Robust Guidance Law Research Articles

Archimedean Spiral-Based Intercept Angle Guidance

This paper focuses on designing an intercept angle guidance law for the planar interception of a stationary target. The underlying geometrical rule is based on an Archimedean spiral, which allows a pursuer to enforce a desired intercept angle or time by generating an appropriate spiral trajectory. An inherent advantage of using the proposed geometrical rule is that the required lateral acceleration to ensure interception is bounded throughout the engagement. The applicability of the geometrical rule is also analyzed against nonmaneuvering moving targets. The geometrical rule is implemented using a sliding-mode control-based nonlinear and robust guidance law. Using the proposed guidance law, the desired intercept angle is achieved in finite time. The theoretical results are validated through numerical simulations. The interception of the target with a specified intercept angle from different initial conditions and with various intercept angles from a given initial condition are shown. The robustness of the controller against disturbances and heading errors is also evaluated.

Robust Nonlinear Disturbance Observer Based Adaptive Guidance Law Against Uncertainties in Missile Dynamics and Target Maneuver

The proposed robust nonlinear disturbance observer based adaptive guidance method considers the nonlinear coupled missile dynamics and rapidly maneuvering target. It also includes unavailable information such as high-order line-of-sight rates and target acceleration as time-varying parametric uncertainties and nonparametric disturbances. An integrated guidance and control model, a robust nonlinear disturbance observer, a nonlinear missile jerk observer, and a robust nonlinear guidance law are proposed, the validity of which is demonstrated by stability analysis and simulations.

Robust Cooperative Guidance Law for Simultaneous Arrival

In the cooperative simultaneous arrival problem, a group of interceptors are guided to simultaneously engage a stationary target. However, some interceptors may not follow the prescribed guidance law during the engagement, which can lead to interception failures. This brief investigates a new robust cooperative simultaneous arrival problem in the presence of misbehaving interceptors. A robust cooperative guidance law (RCGL) integrated with a local filtering algorithm is designed. Without the knowledge of faulty interceptors (no fault diagnosis procedure is needed), the RCGL achieves a simultaneous arrival between normal interceptors if the misbehavior of faulty interceptors can be characterized by a threat model. By characterizing the contracting behavior of the maximum gap between impact time estimates of normal interceptors, sufficient conditions are established to guarantee the convergence of RCGL. Furthermore, regardless of the network connections, the impact times of normal interceptors are upper bounded by the maximum initial time-to-go estimate of normal interceptors. Numerical comparison studies demonstrate the guidance performance of RCGL.

Robust finite-time guidance against maneuverable targets with unpredictable evasive strategies

This paper presents a robust finite-time guidance (RFTG) law to a short-range interception problem. The main challenge is that the evasive strategy of the target is unpredictable because it is determined not only by the states of both the interceptor and the target, but also by external un-modeled factors. By robustly stabilizing a line-of-sight rate, this paper proposes an integrated continuous finite-time disturbance observer/bounded continuous finite-time stabilizer strategy. The design of this integrated strategy has two points: 1) effect of a target maneuver is modeled as disturbance and then is estimated by the second-order homogeneous observer; 2) the finite-time stabilizer is actively coupled with the observer. Based on homogeneity technique, the local finite-time input-to-state stability is established for the closed-loop guidance system, thus implying the proposed RFTG law can quickly render the LOS rate within a bounded error throughout intercept. Moreover, convergence properties of the LOS rate in the presence of control saturation are discussed. Numerical comparison studies demonstrate the guidance performance.

Robust impact angle constraints guidance law with autopilot lag and acceleration saturation consideration

In this paper, for the three-dimensional terminal guidance problem of a missile intercepting a manoeuvring target, a robust continuous guidance law with impact angle constraints in the presence of both an acceleration saturation constraint and a second-order-lag autopilot is developed. First, based on non-singular fast terminal sliding mode and adaptive control, a step-by-step backstepping method is used to design the guidance law. In the process of guidance law design, with the use of a finite-time control technique, virtual control laws are developed, a tracking differentiator is used to eliminate the ‘explosion of complexity’ problem inherent in the traditional backstepping method, and an additional system is constructed to deal with the acceleration saturation problem; its states are used for guidance law design and stability analysis. Moreover, the target acceleration is considered bounded disturbance, but the upper bound is not required to be known in advance, whereas the upper bound is estimated online by a designed adaptive law. Next, finite-time stability of the guidance system is strictly proved by using a Lyapunov method. Finally, numerical simulations are presented to demonstrate the excellent guidance performances of the proposed guidance law in terms of accuracy and efficiency.

Unknown ground moving target tracking using multiple unmanned aerial vehicles

This paper investigates the problem of robust guidance law design for multiple unmanned aerial vehicles to achieve desired formation pattern for standoff tracking of an unknown ground moving target. The proposed guidance law consists of two main parts: relative range regulation and space angle control. For the first mission, a novel control law is proposed to regulate the relative distance between the unmanned aerial vehicle and the ground moving target to zero asymptotically based on adaptive sliding mode control approach. Considering the discontinuous property of the sign function, which is often used in traditional sliding mode control and will result in high-frequency chattering in the control channel, the proposed controller adopts the continuous saturation function for chattering elimination. Besides the continuous property, convergence to the origin asymptotically can be guaranteed theoretically with the proposed controller, which is quite different from traditional boundary layer technique, where only bounded motion around the sliding manifold can be ensured. For asymptotic stability, it is only required that the lumped uncertainty is bounded, but the upper bound may be unknown by virtue of the designed adaptive methodology. For space angle control, a new multiple leader–follower information architecture is introduced and an acceleration command is then derived for each unmanned aerial vehicle to space them about the loiter circle defined by the first controller. Simulation results with different conditions clearly demonstrate the superiority of the proposed formulation.

A novel sliding mode guidance law without line-of-sight angular rate information accounting for autopilot lag

ABSTRACTThis paper proposes a new composite guidance law to intercept manoeuvring targets without line-of-sight (LOS) angular rate information in the presence of autopilot lag. The presented formulation is obtained via a combination of homogeneous theory and sliding mode control approach. Different from some existing observers, the proposed homogeneous observer can estimate the lumped uncertainty and the LOS angular rate in an integrated manner. To reject the mismatched lumped uncertainty in the integrated guidance and autopilot system, a sliding surface, which consists of the system states and the estimated states, is proposed and a robust guidance law is then synthesised. Stability analysis shows that the LOS angular rate can be stabilised in a small region around zero asymptotically and the upper bound can be lowered by appropriate parameter choice. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.

A blended control strategy for intercepting high-speed target in high altitude

To intercept target with high speed in high altitude, a blended control strategy is presented. The control strategy consists of two controls, one is the aerodynamic rudder control which is always switched on, another is the lateral jets control which is switched on only when the state variables’ prediction at impact point suggests that the only aerodynamic rudder control is not enough to achieve interception. The objective of this strategy is to save consumption of lateral jets, which is necessary in the case of limited number of jets. The algorithm of state variables’ prediction at impact point is summarized through recursive calculation using the analytic solutions of state variables of the kinematics with consideration of the dynamics of the interceptor (missile) by piecewise linearization and smart approximation. Considering the uncertain dynamics of the interceptor with blended control, a head pursuit robust guidance law is designed based on time-scale separation and robust control, where, the nonlinear deviation dynamics of the relation that the lead angle of the interceptor changes in proportion with that of the target, and the uncertain acceleration dynamics, are treated as the slow subsystem, while the uncertain pitch angular rate dynamics is treated as the fast subsystem. Numerical simulations are performed to verify the performance of the proposed guidance law.

A hybrid guidance law of LOS acceleration feedback for missile against maneuvering targets

A quantised backstepping robust guidance law of three-dimension(3-D) space for compound control of reaction control jets and aerodynamic surfaces is proposed to attenuate the unknown target manoeuvre in this paper. The presented guidance law guarantees that the rates of line of sight converge to a residual circle centred at the origin whose radius is depended on the target manoeuvres, quantised length and guidance law gains. The simulations are given to illustrate the effectiveness of the proposed guidance law.

Three-dimensional Robust Guidance Law with Impact Angle Constraint and Compensation of Channels Coupling

To deal with the coupling between channels in the guidance system for a bank-to-turn missile and the uncertainty of the measurement signal, a novel three-dimensional guidance law with impact angle constraint and compensation of channels coupling is proposed based on the robust control theory. Firstly, lineof- sight rate is described through vector description, and the representation of channels coupling is presented. Secondly, a guidance law which fulfills L2 performance index is designed by taking the measurement uncertainties as exogenous disturbance under the nonlinear robust control theory. A novel form of guidance law is obtained after joining the coupling term. Simulation results show that the proposed robust guidance law can guarantee the integrity of guidance information, also satisfy the requirements of guidance precision and impact angle constraint, and more robust than the traditional guidance law.

Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

SummaryThis paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher‐order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line‐of‐sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher‐order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line‐of‐sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.

Mars atmospheric entry guidance for reference trajectory tracking based on robust nonlinear compound controller

A robust entry guidance law based on terminal sliding mode and second-order differentiator is designed for trajectory tracking in this paper. The bank angle is regarded as the control variable. A novel nonlinear compound controller is designed to make the system with the trajectory-tracking error and its rate as states be input-to-state stable (ISS) with respect to uncertainties. The terminal sliding mode controller is designed to the problem of entry guidance by using the second-order differentiator to estimate the total disturbances. The proposed nonlinear compound control law by employing the second-order differentiator and the terminal sliding mode controller, provide robustness, higher control precision. Also, simulation results are presented to illustrate the effectiveness of the control strategy.

Sliding-mode-control based robust guidance algorithm using only line-of-sight rate measurement

Robust guidance algorithm using only line-of-sight rate measurement is proposed for the interceptor with passive seeker. The initial relative distance, initial closing velocity and their error boundaries are employed to obtain their estimations according to the interceptor-target relative kinematics. A robust guidance law based on sliding mode control is formulated, in which the boundary of target maneuver is needed and the chattering phenomenon inevitably exists. In order to address the defects above, an estimation to the boundary of the target acceleration is proposed to improve the robust guidance law and the Lyapunov stability analysis is included. The main feature of the robust guidance algorithm is that it reduces the influence of the relative distance, the closing velocity and the target maneuver on the interception and enhances the effect of line-of-sight rate. With two worst conditions of initial measured distance and initial measured closing velocity, performances of the proposed guidance laws are verified via numerical simulations against different target maneuvers.

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.

Robust terminal guidance law design for missiles against maneuvering targets

This paper describes an application of a new terminal guidance law for missiles against maneuvering targets in three-dimensional (3D) environment during the terminal phase. This novel approach is suitable for practical implementation of the guidance law under the circumstance of a guided missile against a maneuvering target. The design procedure is divided into two steps. First, a feedback linearization control scheme is designed to approximately achieve desired tracking of the uncertain missile–target system. Next, a combined optimal robust control scheme is employed to minimize the worst-case effect arising from external disturbances (target's maneuvers) in improving the tracking performance. Simulation examples are presented to illustrate engagement performance of the proposed approach.

Optimal integral sliding mode guidance law based on generalized model predictive control

This article investigates the problem of designing robust guidance laws for intercepting maneuvering targets with desired terminal line-of-sight angle constraint. Based on generalized model predictive control for the nominal system, the discontinuous and continuous integral sliding mode control laws are, respectively, developed. Stability analysis shows that the proposed guidance law can ensure the optimal tracking characteristic of generalized model predictive control algorithm and the line-of-sight angle tracking error as well as the line-of-sight angular rate can converge to zero asymptotically. The effectiveness of the proposed guidance law is validated by applying it to a surface-to-air missile for intercepting a head-on maneuvering target under different scenarios.

Robust finite-time stabilization of uncertain nonlinear systems based on partial stability

This paper presents a new approach to design a robust finite-time partial stabilization for uncertain nonlinear systems. The main contribution of this paper is to divide system state into two subsystems based on their required stability properties, and to stabilize just one of them in finite-time. First, integral sliding mode control is applied and the system is converted to a chain of integrators. Then, a finite-time state feedback controller with dynamical gains is utilized. Since guidance issue is an appropriate example in which stabilization of all of the state variables is not desirable, the proposed approach is employed to design a robust finite-time convergent guidance law. Simulation results justify that the proposed method is reliable in terms of robustness and effectiveness.

A three-dimensional robust nonlinear terminal guidance law with ISS finite-time convergence

ABSTRACTThis paper presents a novel three-dimensional nonlinear terminal guidance law with finite-time convergence for intercepting manoeuvring targets. Different from the usual method of decoupling the missile-target relative motion into two-dimensional planes, this law is designed via using the coupled dynamics. The guidance law is derived based on the theory of finite-time input-to-state stability (ISS), which needs no assumption of the linearisation and the estimation of target accelerations. Under this law, the line-of-sight angular rates can be stabilised to a small domain of convergence around zero in finite time. The convergence rate and convergence domain can be adjusted by changing the guidance parameters. First, a sufficient condition on finite-time ISS of the guidance system is given, and is subsequently used to design the guidance law. Finally, simulation results are provided to show that the proposed guidance law possesses fast convergence rate and strong robustness to target manoeuvres.

Observer-based guidance law against maneuvering targets without line-of-sight angular rate information

This paper presents a robust observer-based finite-time convergent guidance law to intercept maneuvering targets. To avoid the undesired chattering phenomenon existing in classical sliding mode control, the adaptive super-twisting algorithm is first introduced to design a robust guidance law to drive the line-of-sight (LOS) angular rates to a small region around the origin in finite time. The important feature of the proposed adaptation algorithm is in nonoverestimating the values of the guidance law gains, which is achieved by using a ‘detector’ scheme in the updating law. Moreover, with the proposed adaptive law, the presented guidance law requires no information on target maneuvers. Since the LOS angular rate is difficult for a pursuer to measure accurately for some seekers, a novel adaptive super-twisting observer is proposed to estimate it and a composite guidance law is then synthesized. Detailed finite-time stability analysis and comparison results with other guidance laws demonstrate the superiority of the proposed formulation.

Three-dimensional robust diving guidance for hypersonic vehicle

A novel three-dimensional robust guidance law based on H∞ filter and H∞ control is proposed to meet the constraints of the impact accuracy and the flight direction under process disturbances for the dive phase of hypersonic vehicle. Complete three-dimensional coupling relative motion equations are established and decoupled into linear ones by feedback linearization to simplify the design process of the further guidance law. Based on the linearized equations, H∞ filter is introduced to eliminate the measurement noises of line-of-sight angles and estimate the angular rates. Furthermore, H∞ robust control is well employed to design guidance law, and the filtered information is used to generate guidance commands to meet the guidance goal accurately and robustly. The simulation results of CAV-H indicate that the proposed three-dimensional equations can describe the coupling character more clearly than the traditional decoupling guidance, and the proposed guidance strategy can guide the vehicle to satisfy different multiple constraints with high accuracy and robustness.