Acceleration Profile Shapeable Catenary-based Guidance with Arbitrary Impact Time and Angle Constraints

This paper proposed an optimal time-varying proportional navigation guidance law based on sequential convex programming. The guidance law can achieve the desired impact angle and impact time with look angle and lateral acceleration constraints. By treating the multiconstraints’ guidance problem as an optimization problem and changing the independent variable to linearize the problem and constraints, the original nonlinear and nonconvex problem is transformed into a series of convex optimization problem so that it can be quickly solved by sequential convex programming. Numerical simulations compared to nonlinear programming and traditional analytical guidance law demonstrate the effectiveness and efficiency of the proposed algorithm. Finally, the proposed guidance law is verified to satisfy different impact time periods and impact angle constraints.

Based on adaptive sliding mode control method, this paper considers the interception problem to deal with both impact time and angle constraints. The stability and convergence characteristic of proposed guidance law are analyzed. The requirements of the terminal constraints and minimum miss distance can be satisfied. An adaptive law is put forward to adjust the guidance gain. The simulation results indicate that the missile with proposed guidance law can intercept the target successfully with not only desired impact time but also expected impact angle. The interception task can be fulfilled in a satisfactory manner.

A novel two-stage missile guidance law for impact time and angle control is proposed. This guidance law is derived based on the nonlinear engagement dynamics without using small angle assumption. In order to control both impact time and impact angle, a two-stage scheme is developed. This scheme is composed of a nonsingular sliding mode guidance law for the first stage and a switching target strategy for the second stage. The guidance law is switched from the first stage to the second stage when the switching condition is attained, which can ensure that the guidance law is switched at the right time to satisfy impact time constraint. The switching target strategy in the second stage can achieve impact angle control with high accuracy. Impact time and angle can be controlled simultaneously under this two-stage scheme. Numerical simulations are performed to demonstrate the performance of the proposed method.

This paper presents a novel guidance law to intercept non-maneuvering targets with impact angle and lateral acceleration command constraints. Firstly, we formulate the impact angle control to track the desired line-of-sight (LOS) angle, which is achieved by selecting the missile's lateral acceleration to enforce the sliding mode on a sliding surface at impact time. Secondly, we use the Lyapunov stability theory to prove the stability and finite time convergence of the proposed nonlinear sliding surface. Thirdly, we introduce the wavelet neural network (WNN) to adaptively update the additional control command and reduce the high-frequency chattering of sliding mode control (SMC). The proposed guidance law, denoted WNNSMC guidance law with impact angle constraint, combines the SMC methodology with WNN to improve the robustness and reduce the chattering of the system. Finally, numerical simulations are performed to demonstrate the validity and effectiveness of the WNNSMC guidance law.

Three-dimensional adaptive fixed-time cooperative guidance law with impact time and angle constraints

P ROPORTIONAL navigation (PN) is a popular guidance law because of its robustness, simplicity, and ease of implementation. PN guidance law is capable of intercepting both nonmaneuvering and maneuvering targets [1]. PN is also an optimal control effort guidance law in the linearized setting [2]. Modern tactical guidance laws are designed not only to intercept a target but to satisfy other constraints [3] like impact time, impact angle, and other optimality constraints. These guidance laws can often be represented as being comprising of a PN component and other components designed to satisfy other constraints. As these guidance laws require an estimate of the time-to-go, it is important to develop methods to obtain an accurate estimate of the time-to-go for the PNguidance law. An interesting application requiring the estimation of time-to-go is in salvo attack problems [4], in which several missiles, launched at different times, need to achieve interception of the target simultaneously. Using PN guidance law to achieve this task requires an accurate estimation of time-to-go. Impact time, impact angle, and other optimal guidance laws also need information of the time-to-go to compute the guidance command. One of the simplest ways to estimate time-to-go is by computing range over closing velocity (or the negative of the range rate). The range over range rate estimate is accurate only when the closing velocity is constant and the initial heading error is small. Improved methods for time-to-go estimation by solving a linear quadratic control problem is discussed in York and Pastrick [5]. In Tahk et al. [6], a recursive time-to-go method is discussed in which the timeto-go estimates are updated recursively. The time-to-go estimate is updated in every guidance cycle time and a compensationmethod for the time-to-go error is obtained. The time-to-go estimate improves as the engagement proceeds because the guidance law used reduces the heading error. In Sang et al. [7] the commanded guidance history is considered to obtain the time-to-go estimate. The time-to-go estimate in Jeon et al. [4] is obtained as a function of the initial range and heading error. Our time-to-go estimation method also depends on the initial conditions and hence, our results are compared with Jeon et al. [4]. In this Note, an accurate method to obtain a time-to-go estimate of PN guidance law for a stationary target is proposed. The time-to-go for a stationary target is obtained accurately by a simple interpolation. It is shown that from the time-to-go estimate of a particular initial condition, the time-to-go estimate of any other initial condition can be obtained by a simple but elegant time scaling property of the PN guidance law. The time-to-go estimate as a function of the heading error for the particular initial condition is used as the base solution for estimating the time-to-go for other initial conditions. This method also gives estimates for initial conditions with large initial heading errors; even for cases when the missile is launched with a high heading error. Themethod can be used to obtain time-to-go estimates for any initial condition and navigation gain. The time-to-go estimation is extended to constant velocity targets by a simple iterative process. The time-to-go obtained after the initial iteration is exact and need not be computed in every guidance cycle time.

This paper proposes a near‐optimal air‐to‐ground missile guidance law with impact angle and impact velocity constraints based on sequential convex programming. A realistic aerodynamic model is introduced into the problem formulation, such that traditional optimization theory cannot obtain an analytical solution to the optimization problem under state constraints. The original problem is considered as an optimization problem, and the angle of attack is replaced with the angle of attack rate as a new control variable to reconstruct the problem and simplify the solving process. Next, the independent variable is changed in the differential equations to linearize and discretize the problem such that the reconstructed problem can be solved using sequential convex programming. The results obtained by numerical simulations confirmed that the proposed algorithm is valid and faster than the general‐purpose nonlinear optimal control problem solver. Finally, it was verified that different impact angles and impact velocities were achieved.

Given the limitations of escape maneuvers and decoy deployment of combat aircraft under missile attacks; active defense dramatically improves the survival chances by launching active defense missiles to intercept incoming missiles. Different from previous work, this paper implemented impact angle constraints on the defense missile to achieve a better defense effect. The low-cost active defense missile with limited maneuverability is considered to cooperate with the aircraft through three mechanisms, namely two-way cooperation without any predetermined strategy, one-way cooperation with the defense missile employing a linear guidance strategy, and one-way cooperation with independent evasion maneuver for the target. Three optimal cooperative guidance strategies with impact angle constraints were investigated. Finally, a nonlinear two-dimensional model for agents with first-order autopilot dynamics was simulated to verify the performance of the proposed strategies. The simulation results indicated that the cooperative mechanism directly affects the available range of impact angles, and the constraints of a big impact angle can be realized by introducing the nonlinear model parameters and considering the angle variation between the velocity vector and the initial line-of-sight. Furthermore, the two-way cooperative mechanism achieves the best performance and more flexible solutions to accommodate different vehicle maximum overload limits.

Robust extended state observer-based three dimensional integrated guidance and control design for interceptors with impact angle and input saturation constraints

In this paper, an optimal sliding mode guidance law with impact angle constraint is proposed against maneuvering targets. Firstly, the impact angle frame for a static target is extended to a maneuvering target. Then, in this impact angle frame, the optimal reaching law of sliding mode is proposed to design an optimal sliding mode guidance law which is robust to target maneuvers and satisfies an impact angle constraint. The optimal sliding mode guidance law with impact angle constraint is also extended to the three-dimensional case. Numerical simulations in different scenarios with a realistic missile model show that the guidance law can intercept a maneuvering target with a desired impact angle, and the control effort is close to the optimal value, which verifies that the proposed optimal sliding mode guidance law has both robustness and optimality.

With the widespread informationization in modern warfare, higher requirements are required for monitoring the high-value target’s movement state and the corresponding attack conditions. Since the impact-angle constraint guidance law can improve the striking effect of a missile, the study of the hitting conditions and corresponding angle range of the attack angle constraint guidance law has become particularly important. This paper proposes a relationship between the missile’s line-of-sight and flight-path angle under terminal conditions and defines the line-of-sight selection region. Then, we analyze the selection method of the line-of-sight restriction at the end of the missile’s terminal phases. Additionally, Cauchy’s inequality is used to derive the mathematical expressions for line-of-sight selection region under extreme and ideal conditions when employing the developed guidance law to intercept non-maneuvering targets. Finally, a thorough analysis and numerous simulations demonstrate that the line-of-sight angle always falls within the extreme selection region during the entire flight and before hitting the target at the expected impact angle. Compared with a head-on interception, the line-of-sight selection region of the tail-chase case is broader, and the selection region range increases with the upward trend of the acceleration limit.

The problem of impact angle constrained distributed cooperative guidance against maneuvering targets with undirected communication topologies is studied. A novel distributed cooperative guidance strategy is proposed to realize simultaneous attack with impact angle constraint. Firstly, the kinematic equations for the engagement are established. According to the engagement equations, the cooperative guidance problem is divided into two units, which include the cooperation of both impact time and impact angle. Secondly, the guidance algorithm is designed separately for simultaneous attack and dealing with the impact angle constraints. The problem is transformed into a consensus problem via disturbance compensation and feedback linearization technique. The convergence of the guidance algorithm is proven by using the consensus theory. Finally, numerical simulations are presented to verify the effectiveness of the proposed cooperative guidance law.

This study presents a guidance law to intercept non‐manoeuvring targets at a desired impact angle. The desired impact angle, defined in terms of a desired line‐of‐sight angle, is achieved by selecting the missile's lateral acceleration to enforce the sliding mode on a sliding surface. Then, the authors use the Lyapunov stability theory to prove the stability of the proposed non‐linear sliding surface. Furthermore, they introduce the adaptive neuro‐fuzzy inference system (ANFIS) to adaptively update the additional control command and reduce the high‐frequency chattering of sliding mode control (SMC). The proposed guidance law, denoted ANFSMC guidance law with impact angle constraint, combines the SMC methodology with ANFIS to enhance the robustness and reduce the chattering of the system. The effectiveness of the ANFSMC guidance law is also verified by the numerical simulations.

Optimum filter theory has nowadays well stated applications in many scientific and technical fields, from communications to biomedical engineering, from nuclear electronics to safety systems, which need accurate estimations of a various number of parameters, extracted from signals detected in noisy environments. The work deals with the experimental implementation of a relaxed constraints fulfillment technique, which allows achieving constraint accomplishments up to the required level of precision, to avoid further and needless degradation in measurement resolution. In particular, the implemented processing technique leads to a class of optimum filters with arbitrary constraints in time and frequency. The implementation has been performed into a digital fully configurable architecture that, in addition to signal generator for emulation of radiation detectors and front-end electronics, also acts as processor of signals from radiation detectors. The experimental implementation has been carried out, tested and fully validated.

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity