Time Control Guidance Research Articles

Autonomous cooperative guidance based on distributed consensus and self-management

As for the time-space cooperative guidance under complex offense–defense game conditions, this article proposes a distributed time-space cooperative guidance strategy based on consensus theory and missile group (MG) self-management. The strategy consists of a three-layer cooperative guidance system: the lower layer is the impact time and angle control guidance (ITACG) based on optimal control with minimum energy consumption. The middle layer is the time-space cooperative control strategy via distributed consistency with the time-to-go as the coordination variable. The upper layer is the MG self-management strategy considering the complex attack–defense conditions. The simulation results show that the cooperative strategy can achieve simultaneous attack at different directions and improve the penetration probability and the ability to respond to the attack–defense situation effectively.

Three Dimensional Impact Time Control Guidance Law with Field of View Constraint

Three Dimensional Impact Time Control Guidance Law with Field of View Constraint

Nonsingular PNG-Based Impact Time Control Guidance with Lower Dependence on Time-to-Go Estimate

In a bid to take advantage of natural characteristics of the proportional navigation guidance (PNG) in practical engineering, the PNG-based impact time control guidance (ITCG) continues to be a popular alternative for achieving the desired impact time of a missile. For most such ITCG, the performance is dependent on the accuracy of the time-to-go estimation. Along the lines of the development of PNG-based ITCG in earlier studies, a nonsingular ITCG is proposed on the basis of nonlinear formulations. It is demonstrated that, by theoretical analysis and numerical simulation, this proposed ITCG is shown to be advantageous in certain circumstances. By deriving a novel additional acceleration command, the proposed law is of lower dependence on time-to-go estimate and is capable of eliminating some singularities, leading to wider adjustable range of the desired impact time and better adaptability to more conditions. This research is expected to be supplementary to those presented in the current research literature.

Three-Dimensional Impact Time and Angle Control Guidance Based on MPSP

A new nonlinear guidance law for air-to-ground missile cooperation attacks is proposed in this paper. This guidance law enables missiles with different initial conditions to attack targets simultaneously, and it can also precisely satisfy the terminal impact angle conditions in both flight-path angle and heading angle. The guidance law is devised using the model predictive static programming (MPSP) method, and the control saturation constraint is incorporated in the MPSP algorithm. The first-order-lag acceleration of the missile is taken as the state variable to realize the convergence of the terminal acceleration to zero. Moreover, a collision avoidance strategy for three-dimensional missile cooperative flight is proposed. The simulation results show that the guidance law can make the missiles hit the target accurately at the same time with the ideal impact angles and can realize the control saturation constraints of the missiles. This can increase the attack effects and is significant for collaborative attacks.

Backstepping-Based Impact Time Control Guidance Law for Missiles With Reduced Seeker Field-of-View

This paper proposes a guidance law that achieves the desired terminal impact time without violating a seeker's field-of-view (FOV) limits. In order to derive the guidance law, kinematic conditions for impact time control are defined, and the backstepping control technique is applied for the satisfaction of the conditions. As a virtual control input for the backstepping structure, the missile lead angle, which represents the angle between the line-of-sight (LOS) and missile velocity vector, is used and its magnitude is limited by a prescribed limit. Then, the seeker's look angle can also be confined within a specific range because the seeker look angle is mainly determined by the difference between the LOS and the velocity vector. This capability to confine the seeker's look angle with achieving the desired impact time is the main contribution of the paper. To evaluate the performance of the proposed law, numerical simulation is conducted. The result demonstrates that the proposed guidance law enables the missile to simultaneously achieve the interception and desired impact time without violating the prespecified FOV limits.

Sliding Mode Guidance Law for Impact Time Control Without Explicit Time-to-Go Estimation

This paper presents an impact time control guidance law that does not perform explicit time-to-go estimation. In order to satisfy the interception and the desired impact time constraint simultaneously, a sliding surface variable formulated as a sum of the relative range and the desired time-to-go is defined, weighted by two nonzero weighting functions. Then, the achievement of the sliding mode satisfies the following equivalence: The relative range is zero if and only if the elapsed time equals to the desired impact time. It means that both the interception and impact time control can be satisfied at the same time in the sliding mode. The impact time control guidance law is derived to enforce the defined surface variable to the sliding mode. Because the law is designed based on the capture condition without separate time-to-go estimation process, the achievement of the sliding mode always guarantees the interception of the target at the desired impact time. In addition, the proposed law can be applied to an engagement considering nonstationary targets in a straightforward manner because the corresponding time-to-go estimation is not needed. Simulation results demonstrate that the proposed guidance law has better performance in comparison with the existing guidance law, in respect of satisfying the desired impact time constraint against a nonstationary target.

Impact time and angle control guidance independent of time-to-go prediction

A novel cruise guidance method that can meet the terminal latitude and longitude, time and angle constraints independent of time-to-go prediction is studied in this paper. The impact time and angle control guidance (ITACG) goal is achieved through two steps. The first step is the construction of the complete motion model, the constant altitude and velocity guidance laws, and the optimal proportional guidance law which can satisfy the terminal position constraint based on the in-plane relative motion equation. The impact time control is the second step, which can be achieved by the integrated utilization of optimal guidance and maneuvering flight. Additional maneuvering trajectories used to control the impact time are designed in both cases with and without angle constraint, and the maneuvering parameters are directly solved online without time-to-go prediction. Simulation results verify the effectiveness of the guidance method, as well as the adaptability to different initial conditions and terminal constraints.

A composite impact-time-control guidance law and simultaneous arrival

A new composite impact time control guidance law is proposed for simultaneous attack against a ground target. The guidance strategy is composed of two phases. Specifically, the first phase is to guide the missile to proper switching relative range for the second phase. After which, the second phase will lead the missile to the target with a desired impact time by using the proposed Lyapunov based guidance scheme. The impact time is given in a simple analytical form of initial states and switching relative range, the value of which is determined to control the impact time. The proper range of the switching state is analyzed considering the line of sight angle constraint. And the permissible range for impact time can be calculated corresponding to the proper switching state. Two classes of simultaneous attack are considered to demonstrate the effectiveness of the impact time control. One is the sequential launch, and the other is a salvo launch of multiple missiles from different positions. Numerical simulations are carried out to verify the performance of the proposed methodology.

Impact time control guidance law for large heading errors

Impact time control guidance law for large heading errors

Impact Angle and Time Control Guidance Under Field-of-View Constraints and Maneuver Limits

This paper proposes a guidance law which considers the constraints of seeker field-of-view (FOV) as well as the requirements on impact angle and time. The proposed guidance law is designed for a constant speed missile against a stationary target. The guidance law consists of two terms of acceleration commands. The first one is to achieve zero-miss distance and the desired impact angle, while the second is to meet the desired impact time. To consider the limits of FOV and lateral maneuver capability, a varying-gain approach is applied on the second term. Reduction of realizable impact times due to these limits is then analyzed by finding the longest course among the feasible ones. The performance of the proposed guidance law is demonstrated by numerical simulation for various engagement conditions.

A New Impact Time and Angle Control Guidance Law for Stationary and Nonmaneuvering Targets

A guidance problem for impact time and angle control applicable to cooperative attack is considered based on the sliding mode control. In order to satisfy the impact angle constraint, a line-of-sight rate polynomial function is introduced with four tuning parameters. And the time-to-go derivative with respect to a downrange orientation is derived to minimize the impact time error. Then the sliding mode control surface with impact time and angle constraints is constructed using nonlinear engagement dynamics to provide an accurate solution. The proposed guidance law is easily extended to a nonmaneuvering target using the predicted interception point. Numerical simulations are performed to verify the effectiveness of the proposed guidance law for different engagement scenarios.

POLYNOMIAL FUNCTION BASED GUIDANCE FOR IMPACT ANGLE AND TIME CONTROL

In this paper, missile homing guidance laws to control the impact angle and time are proposed based on the polynomial function. To derive the guidance commands, we first assume that the acceleration command profile can be represented as a polynomial function with unknown coefficients. After that, the unknown coefficients are determined to achieve the given terminal constrains. Using the determined coefficients, we can finally obtain the state feedback guidance command. The suggested approach to design the guidance laws is simple and provides the more generalized optimal solutions of the impact angle and time control guidance.

GUIDANCE LAW FOR IMPACT TIME AND ANGLE CONTROL WITH CONTROL COMMAND RESHAPING

In this article, a more generalized form of the impact time and angle control guidance law is proposed based on the linear quadratic optimal control methodology. For the purpose on controlling an additional constraint such as the impact time, we introduce an additional state variable that is defined to be the jerk (acceleration rate). Additionally, in order to provide an additional degree of freedom in choosing the guidance gains, the performance index that minimizes the control energy weighted by an arbitrary order of time-to-go is considered in this work. First, the generalized form of the impact angle control guidance law with an additional term which is used for the impact time control is derived. And then, we also determine the additional term in order to achieve the desired impact time. Through numbers of numerical simulations, we investigate the superiority of the proposed guidance law compared to previous guidance laws. In addition, a salvo attack scenario with multiple missile systems is also demonstrated.

Impact time control guidance with field-of-view constraint accounting for uncertain system lag

The problem of impact time control guidance with seeker’s field-of-view constraint in the presence of uncertain system lag is addressed. A novel two-step control approach based impact time control guidance law with seeker’s field-of-view constraint is proposed. Specifically, in the first step, a state constrained robust adaptive control law, using the dynamic surface control method combining with the control integral barrier Lyapunov function technique, is synthesized to achieve the required robust tracking performance with respect to the desired trajectory of lead angle in the presence of uncertain system lag and other uncertainties. In the second step, the desired trajectory of lead angle is generated online to guarantee target interception at the designated impact time under the assumption of ideal autopilot dynamics while not violating the seeker’ field-of-view constraint. The proposed guidance law ensures the seeker’s field-of-view constraint does not be violated in the presence of uncertain system lag and other uncertainties. Numerical simulations are provided to illustrate the effectiveness of the proposed guidance law.

Lyapunov-based impact time control guidance laws against stationary targets

Nonlinear guidance laws that consider impact time constraints are proposed. Two-dimensional and three-dimensional impact time control guidance laws are derived using Lyapunov stability theory. Under the consideration of the nonlinear kinematics, it is shown that the missile states converge to the desired equilibrium point by the Lyapunov stability theory. The singularity issue of the proposed guidance laws is also analyzed. Numerical simulations are performed to verify the performance of the proposed guidance laws.

Impact time control guidance law with large impact angle constraint

The problem of impact time control with large impact angle constraint is addressed. The dynamics of impact time error under the biased proportional navigation based impact angle control guidance law is first derived for the case of large impact angle constraint. Based on the impact time error dynamics, an additional control term is designed to drive the impact time error to converge in finite time. The resultant impact time and impact angle control guidance law comprises the biased proportional navigation based impact angle control guidance law and an additional term. The first term is used to achieve zero miss distance with the designated impact angle, and the second term is used to control the impact time. Compared with the existing impact time and impact angle control guidance law, which is shown to be only applicable for the case of small impact angle constraint, its application is not limited by the magnitude of the designated impact angle. Finite time convergence of the closed-loop guidance system under the proposed impact time and impact angle control guidance law is proved. Numerical simulations are performed to verify the effectiveness of the proposed impact time and impact angle control guidance law, especially for case of large impact angle constraint.

Impact time control guidance law with field of view constraint

The problem of Impact Time Control Guidance (ITCG) with field-of-view (FOV) constraint is investigated. The proposed ITCG law is a combination of the well-known Proportional Navigation Guidance (PNG) law and an additional biased term of impact time error, which is defined as the difference between the impact time by PNG and the prescribed one. A rule of the cosine of weighted leading angle in the biased term is used to guarantee that the FOV constraint is not violated during the engagement. Stability of the closed-loop guidance system is proved strictly. Numerical simulation results are presented to demonstrate the effectiveness of the proposed guidance law.

Cooperative Rendezvous Guidance using Sliding Mode Control for Interception of Stationary Targets

In this paper, a cooperative rendezvous guidance, or salvo attack guidance strategy, using impact time constrained guidance law, is proposed for stationary targets. The impact time constrained guidance law is derived using nonlinear engagement dynamics and the concept of sliding mode control. The proposed guidance scheme is based on combining the idea of coordination algorithm and impact time control guidance law. The coordination among all the interceptors are established by using a centralized coordination algorithm. Here, the desired impact time is determined in real-time in such a way as to minimize the total switching surface deviations. In order to calculate the desired impact time, only time-to-go information of all the interceptors are required. Numerical simulation results are presented to validate the proposed guidance schemes.

A biased proportional navigation guidance law with large impact angle constraint and the time-to-go estimation

For large impact angle control problem (here, the “large impact angle” means the impact angle in the closed interval from −180° to 180°), estimating the time-to-go accurately is the key of impact time and impact angle control guidance (ITIACG). The objectives of this paper are to construct a new impact angle control guidance (IACG) law suitable for large impact angle control and present a time-to-go estimation procedure for the new IACG law suitable for designing ITIACG law. The constructed IACG law is a biased proportional navigation guidance law with large impact angle constraint, the rule of the cosine of the lead angle in the biased term is to guarantee that the lead angle remains in the open interval from −90° to 90°, which is required in the development of time-to-go estimation procedure. To estimate the time-to-go, by introducing a self-convergent angle named as alfa, the closed equations of motion are transformed to a different form, which can be solved conveniently under the assumption of small lead angle. For the case of large lead angle, the time interval of time-to-go is partitioned into n segments, the maximum increment of lead angle is supposed to be a small angle in each segment, the transformed closed equations of motion can be expressed as function of alfa angle and solved analytically. A geometric approach is proposed to determine conservatively a suitable alfa angle to guarantee that the maximum increment of lead angle is a small angle in each segment. The time-to-go estimation procedure for the new IACG law are illustrated. Simulations are performed to verify the effectiveness of the proposed IACG law and the accuracy of the time-to-go estimation procedure.

Augmented Polynomial Guidance With Impact Time and Angle Constraints

In this paper, a new impact time and impact angle control guidance law for homing missiles against a stationary target is proposed. To derive a state feedback command for the proposed law with terminal constraints on the impact time and angle, we introduce a polynomial function of the guidance command with three unknown coefficients, one of which is determined to achieve the impact time requirement. The others are determined to satisfy the terminal impact angle constraint, as well as the zero miss distance. Because the proposed guidance law has arbitrary guidance gains, it is possible to shape the intercept trajectory and acceleration command profile by choosing proper gains in relation to the missile's capability, operational conditions, and so on.