An Intercept Guidance Law with Impact-Angle-Constrained Based on Linear Gauss Pseudospectral Model Predictive Control

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

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.

In this paper, a nonsingular, essentially continuous and finite-time convergent impact angle constrained guidance law for intercepting stationary, constant speed, and maneuvering targets is developed using advanced terminal sliding mode control schemes and extended state observer. In order to achieve the specified intercept angle in finite time without singularity, the nonsingular fast terminal sliding mode control algorithm is employed to construct sliding surface. The fast terminal sliding mode control technique is used to establish the reaching law, so the system trajectory converges quickly from initial state to the switching surface in the whole reaching phase and the proposed guidance law is essentially continuous. Noticing the interception of a maneuvering target, the unknown target acceleration is estimated and compensated using extended state observer. Due to its inherent attribute of singularity-free, continuity, and faster convergence rate, no approximation is necessary in the implementation of the proposed guidance law, so better tracking accuracy of the desired intercept angle in a shorter time with a smoother guidance command can be guaranteed compared with conventional terminal sliding mode guidance law. A large number of numerical simulations are implemented to justify the effectiveness of the proposed guidance law.

Accounting for the autopilot as second-order dynamics, an observer-based guidance law with terminal impact angle constraint is designed using the dynamic surface control method. Some first-order low-pass filters are introduced into the designing process to avoid the occurrence of high-order derivatives of the line of sight (LOS) angle in the expression of the guidance law such that the guidance law can be implemented in practical applications. The proposed guidance law is effective in compensating for the second-order autopilot lag. In simulation of intercepting targets with sinusoidal acceleration, the guidance law is compared with the biased proportional navigation guidance (BPNG) law in the presence of missile autopilot lag. Simulation results show that the proposed observer-based guidance law with terminal impact angle constraint is able to guide a missile with large autopilot lag to impact a target with a desired angle and achieve a small miss distance, even if the target escapes in a great and fast maneuver.

The model predictive control method can be effective for converter control in distributed power generation but requires a large amount of computation, leading to a considerable time delay in the actuation. If the delay is not reflected, the system performance could get worse. This paper presents a two-step (horizon) prediction algorithm of model predictive control technique for grid-tied inverters used in wind turbine systems. The control objectives such as active and reactive power flow and switching loss reduction are reflected in the objective function of the controller. The proposed model predictive control strategy is verified numerically by using MATLAB/Simulink.

In this work, design of three-dimensional (3D) proportional navigation guidance law based on input-output linearization (IOL) for tactical missiles is proposed. For the three-dimensional nonlinear missile-target engagement dynamics, the line-of-sight (LOS) rates in pitch and yaw planes are taken as outputs and the IOL theory is used to derive the guidance laws without ignoring the cross-coupling terms. Simulations are carried out by considering maneuvering target, and the results are presented to showcase the efficacy of the proposed design. Further, comparison of the performance of the proposed guidance law with augmented proportional navigation guidance(APNG) laws is carried out and the related results are presented. Lastly, implementation issues of the proposed guidance law are discussed.

Terminal guidance law against the maneuvering target is always the focal point. Most of the literatures focus on estimating the acceleration of target and time to go in guidance law, which are difficult to acquire. This paper presents a terminal guidance law based on receding horizon control strategy. The proposed guidance law adopts the basic framework of receding horizon control, and the guidance process is divided into several finite time horizons. Then, optimal control theory and target motion prediction model are used to derive guidance law for minimum time index function with continuous renewal of original conditions at the initial time of each horizon. Finally, guidance law performs repeated iteration until intercepting the target. The guidance law is of subprime optimal type, requiring less guidance information, and does not need to estimate the acceleration of target and time to go. Numerical simulation has verified that the proposed guidance law is more effective than traditional methods on constant and sinusoidal target with bounded acceleration.

This chapter presents the results of experiments comparing different computationally efficient model predictive control (MPC) methods applied to a laboratory device, demonstrating the active vibration control (AVC) of lightly damped mechanical structures. Because of the combination of long prediction horizons, short sampling times and large actuator-disturbance asymmetry, the implementation of the predictive control strategy on lightly damped vibrating structures is highly demanding. The vibration damping effect and online timing properties of model predictive control algorithms such as infinite horizon cost dual-mode quadratic programming based MPC (QPMPC), pre-computed explicit multi-parametric programming based MPC (MPMPC), minimum-time MPMPC and the very efficient but suboptimal Newton–Raphson based MPC (NRMPC); all with guaranteed stability and constraint feasibility are analyzed in different disturbance and loading scenarios. All MPC methods along with the baseline linear quadratic (LQ) controller decrease vibration settling to equilibrium by an order of magnitude time. The damping effect of all investigated MPC strategies is comparable with a slight decrease in performance for the suboptimal minimum-time MPMPC and NRMPC controllers. Due to the excessive online computational needs of QPMPC, it is a very unlikely candidate for lightly damped vibrating systems given currently available hardware. The online timing analysis presented here demonstrates that MPMPC provides significantly shorter online execution times, however its suboptimal minimum-time version does not bring a convincing improvement. NRMPC can provide online execution times on par with linear quadratic controllers; however, its suboptimality becomes excessive with increasing prediction model orders.

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.

A novel nonlinear impact angle guidance law for stationary targets, based on Lyapunov stability theory, is proposed in this work. In the proposed guidance law, nonlinear line-ofsight dynamics of the engagement geometry between the pursuer and stationary target is studied and the state equations for the line-of-sight angle and its rate are derived. The lineof-sight angle is aimed to be controlled to satisfy impact angle constraints. Then a sliding manifold which drives the line-of-sight angle and its rate to exponential stability is constituted. Robust Control Lyapunov Function is introduced to the system to control the line-of-sight dynamics to head it towards defined sliding manifold. The necessary commands are analytically calculated. Finally the comparison with a different impact angle control guidance law is performed to summarize the proposed guidance law performance.

A Backstepping guidance (BSG) law with saturating actuator is proposed for nonlinear kinematics of missile-target motion in the three-dimensional (3D) spherical coordinates system. The most important characteristic of Backstepping control (BSC) is high robustness. The proposed guidance law can reduce interception time and increase robustness in comparison with other guidance laws. In the proposed guidance outline, a Backstepping guidance law is designed to eliminate the effect of external perturbation. Then, it is illustrated that derived guidance law stabilize system. Some scenarios are considered for the engagement and simulated. Simulation results confirm above pretensions.

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.

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 centralized control for a wind farm using model predictive control (MPC) method. In order to solve intra-day unit commitment (UC) problem, the UC problem is solved by using the MPC method with short-term wind power forecasting. We introduce a new dynamics model for the UC with some constraints to utilize the benefits of the MPC method. The objective function considering the operation and maintenance costs is formulated by adding a new variable in order to average the operating time of each wind turbine (WT) within the whole time. The proposed method could solve the UC problems on-line using the prediction time horizon that could be selected flexibly considering time horizon based on wind power forecasting errors. From the simulation study using 10 WTs, we observed that the proposed dynamics model of UC effectively provided the optimal solution to each scenario. Numerical study will validate that the proposed method can be applied to solving the UC problem of a large scale wind farm by aggregating WTs.

In this paper, a suboptimal guidance law with the terminal constraints on impact angle, acceleration, and time-derivative of acceleration (jerk) is presented. The proposed homing guidance problem is an over-determined problem, i.e., the number of constraints is much larger than the order of system. Since it is difficult to solve the problem by using the conventional optimal control theory, we newly introduce the control input which consists of an additional feed-forward command and the optimal feedback command. The additional feed-forward command is defined as a polynomial function of time-to-go with two degree-of-freedoms. Here, the coefficients of the function in the feed-forward command are determined to satisfy the constraints on terminal acceleration and jerk. The optimal feedback command in consideration of a feed-forward command is determined by Schwartz inequality. The guidance command obtained from the proposed scheme shows a similar form of the biased proportional navigation (BPN) guidance obtained by the optimal control theory. However, the proposed guidance law is less sensitive to the time-to-go estimation error than the BPN law, and it can be easily implemented in the real system. Furthermore, since the coefficients of time-to-go in the feed-forward command remain as design parameters, the proposed guidance law provides more flexibility in application aspect such as trajectory shaping. The characteristics of the proposed guidance law is studied and its performance is also evaluated through numerical simulation.