Generalized formulation of linear nonquadratic weighted optimal error shaping guidance laws

This study presents a novel extension to the theory of optimal guidance laws represented by the nontraditional class of performance indices: nonquadratic-type signal Lp" role="presentation">Lp norm for the input weighted by an arbitrary positive function. Various missile guidance problems are generally formulated into a scalar terminal control problem based on the understanding of the predictor–corrector nature. Then, a new approach to derive the optimal feedback law, minimizing the nonquadratic performance index, is proposed by using the Hölderian inequality. The proposed extension allows a more general family of formulations for the design of closed-form feedback solutions to various guidance problems to be treated in a unified framework. The equivalence between the proposed approach and other design methodologies is investigated. In general, the type of input norm mainly determines the variability of input during the engagement while trading off against the rate of error convergence. The analytic solution derived in this study is verified by comparison with the solution from numerical optimization, and the effect of the exponent p" role="presentation">p in the performance index on the trajectory and command is demonstrated by numerical simulations

General Vector Explicit - Impact Time and Angle Control Guidance

This thesis proposes and evaluates a new cooperative guidance law called General Vector Explicit - Impact Time and Angle Control Guidance (GENEX-ITACG). The motivation for GENEX-ITACG came from an explicit trajectory shaping guidance law called General Vector Explicit Guidance (GENEX). GENEX simultaneously achieves design specifications on miss distance and terminal missile approach angle while also providing a design parameter that adjusts the aggressiveness of this approach angle. Encouraged by the applicability of this user parameter, GENEX-ITACG is an extension that allows a salvo of missiles to cooperatively achieve the same objectives of GENEX against a stationary target through the incorporation of a cooperative trajectory shaping guidance law called Impact Time and Angle Control Guidance (ITACG). ITACG allows a salvo of missile to simultaneously hit a stationary target at a prescribed impact angle and impact time. This predetermined impact time is what allows each missile involved in the salvo attack to simultaneously arrived at the target with unique approach angles, which greatly increases the probability of success against well defended targets. GENEX-ITACG further increases this probability of kill by allowing each missile to approach the target with a unique approach angle rate through the use of a user design parameter. The incorporation of ITACG into GENEX is accomplished through the use of linear optimal control by casting the cost function of GENEX into the formulation of ITACG. The feasibility GENEXITACG is demonstrated across three scenarios that demonstrate the ITACG portion of the guidance law, the GENEX portion of the guidance law, and finally the entirety of the guidance law. The results indicate that GENEX-ITACG is able to successfully guide a salvo of missiles to simultaneously hit a stationary target at a predefined terminal impact angle and impact time, while also allowing the user to adjust the aggressiveness of approach

Bank-to-turn control technology survey for homing missiles

The potential advantages of bank-to-turn control are summarized. Recent and current programs actively investigating bank-to-turn steering are reviewed and critical technology areas concerned with bank-to-turn control are assessed

Energy-optimal waypoint-following guidance considering autopilot dynamics

This paper addresses the problem of energy-optimal waypoint-following guidance for an Unmanned Aerial Vehicle with the consideration of a general autopilot dynamics model. The proposed guidance law is derived as a solution of a linear quadratic optimal control problem in conjunction with a linearized kinematics model. The algorithm developed integrates path planning and following into a single step and is able to be applied to a general waypoint-following mission. Theoretical analysis reveals that previously suggested optimal point-to-point guidance laws are special cases of the proposed approach. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed formulations

Guidance and control for defense systems against ballistic threats

A defense system against ballistic threat is a very complex system from the engineering point of view. It involves different kinds of subsystems and, at the same time, it presents very strict requirements. Technology evolution drives the need of constantly upgrading system’s capabilities. The guidance and control fields are two of the areas with the best progress possibilities. This thesis deals with the guidance and control problems involved in a defense system against ballistic threats. This study was undertaken by analyzing the mission of an intercontinental ballistic missile. Trajectory reconstruction from radar and satellite measurements was carried out with an estimation algorithm for nonlinear systems. Knowing the trajectory is a prerequisite for intercepting the ballistic missile. Interception takes place thanks to a dedicated tactical missile. The guidance and control of this missile were also studied in this work. Particular attention was paid on the estimation of engagement’s variables inside the homing loop. Interceptor missiles are usually equipped with a seeker that provides the angle under which the interceptor sees its target. This single measurement does not guarantee the observability of the variables required by advanced guidance laws such as APN, OGL, or differential games-based laws. A new guidance strategy was proposed, that solves the bad observability problems and returns satisfactory engagement performances. The thesis is concluded by a study of the interceptor most suitable aerodynamic configuration in order to implement the proposed strategy, and by the relative autopilot design. The autopilot implements the lateral acceleration commands from the guidance system. The design was carried out with linear control techniques, considering requirements on the rising time, actuators maximum effort, and response to a bang-bang guidance command. The analysis of the proposed solutions was carried on by means of numerical simulations, developed for each single case-study

Optimal impact angle guidance for exo-atmospheric interception utilizing gravitational effect

This paper aims to develop a new optimal intercept angle guidance law for exo-atmospheric interception by utilizing gravity. A finite-time optimal regulation problem is formulated by considering the instantaneous zero-effort-miss (ZEM) and the intercept angle error as the system states. The analytical guidance command is then derived based on Schwarz's inequality approach and Lagrange multiplier concept. Capturability analysis using instantaneous linear time-invariant system concept is also presented to provide better insights of the proposed guidance law. Theoretical analysis reveals that the proposed optimal guidance law encompasses previously suggested optimal impact angle constrained guidance laws. Numerical simulations with some comparisons clearly demonstrate the effectiveness of the proposed guidance law

Current Trends in Tactical Missile Guidance

The problem of tactical missile guidance is very challenging and has been treated using several basic metlfodologies in the past four decades. Major techniques can be grouped underclassical guidance laws, modern guidance laws, l'aws for manoeuvring targets, predictive guidance for endgame scenario, and guidance laws based on intelligent control methods. Each technique has some advantages and disadvantages while implementing in a practical system. Guidance law selection is dictated by nature of flight profile like boost, midcourse, terminal homing, etc, and also miss-distance and a single-shot kill probability. This paper presents a brief survey of the existing techniques and current trends in tactical missile guidance

Optimal terminal guidance for exoatmospheric interception

AbstractIn this study, two optimal terminal guidance (OTG) laws, one of which takes into account the final velocity vector constraint, are developed for exoatmospheric interception using optimal control theory. In exoatmospheric interception, because the proposed guidance laws give full consideration to the effect of gravity, they consume much less fuel than the traditional guidance laws while requiring a light computational load. In the development of the guidance laws, a unified optimal guidance problem is put forward, where the final velocity vector constraint can be considered or neglected by properly adjusting a parameter in the cost function. To make this problem analytically solvable, a linear model is used to approximate the gravity difference, the difference of the gravitational accelerations of the target and interceptor. Additionally, an example is provided to show that some achievements of this study can be used to significantly improve the fuel efficiency of the pulsed guidance employed by the interceptor whose divert thrust level is fixed

Advanced Centaur explicit guidance equation study Final report

Generalized equations and in-flight computer requirements for Centaur guidance and control and advanced mission plannin

Augmented State Linear Covariance Applications for Nonlinear Missile Engagements

Sustained actuator saturation is a common occurrence for missile engagements. The saturation nonlinearity creates some difficulty for high-fidelity linear analysis methods. This dissertation investigates three methods of modeling actuator saturation in an advanced linear analysis. The linear covariance tools from this dissertation run extremely fast and provide several advantages over other linear missile engagement analysis methods. First, a simulation is developed and validated for a target engagement scenario without actuator saturation. Next, saturations are introduced to the problem, along with the first analysis method: statistical linear covariance analysis. This method combines the augmented state linear covariance framework with the statistical linearization technique. The second method considered is tunable linear covariance analysis. Tunable linear covariance analysis utilizes a switching parameter to determine when to switch the dynamics of the problem. The final method is called event trigger linear covariance analysis. This method involves switching GN&C modes using a constraint equation and a covariance shaping matrix. All three analysis methods are validated using Monte Carlo methods, and statistical linear covariance analysis is found to be the most robust and accurate of the three methods. This method is utilized to rapidly analyze missile engagement performance under varying levels of saturation. The parameters of the analysis include guidance laws, sensor accuracy levels, target evasive maneuvers, and actuator responsiveness