Trajectory shaping guidance law based on virtual angle with terminal constraints

A trajectory shaping guidance law based on virtua angle （TSGLBVA） is proposed for a re-entry vehicle with the constraints of terminal impact angles and their time derivatives. In the view of differential properties of the maneuvering trajectory, a virtual angle and a virtual radius are defined. Also, the shaping trajectory of the vehicle is established by the polynomials of the virtual angle. Then, four optimized parameters are selected according to the theorem of parameters transformation presented in this paper. Finally, a convergent variant of the Nelder-Mead algorithm is adopted to obtain the reference trajectory, and a trajectory feedback tracking guidance law is designed. The simulation results demonstrate that the TSGLBVA ensures the re-entry vehicle to impact a target precisely from a specified direction with smal terminal load factor command, as well as to obtain a maximum or constrained terminal velocity according to various requirements.

A trajectory shaping guidance law with field-of-view angle constraint and terminal limits

In this paper, a trajectory shaping guidance law,which considers constraints of field-of-view(FOV) angle, impact angle, and terminal lateral acceleration, is proposed for a constant speed missile against a stationary target. First, to decouple constraints of the FOV angle and the terminal lateral acceleration, the third-order polynomial with respect to the line-ofsight(LOS) angle is introduced. Based on an analysis of the relationship between the looking angle and the guidance coefficient,the boundary of the coefficient that satisfies the FOV constraint is obtained. The terminal guidance law coefficient is used to guarantee the convergence of the terminal conditions. Furthermore, the proposed law can be implemented under bearingsonly information, as the guidance command does not involve the relative range and the LOS angle rate. Finally, numerical simulations are performed based on a kinematic vehicle model to verify the effectiveness of the guidance law. Overall, the work offers an easily implementable guidance law with closed-form guidance gains, which is suitable for engineering applications.

Terminal Angular Constraint Integrated Guidance and Control for Flexible Hypersonic Vehicle with Dead-Zone Input Nonlinearity

This paper presents an integrated guidance and control model for a flexible hypersonic vehicle with terminal angular constraints.The integrated guidance and control model is bounded and the dead-zone input nonlinearity is considered in the system dynamics.The line of sight angle,line of sight angle rate,attack angle and pitch rate are involved in the integrated guidance and control system.The controller is designed with a backstepping method,in which a first order filter is employed to avoid the differential explosion.The full tuned radial basis function(RBF)neural network(NN)is used to approximate the system dynamics with robust item coping with the reconstruction errors,the exactitude model requirement is reduced in the controller design.In the last step of backstepping method design,the adaptive control with Nussbaum function is used for the unknown dynamics with a time-varying control gain function.The uniform ultimate boundedness stability of the control system is proved.The simulation results validate the effectiveness of the controller design.

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.

AN ANT COLONY ALGORITHM FOR YARD TRUCK SCHEDULING AND YARD LOCATION ASSIGNMENT PROBLEMS WITH PRECEDENCE CONSTRAINTS

This paper examines the yard truck scheduling,the yard location assignment for discharging containers,and the quay crane scheduling in container terminals.Taking into account the practical situation,we paid special attention to the loading and discharging precedence relationships between containers in the quay crane operations.A Mixed Integer Program（MIP） model is constructed,and a two-stage heuristic algorithm is proposed.In the first stage an Ant Colony Optimization（ACO） algorithm is employed to generate the yard location assignment for discharging containers.In the second stage,the integration of the yard truck scheduling and the quay crane scheduling is a flexible job shop problem,and an efficient greedy algorithm and a local search algorithm are proposed. Extensive numerical experiments are conducted to test the performance of the proposed algorithms.

Robust guidance method with terminal impact angle constraint for autonomous underwater vehicle

Based on robust control design method,a variable structure guidance method is proposed for autonomous underwater vehicle(AUV) during the guiding course with terminal impact angle constraint.Considering the intercept geometry,a sliding mode controller is proposed for controlling the hne of sight angle rate and the impact angle,based on the principle which controls the line of sight angle rate to approach zero and the terminal angle to approach the expected value more quickly as the distance decreases.Simulation results show that,with the application of the proposed method,small miss distance is achieved and the expected impact angle is reached.In addition,the system is robust to the target maneuvering.

Model Predictive Control Synthesis Approach of Electrode Regulator System for Electric Arc Furnace

In electric are furnace smelting, electrode regulator system is a key link. A good electrode control algorithm will reduce energy consumption effectively and shorten smelting time greatly. The offline design online synthesis model predictive control algorithm is proposed for electrode regulator system with input and output constraints. On the offline computation, the continuum of terminal constraint sets will be constructed. On the online synthesis, the time-varying terminal constraint sets will be adopted and at least one free control variable will be introduced to solve the min-max optimization control problem. Then Lyapunov method will be adopted to analyze closed-loop system stability. Simulation and field trial results show that the proposed offline design online synthesis model predictive control method is effective.

Optimal guidance of extended trajectory shaping

To control missile＇s miss distance as well as terminal impact angle, by involving the timeto-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory.An extended trajectory shaping guidance（ETSG） law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile＇s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.

Open-loop solution of a defender–attacker–target game:penalty function approach

A defender–attacker–target problem with non-moving target is considered.This problem is modelled by a pursuit-evasion zero-sum differential game with linear dynamics and quadratic cost functional.In this game,the pursuer is the defender,while the evader is the attacker.The objective of the pursuer is to minimise the cost functional,while the evader has two objectives:to maximise the cost functional and to keep a given terminal state inequality constraint.The open-loop saddle point solution of this game is obtained in the case where the transfer functions of the controllers for the defender and the attacker are of arbitrary orders.