Sliding Mode Guidance Research Articles

Three-Dimensional Impact Angle and Time Control Guidance Law Based on Two-Stage Strategy

In this article, a 3-D nonlinear guidance law is developed for attacking a stationary target with desired impact angle and time. The guidance law is divided into two stages—impact angle control guidance (IACG) and proportional navigation guidance (PNG). In the IACG stage, a sliding-mode guidance law is established to guarantee the satisfaction of the impact angle constraint, and in the second stage, the 3-D PNG law is applied to ensure zero miss distance. The switch between the IACG and the PNG stages is determined by a guidance parameter related to the impact time constraint. By the virtue of Newton iteration method, an appropriate guidance parameter is obtained by solving an implicit nonlinear equality after a small number of iterations. Several numerical simulations are conducted to verify the feasibility and effectiveness of the proposed guidance law under different scenarios.

A new three-dimensional adaptive sliding mode guidance law for maneuvering target with actuator fault and terminal angle constraints

In this paper, an adaptive terminal sliding mode guidance law is designed to intercept the maneuvering target with terminal line of sight angle constraints in three-dimensional space, and the actuator failure is considered. First, the relative kinematics model of three-dimensional space missile target considering fault is established. Then, the guidance law is designed by using the nonsingular fast terminal sliding mode method, which makes the tracking error and rate converge in finite time; Aiming at the problem of uncertain disturbance and fault in the model, the adaptive method is used to evaluate online. Finally, the Lyapunov stability theorem is used to prove that the missile target system is closed-loop stable under the proposed guidance law. Simulation results verify the performance of the proposed guidance law.

Adaptive improved super-twisting integral sliding mode guidance law against maneuvering target with terminal angle constraint

This paper investigates the maneuvering target interception problem considering terminal angle constraint, the input saturation and the second-order autopilot lag with the unavailable missile's acceleration. The considering problem is formulated as an output feedback control problem of a four-order nonlinear uncertain weakly observable system, which is challenging to address by general composite methods directly. Hence, the liner normal equivalent control model of the original guidance system is firstly derived to facilitate the extended state observer (ESO) based method design. Then, a nonlinear ESO is introduced to estimate the unmeasured system states and modeled disturbances as well as compensate for control saturation. Thereafter, the ESO-based guidance scheme is developed by integrating a novel four-order integral sliding mode manifold and an adaptive improved super-twisting algorithm. The main novelty is that a novel integral sliding mode manifold is proposed to replace the linear sliding mode manifold of super-twisting sliding mode to further reduce the convergent time of closed-loop system states. Besides, the conventional super-twisting algorithm is improved by modifying the reaching law and designing the adaptive gains to guarantee the continuity of guidance command and suppress the large constant gains and parameter uncertainties. Notably, only the output relative information is utilized in its design process. Numerical simulations validate the previous analyses and show the superiorities in reducing the energy consumption in high maneuvering target interception and achieving robustness to a certain margin under various uncertainties.

Second-Order Sliding Mode Guidance Law of a Nonsingular Fast Terminal with a Terminal Angular Constraint

Second-Order Sliding Mode Guidance Law of a Nonsingular Fast Terminal with a Terminal Angular Constraint

Terminal angle constrained time‐varying sliding mode guidance law with autopilot dynamics and input saturation

AbstractTo intercept the maneuvering target at a desired terminal angle, this paper presents a time‐varying sliding mode guidance law with consideration of the second‐order autopilot dynamics and input saturation. To achieve the finite‐time interception and satisfactory overload characteristics, a time‐varying sliding mode guidance law is developed, which enables the line‐of‐sight (LOS) angle error to converge into a small neighborhood of the origin at the interception time. An auxiliary system is constructed to reduce the adverse effect generated from the input saturation. Moreover, with the aid of extended state observers, the proposed guidance law requires no information on the target acceleration and the acceleration derivative of the interceptor. The performance of this guidance law is verified via the numerical simulations.

Cooperative Smooth Nonsingular Terminal Sliding Mode Guidance with Tracking Differentiator for Active Aircraft Defense

Aimed at the poor performance of guidance algorithms designed based on a linearized model in active defense under large leading angle deviation, both-way and one-way cooperative sliding mode guidance algorithms based on the smooth nonsingular terminal sliding mode for the defense missile are proposed. The relative kinematics and linearized models of the target, the active defense missile, and the attacking missile are established. In the design process, two smooth nonsingular terminal sliding mode surfaces are constructed based on zero-effort miss distance and zero-effort velocity, as well as their integral values. A tracking differentiator is introduced for excessive initial command deviation to meet the overload constraints of the active missile and the target. The sensitivity of guidance law to the estimated time-to-go error is reduced, and the target is allowed to perform an independent evasive maneuver. The effectiveness of the proposed guidance strategy is verified by numerical simulation and compared to the existing guidance strategies, the high accuracy, anti-chattering, and strong robustness of the proposed guidance algorithm are verified.

Three-dimensional prescribed performance sliding mode guidance law for intercepting maneuvering target

This article describes three-dimensional sliding mode guidance laws with prescribed performance. The proposed guidance laws can ensure that the line of sight (LOS) angle converges according to the prescribed performance, and the convergence rate, the steady-state error and the maximum overshoot can be preset in advance. By combining the LOS tracking error with the performance constraint function, a new error variable function is designed, and then the prescribed performance control problem is transformed into that of the boundedness of the error variable function. The key concept in this approach is to design a new sliding mode surface to ensure that the error variable function is bounded, so as to ensure that the system state converges according to the prescribed performance. Additionally, this article discusses the problem whereby the upper bound of the aggregate uncertainty, including the target information, is unavailable. An adaptive guidance law is presented for this scenario. Finally, simulations comparisons are conducted with other forms of guidance laws. Simulation results show that the guidance laws proposed in this article achieve effective performance.

Three-dimensional impact angles constrained integral sliding mode guidance law for missiles with input saturation

This paper proposes the three-dimensional impact angles constrained integral sliding mode guidance laws for the missile with the constraint of the input saturation. To solve the problem of the input constraint, an integral sliding mode surface is given for the first time by using the saturation function. The first three-dimensional integral sliding mode guidance law can solve the impact angle constraint and the target accelerations with known upper bound, while the second one can solve the impact angle constraint, input saturation, and the target accelerations with unknown upper bound simultaneously. Finally, numerical simulations are used to verify the effectiveness of the guidance laws.

A new three-dimensional fixed time sliding mode guidance with terminal angle constraints

In this paper, a continuous fixed-time guidance law with terminal angle constraints considering coupled dynamics is proposed for intercepting maneuvering targets in three-dimensional space. First, a fast fixed-time nonsingular sliding manifold is designed to guarantee the line-of-sight angle tracking errors and angular rates to zero in a fixed time. Next, a novel sliding mode reaching law is proposed to weaken the chattering phenomenon and guarantee guidance system states converge to sliding mode manifold in a fixed time. Finally, numerical simulations are conducted to validate the effectiveness and superiority of the proposed guidance law.

Three-dimensional adaptive fixed-time guidance law against maneuvering targets with impact angle constraints and control input saturation

This paper presents an adaptive fixed-time guidance law for the three-dimensional interception guidance problem with impact angle constraints and control input saturation against a maneuvering target. First, a coupled guidance model formulated by the relative motion equation is established. On this basis, a fixed-time disturbance observer is employed to estimate the lumped disturbances. With the help of this estimation technique, the adaptive fixed-time sliding mode guidance law is designed to accomplish accurate interception. The stability of the closed-loop guidance system is proven by the Lyapunov method. Simulation results of different scenarios are executed to validate the effectiveness and superiority of the proposed guidance law.

Saturated super-twisting sliding mode missile guidance

This paper concentrates on developing a missile terminal guidance law against a highly maneuvering target whose maneuvering acceleration is very close to that of the missile or even exceeds the missile normal acceleration in a finite period of time. A new saturated super-twisting algorithm is proposed and applied to the design of missile guidance law. The proposed algorithm has the advantages of simple structure, easy parameter tuning rules and a full utilization of the limit control input. The designed saturated super-twisting sliding mode guidance law is then employed in a missile guidance system. Simulation and its superior performance against strong maneuvering targets is demonstrated.

Terminal Distributed Cooperative Guidance Law for Multiple UAVs Based on Consistency Theory

In order to realize a saturation attack of multiple unmanned aerial vehicles (UAVs) on the same target, the problem is transformed into one of multiple UAVs hitting the same target simultaneously, and a terminal distributed cooperative guidance law for multiple UAVs based on consistency theory is proposed. First, a new time-to-go estimation method is proposed, which is more accurate than the existing methods when the leading angle is large. Second, a non-singular sliding mode guidance law (NSMG) of impact time control with equivalent control term and switching control term is designed, which still appears to have excellent performance even if the initial leading angle is zero. Then, based on the predicted crack point strategy, the NSMG law is extended to attack maneuvering targets. Finally, adopting hierarchical cooperative guidance architecture, a terminal distributed cooperative guidance law based on consistency theory is designed. Numerical simulation results verify that the terminal distributed cooperative guidance law is not only applicable to different forms of communication topology, but also effective in the case of communication topology switching.

Over-flight and standoff tracking of a ground target with a fixed-wing unmanned aerial vehicle based on a unified sliding mode guidance law

Target tracking of ground targets is a significant application of unmanned aerial vehicles (UAVs) in civil and military fields. There are two common modes for target tracking: over-flight tracking and standoff tracking. Each tracking method has a wide application prospect. However, many researchers have studied these two tracking methods separately and designed different guidance laws, which is not conducive to practical application. In this paper, a new guidance law based on sliding mode guidance (SMG) is proposed for tracking a stationary target, which is compatible with the two tracking modes. The stability and finite-time convergence of the guidance law are proved. Then, the guidance is extended to tracking a moving target. The numerical simulations are carried out for the tracking problems of ground targets, and the results verify the effectiveness of the proposed guidance law.

Three-dimensional time-varying sliding mode guidance law against maneuvering targets with terminal angle constraint

This paper deals with the problem of intercepting maneuvering targets with terminal angle constraints for missiles subjected to three-dimensional non-decoupling engagement geometry. To achieve the finite-time interception and satisfactory overload characteristics, a time varying sliding mode control methodology is developed based on a time base generator function. The main feature of the proposed guidance law guarantees the Line-of-Sight (LOS) angles to converge to small neighborhoods of the desired values at the interception time. First, a fractional power extended state observer is used to estimate the unknown target acceleration, which can significantly reduce the adaptive switching gain. The fractional power extended state observer enjoys the advantage of better noise tolerance. Then, a newly designed sliding mode surface is constructed by introducing a time base generator function and the time-varying sliding mode guidance law is developed based on this time-varying sliding surface. The proposed guidance law significantly reduces the overload magnitudes. Numerical simulations are carried out to verify the performance of the proposed guidance law.

Optimal predictive sliding-mode guidance law for intercepting near-space hypersonic maneuvering target

The design of optimal guidance law for intercepting a near-space hypersonic maneuvering target with bounded inputs is considered. Firstly, a maneuvering model for near-space hypersonic aircraft is given. Then, the aircraft acceleration prediction can be obtained using this model with two neural networks. By using the target acceleration prediction, which is taken into account when calculating the Zero Effort Miss (ZEM), an optimal sliding-mode guidance law is proposed to fulfill the guidance task. An adaptive sliding-mode switch term is designed to deal with actuator saturation and prediction errors. Finally, numerical simulations show that the proposed guidance law can reduce the energy consumption and the terminal acceleration command of the interceptor effectively.

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.

A Multiple Power Reachable Sliding Mode Control Approach for Guidance of Miniature Laser Beam Riding Steered Munition

For a two-stage launch miniature shoulder munition steered with a laser beam riding system, the laser beam points to the target with a limited field radius and approximate straight-line spatial path; thus, the munition could not fly into the laser information field after the powered flight. The miniature munition dynamics are established firstly; then, an adaptive multiple power reachable sliding mode controller is presented and adopted to constrain both the trajectory inclination and pitch angle, which makes the munition enter the field and fly under control in the field with desired attitude angles, respectively. Considering the constraints of the incidence angle and the radius of the laser information field, an arctangent function curve is selected as the expected trajectory, and an adaptive multiple power reachable integral sliding mode guidance law is detailed, which makes the munition trajectory approach and converges to the expected curve fastly with limited acceleration. Therefore, the miniature munition flight trajectory is planned and optimized. Convergence and stability are analyzed based on the Lyapunov method. The numerical simulation against the stationary target is performed to fully demonstrate the efficacy of the proposed method.

Design on adaptive weighted guidance law for underwater intelligent vehicle tracking target

In future naval warfare, the accurate attack of underwater intelligent vehicles on targets will become more and more important. Therefore, it is very important to study the guiding method which has the key influence on tracking targets. In the guidance process of intelligent navigation system, the estimation of guidance information by the agent is influenced by confrontation and interference, which often results in the decrease of the guidance accuracy of UUV under the single guidance law. In this paper, the estimated information is classified according to the different types of guidance target information combining to the advantages of three guidance methods, namely fixed advance angle, extended proportional guidance law and adaptive sliding mode guidance law. Then the fuzzy weight coefficient calculation method is used to get the weight coefficients of all kinds of information to form the adaptive weighted guidance law. The target tracking effects of each guidance method is simulated and compared in the simulation environment of the target maneuver and the target non-maneuver respectively.

Fractional Sliding Mode Guidance Law for High Speed Maneuvering Targets

Fractional Sliding Mode Guidance Law for High Speed Maneuvering Targets

Three-dimensional sliding mode guidance law for maneuvering target with prescribed performance and input saturation

The three-dimensional sliding mode guidance laws with prescribed performance and saturation actuator are proposed for maneuvering target. The proposed guidance laws can ensure the line of sight (LOS) angle converges according to the prescribed performance with actuator saturation and the convergence rate, the steady state error and the maximum overshoot can be preset in advance. A novel transformed error function is designed by combining the LOS tracking error with the performance constraint function. Then, to further solve the problem of input saturation, the saturation function and auxiliary system are introduced. Additionally, this paper discusses the problem whereby the upper bound of the aggregate uncertainty, including the target information, is unavailable. An adaptive sliding mode guidance law with prescribed performance is presented for this scenario. Experiments comparisons are conducted with other forms of guidance laws. Simulation results show that the guidance laws proposed in this paper achieve effective performance.