derivative of virtual control laws. This prevents the inherent “differential explosion” of the backstepping technique. The uniform boundedness of the closed-loop system is demonstrated via the Lyapunov method. Finally, numerous numerical simulations are carried out, and the simulation results verify the effectiveness of the proposed guidance laws.

Robust guidance law for cooperative aerial target circumnavigation of UAVs based on composite system theory

Unmanned aerial vehicles (UAVs) are widely used in many fields and relevant research is becoming widespread. However, there are still many problems in the control design of multiple UAVs. This paper proposes a new robust guidance law for the cooperative circumnavigation of an aerial target by multiple UAVs. By incorporating an altitude channel, the controlled fixed-wing UAV was modeled as a simplified three-dimensional (3D) nonlinear dynamic system. Unlike existing studies, tracking and cooperation were considered as a composite system, and the coupling of the UAV linear velocity and angular velocity was considered in the design process. The proposed guidance law considers both the input and output constraints, which represent the system uncertainties and output limits, respectively, and are used to verify the robustness of the guidance law. The robust stability of the disturbed cooperative target circumnavigation system in 3D space is ensured through a strict mathematical proof. Finally, the effectiveness and superiority of the proposed robust guidance law are demonstrated by simulations using a UAV unicycle model and a six-degree-of-freedom (6-DOF) model.

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 Deployment Approach Toward Time-Energy Efficient Robust Performance for Interceptors

Abstract This paper proposes an automatic time-energy efficient robust control (ATERC) deployment approach for selecting either a near-optimal closed-loop control law or a robust control law based on the requirement of the system. The near-optimal closed-loop control law is designed by applying the population-based sine-cosine algorithm (SCA) to the considered interceptor problem. While the robust control law is formulated by using an artificial time delayed control (TDC) approach. In presence of external disturbances, the ATERC methodology deploys the TDC-based robust guidance law to the interceptor, while in the absence of such uncertainties the SCA-based near-optimal guidance law is applied in order to improve the time-energy minimization. This guidance approach also incorporates input saturation which expands its applicability. Using Lyapunov stability analysis, this work establishes an uniformly ultimately bounded (UUB) stability for the discussed system on application of the proposed control approach. Extensive simulation studies involving nonmaneuvering targets and targets performing bank-to-bank maneuver, affirms the efficiency of the proposed approach.

Distributed Path Following of Multiple Under-Actuated Autonomous Surface Vehicles Based on Data-Driven Neural Predictors via Integral Concurrent Learning

This article addresses the problem of distributed path following of multiple under-actuated autonomous surface vehicles (ASVs) with completely unknown kinetic models. An integrated distributed guidance and learning control architecture is proposed for achieving a time-varying formation. Specifically, a robust distributed guidance law at the kinematic level is developed based on a consensus approach, a path-following mechanism, and an extended state observer. At the kinetic level, a model-free kinetic control law based on data-driven neural predictors via integral concurrent learning is designed such that the kinetic model can be learned by using recorded data. The advantage of the proposed method is two-folds. First, the proposed formation controllers are able to achieve various time-varying formations without using the velocities of neighboring vehicles. Second, the proposed control law is model-free without any parameter information on kinetic models. Simulation results substantiate the effectiveness of the proposed robust distributed guidance and model-free control laws for multiple under-actuated ASVs with fully unknown kinetic models.

Three-dimensional fixed-time robust cooperative guidance law for simultaneous attack with impact angle constraint

This paper proposes a three-dimensional (3-D) robust nonlinear cooperative guidance law for multiple missiles to simultaneously attack a maneuvering target at desired impact angles. Since the flight time of terminal guidance is very short, the fast convergence of guidance errors is a vital demand, especially when the initial errors are huge and the target is maneuvering. By utilizing the theory of fixed time convergence, a distributed sliding surface that only utilizes the information from adjacent missiles is first designed, whose convergence time is independent of initial conditions. In order to avoid the performance degradation due to the estimation error of time-to-go, the consensus variables of the fixed-time sliding surface are chosen as range-to-go and radial relative velocity. Then, a robust cooperative guidance law along the line-of-sight (LOS) direction is proposed to bring the multi-missile system to reach the sliding surface in finite time. Thus, the simultaneous attack to a maneuvering target can be guaranteed. Next, the guidance laws in the elevation and azimuth direction of LOS are developed to ensure the fixed-time convergence of LOS angles. The fixed-time stability is proved through the Lyapunov theory and bi-homogenous property. Simulation results indicate that the impact time of each missile under the proposed guidance law is the same, without any deviation. Compared with the state-of-the-art methods, the convergence time of LOS angles is shortened by about 30%. In addition, the miss distance and errors of LOS angles can be reduced by more than 80%.

Robust Head-Pursuit Guidance Accounting for Hit-to-Kill and Angle Constraints

In this paper, the hit-to-kill strategy is introduced to solve the three-dimensional (3D) robust head-pursuit (HP) interception problem considering the line-of-sight (LOS) angle constraints. Firstly, a target based relative dynamic model is proposed to be the nominal model for designing the robust HP guidance laws, where the HP interception problem is formulated as a target passively chases after the interceptor missile. Secondly, the 3D retro-proportional navigation (RPN) guidance law is reinterpreted from the point of control theory, which forces the corresponding guidance system asymptotically stable. Meanwhile, the concept of nullifying the LOS angular rates is successfully introduced to solve the 3D robust HP guidance problem via the sliding mode control. Thirdly, the LOS angles constrained robust HP guidance law is proposed based on the nonsingular terminal sliding mode control. The stabilities of the presented guidance laws are analyzed via the Lyapunov approach. The simulation results are in agreement with the theoretical statements.

Two-Stage Guidance Law With Constrained Impact via Circle Involute

The mission of simultaneous attack and warhead lethality enhancement requires the constraints on impact time and angle in the guidance design. To this end, a two-stage guidance law considering constrained impact as well as the robustness against external disturbances and heading errors is proposed. The first stage is based on a circle involute geometrical rule that guarantees the desired velocity direction at the involute's end. With this goal achieved, the involute guidance is switched to the guidance of nullifying line-of-sight rate such that near-zero maneuver in the second stage is ensured. To achieve both impact time and angle constraints, a simple parameter determination approach is provided to find explicit solutions for the desired two-stage trajectory. Meanwhile, a robust two-stage guidance law is constructed to implement the geometrical rule, guarantee terminal constraints, and ensure robustness. The proposed technique is easy to implement, in that it does not involve model linearization, time-to-go estimation, and numerical optimization routine. Additionally, the achievable range of different constraints is analyzed considering practical issues such as initial launch angles, initial line-of-sight angles, and acceleration limits. Extensive simulations are carried out in various engagement scenarios under uncertainties and disturbances to validate the effectiveness and robustness of the proposed guidance law.

Re-entry trajectory tracking of reusable launch vehicle using artificial delay based robust guidance law

A Reusable Launch Vehicle (RLV), during the re-entry phase of its flight, experiences uncertain environment and extreme turbulence. This calls for an effective control strategy to guide the vehicle efficiently on a trajectory that allows safer landing conditions while providing robustness against external disturbances and system uncertainties. In this regard, a Time-Delayed Control (TDC) strategy has been proposed to track the space vehicle on a predetermined trajectory in the presence of these uncertainties. In the proposed approach, the system vector and the uncertainties are lumped into a single function which is estimated using the input and output data from the previous instant. Theoretical analysis of the control strategy executed using Lyapunov’s method, proves Uniformly Ultimately Bounded (UUB) stability of the closed loop system. The efficacy of the proposed approach has been verified through simulation studies which affirm robust tracking of the optimal trajectory generated through Pseudo-Spectral method (PSM), in the presence of time-varying uncertainties.

Reduced‐order observer‐based robust drag‐tracking guidance for uncertain entry vehicles

SummaryThis article studies the drag‐tracking guidance design problem of entry vehicles with low lift‐to‐drag ratio. Taking issues of uncertainty and input saturation into account, we develop a reduced‐order observer‐based robust output feedback guidance law, making the drag‐tracking error converge near zero. Our study not only achieves robust drag‐tracking guidance against inherently existing uncertainty, but also removes the redundant drag estimation in the literature. The Monte Carlo simulation is done to illustrate the advantage of the developed method.

Three‐dimensional impact angle‐constrained adaptive guidance law considering autopilot lag and input saturation

AbstractThis work investigates three‐dimensional accurate guidance problem in the presence of impact angle constraint, input saturation, autopilot lag, and external disturbance, and presents a robust adaptive guidance method for maneuvering targets. More specifically, based on integral Lyapunov control algorithm, a robust guidance law, which can drive both terminal line‐of‐sight angle error and its rate to a small region around zero, while resisting the terrible influence caused by external disturbance, is proposed in this work. To deal with input saturation, guidance command is separated into two parts: real input and saturation error, and an adaptive control technique is employed to compensate the influence resulting from external disturbance and saturation error. Moreover, regarding autopilot lag as a first‐order dynamics, a backstepping designed controller with an adaptive term is proposed. Numerical simulations are carried out and their results demonstrate the proposed properties.

A robust three-dimensional cooperative guidance law against maneuvering target

This paper proposes a robust three-dimensional cooperative guidance law (RTCGL) against a maneuvering target. When some missiles are intercepted during the engagement, this RTCGL integrated with a local filtering algorithm can ensure that the rest missiles hit the maneuvering target simultaneously. The pitch acceleration command is designed based on an augmented proportional navigation guidance law and can make the missile’s trajectory fall into its yaw plane. Then the three-dimensional cooperative problem is converted into a planar one. The yaw acceleration command consists of a guidance component for homing and a coordination component for simultaneous arrival. Numerical simulation results are presented to verify the effectiveness of the cooperative guidance law.

The approach of partial stabilisation in design of discrete-time robust guidance laws against manoeuvering targets

ABSTRACTIn this paper, a robust three-dimensional guidance law against manoeuvering targets is designed using the approach of discrete-time partial stabilisation. In the proposed method, the equations of the guidance problem are divided into two subsystems where the asymptotic stability is desired only for the first one. The control input of the second subsystem is designed such that the collision to be ensured in a short time. Despite recent advances in technology and implementation of digital controllers, the design of guidance laws with the approach of discrete-time partial stabilisation has not been done, till now. One of the advantages of this paper is to design a discrete-time guidance law even with the difficulties of the discrete-time Lyapunov theorem. Moreover, the Lyapunov function is chosen based on the physics of the guidance problem (making the rate of line of sight (LOS) rotation close to zero), and it is shown that it is not possible to asymptotically stabilise the system in the case of manoeuvering targets. Nevertheless, to guarantee the collision with the target, it is enough to limit the rotation rate of LOS to a small value. Finally, simulation results are given to show the appropriate performance of the proposed guidance law.

Compound robust flight time and heading angle constrained guidance law

Abstract This work studies accurate interception problem for salvo-attack missions and proposes a robust guidance law in the presence of impact time and angle constraints. First, the dynamic model for planar homing endgame guidance is built. Different with conventional guidance dynamic model, this work takes the derivative with respect to range, rather than time. Next, the trajectory of desired line-of-sight is formed and a time-to-go prediction method is introduced. On this basis, according to sliding mode methodology, a sliding manifold consisting the knowledge of time-to-go and line-of-sight angle is built and an integrated Lyapunov control method based guidance law is deduced to force this sliding manifold converge to a small region around zero in finite time, so that the missile will intercept target with a desired flight time and a heading angle. Detailed theoretical analysis and numerical simulations verified above properties.

Robust intercept guidance law with predesigned zero-effort miss distance convergence for capturing maneuvering targets

In this paper, a homing guidance in a two-dimensional target-interceptor scenario is studied with an unknown target maneuver strategy. In order to capture the target with acceptable accuracy, a robust guidance law with a predesigned zero-effort miss (ZEM) distance convergence for the interceptor is proposed. In order to guarantee the ZEM distance to converge into a small region around the predesigned terminal value within a finite time, a novel function of ZEM distance is proposed. The ZEM distance convergence profile can be reasonably controlled according to the interceptor's initial state. Based on the designed profile, an initial delay control and prescribed performance control are utilized to achieve a high terminal miss distance accuracy and account for uncertainties caused by the target's unknown maneuverability. Four maneuvering strategies of the target are tested to verify the performance of the proposed guidance law.

Designing of Three-dimensional Robust Guidance Law Using Adaptive Dynamic Programming with Input Saturation Constraint

In this paper, a three-dimensional robust guidance law for a surface to air missile considering actuator saturation and first order dynamic for autopilot system has been designed in order to enhance the performance of defense systems. To attain this goal, first, modeling of the system in 3D spherical coordination using engagement basics has been derived and after that, appropriate cost function for collision of missile and target considering actuator constraints and in absence of target maneuver information has been formulated. Hamilton-Jacobi-Isaacs (HJI) differential equation inequality should be solved according to robust control literature for achieving guidance law which unfortunately does not have closed form solution in our case study problem. Therefore, to overcome this challenge, using adaptive dynamic programming theory for solving acquired HJI, algorithm for designing robust guidance law has been presented. Simplification solving of differential inequality and also guaranteeing robustness of the controller are the most important feature of the proposed algorithm. Numerous simulations for targets with different maneuvering capabilities and comparison of the proposed method with conventional augmented proportional navigation, show effectiveness of designed 3D robust guidance law.

A robust hybrid nonlinear guidance law for intercepting a non-cooperative maneuvering target

ABSTRACTThis paper has proposed a new robust hybrid nonlinear guidance law, which accounts for a missile’s terminal line-of-sight (LOS) angle constraint, in order to intercept a non-cooperative maneuvering target. The proposed hybrid nonlinear guidance strategy consists of two phases; in the first phase, a guidance law named PIGL is derived from prescribed performance control and the inertial delay control method. In PIGL, a revised prescribed performance function is put forward, and a prescribed performance controller with unknown uncertainties is then derived. The controller smoothly drives both the LOS angle and its rate to a predesigned small region under unknown uncertainties that are induced by target’s maneuvers within a fixed time. Then, a guidance law named SIGL is activated, which is derived from sliding mode control and inertial delay control. By driving the desired sliding mode variable to zero within a finite time, the SIGL guidance law is able to achieve high terminal interception accuracy. The robustness of both of the proposed sub-guidance laws has been proved explicitly in this paper. The hybrid guidance law has the advantage of a tunable convergence rate of the LOS angle and the rate of the LOS angle at the beginning period, by which an excessive large initial maneuver can be avoided. Meanwhile, the hybrid guidance law also has the advantage of lower sensitivity to errors in the estimation of the time-to-go.

Robust Three-Dimensional Guidance Law Design against Maneuvering Targets with Approach of Discrete-time Partial Stabilization

Robust Three-Dimensional Guidance Law Design against Maneuvering Targets with Approach of Discrete-time Partial Stabilization

Three-dimensional terminal angle constrained robust guidance law with autopilot lag consideration

Based on sliding mode control theory and back stepping design technique, this paper proposes a robust guidance law considering autopilot dynamics for maneuvering target interception in three-dimensional environment and terminal angle constraints. The proposed guidance law is summarized as an “observer–controller” system. More specifically, to estimate the knowledge of target maneuvers, an adaptive second-order sliding mode observer is presented whose design parameters can be adjusted autonomously according to the estimation error, and a nonsingular switchable sliding manifold based finite time convergent controller is proposed to drive the line-of-sight angle error and angular rate to a small region around zero, further, enable the missile accurately intercept the target in finite time. Finally, by formulating the autopilot lag as a first-order or second-order dynamics, the higher-order comprehensive model is built and complex guidance laws are presented. The simulation results demonstrated the proposed properties.