Active Target Defense Differential Game with a Fast Defender

This paper addresses the active target defense differential game where an Attacker missile pursues a Target aircraft. A Defender missile is fired by the Target's wingman in order to intercept the Attacker before it reaches the aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the distance between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while the Attacker tries to minimize said distance. The results shown here extend previous work. We consider here the case where the Defender is faster than the Attacker. The solution to this differential game provides optimal heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker and it also provides the optimal heading angle for the Attacker to minimize the said distance.Comment: 9 pages, 8 figures. A shorter version of this paper will be presented at the 2015 American Control Conferenc

Integrated Guidance and Control of Missiles with Θ-D Method

A new suboptimal control method is proposed in this study to effectively design an integrated guidance and control system for missiles. Optimal formulations allow designers to bring together concerns about guidance law performance and autopilot responses under one unified framework. They lead to a natural integration of these different functions. by modifying the appropriate cost functions, different responses, control saturations (autopilot related), miss distance (guidance related), etc., which are of primary concern to a missile system designer, can be easily studied. A new suboptimal control method, called the θ-D method, is employed to obtain an approximate closed-form solution to this nonlinear guidance problem based on approximations to the Hamilton-Jacobi-Bellman equation. Missile guidance law and autopilot design are formulated into a single unified state space framework. The cost function is chosen to reflect both guidance and control concerns. The ultimate control input is the missile fin deflections. A nonlinear six-degree-of-freedom (6-DOF) missile simulation is used to demonstrate the potential of this new integrated guidance and control approach

Sequential quadratic programming solutions to related aircraft trajectory optimization problems

Aircraft performance optimization continues to play an important role in the aerospace sciences. The studies undertaken in this dissertation explore the performance of high-speed aircraft with regard to missile evasion, minimum-time-to-climb, minimum-time-to-turn, and the unorthodox approach of obtaining a robust optimality-based control law for real-time aircraft control. The dissertation includes four papers presented or accepted for presentation at major conferences and presently in various stages of review for publication in scholarly journals;The similarity in each paper, in addition to the focus on optimal aircraft trajectories, is that an existing nonlinear programming method, sequential quadratic programming (SQP), is used to treat each trajectory optimization problem. This approach is suitable since the emphasis is on applications and problem solving, and the method is accurate and computationally inexpensive. Also, the flexibility of SQP allows for performance index, mathematical model, and constraint changes with relatively little reprogramming. This enables a wide range of trajectory optimization problems to be formulated and studied;In the study of the aircraft missile-evasion problem in horizontal planar flight, unlike earlier investigations, the full original equations of motion are used. Also, no linearization about a nominal pursuit triangle is done. The velocity ratio, that is, the velocity of the aircraft to the velocity of the missile for the duration of the confrontation, becomes a major factor in deciding optimal evasive strategies. Evasion against a surface-to-air missile involves a large nonlinear optimal control problem of dynamic order of at least thirteen. Inward , outward , pull-up, dive, and inverted pull-down evasive maneuvers are investigated. The results show that the missile enters the hit region of the aircraft for constrained vertical plane flight, but not for constrained horizontal flight. The optimal throttle setting for constrained horizontal plane flight is of bang-bang type;For the minimum-time turn problems, having free final velocity provides the biggest impact on turn times, which can be reduced by as much as fifty percent. For a wide range of final energies studied in the three-dimensional turns, it was found that the aircraft tends to initially lose altitude in the optimal turn even though the nominal control from which the optimization process started corresponds to an initial climbing turn. This tendency of favoring kinetic energy over potential energy had not been featured in earlier papers;Finally, the investigation of optimality-based control laws for real-time aircraft control is a significant departure from the usual open-loop solutions to trajectory optimization problems. It was found that the robustness of the optimal control obtained from the optimality-condition is not guaranteed, but by introducing a certain correction term, it can be enhanced significantly. It appears that this technique of enhancing robustness has not been used until now

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

Adaptive True Proportional Navigation Guidance Based On Heuristic Optimization Algorithms

The PN-guidance (Proportional Guidance) still continues to be improved, because it is the simplest, cheapest and most reliable algorithm. One of the most important techniques to improve PN-guidance is to adapt the navigation constant depending on time. In this study, first, the entire adaptation methods for PN-guidance are classified, then the adaptation process is online achieved by using heuristic optimization during guiding the missile. The novelty of this study is that the heuristic optimization approach is used at the first time to update the navigation constant of PN-guidance. It is considered that having short program code, fast convergence speed and just simple algebraic computations without derivative are vital advantages of heuristic algorithms using into missile systems. In this scope, an Adaptive True-PN (ATPN) guidance algorithm is designed by optimizing navigation constants varying according to the target behavior. The results show that while the acceleration gap of the pitch axis decreases 21.8%, the acceleration gap of yaw axis reduces 39.68%. These reductions mean that while the missile guided by ATPN is maneuvering, it is exposed to less acceleration and less strain. &nbsp

Application of singular perturbation methods for three-dimensional minimum-time interception

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76166/1/AIAA-20647-787.pd

Optimal Control Methods for Missile Evasion

Optimal control theory is applied to the study of missile evasion, particularly in the case of a single pursuing missile versus a single evading aircraft. It is proposed to divide the evasion problem into two phases, where the primary considerations are energy and maneuverability, respectively. Traditional evasion tactics are well documented for use in the maneuverability phase. To represent the first phase dominated by energy management, the optimal control problem may be posed in two ways, as a fixed final time problem with the objective of maximizing the final distance between the evader and pursuer, and as a free final time problem with the objective of maximizing the final time when the missile reaches some capture distance away from the evader.These two optimal control problems are studied under several different scenarios regarding assumptions about the pursuer. First, a suboptimal control strategy, proportional navigation, is used for the pursuer. Second, it is assumed that the pursuer acts optimally, requiring the solution of a two-sided optimal control problem, otherwise known as a differential game. The resulting trajectory is known as a minimax, and it can be shown that it accounts for uncertainty in the pursuer\u27s control strategy. Finally, a pursuer whose motion and state are uncertain is studied in the context of Receding Horizon Control and Real Time Optimal Control. The results highlight how updating the optimal control trajectory reduces the uncertainty in the resulting miss distance

Impact angle control guidance synthesis for evasive maneuver against intercept missile

This paper proposes a synthesis of new guidance law to generate an evasive maneuver against enemy’s missile interception while considering its impact angle, acceleration, and field-of-view constraints. The first component of the synthesis is a new function of repulsive Artificial Potential Field to generate the evasive maneuver as a real-time dynamic obstacle avoidance. The terminal impact angle and terminal acceleration constraints compliance are based on Time-to-Go Polynomial Guidance as the second component. The last component is the Logarithmic Barrier Function to satisfy the field-of-view limitation constraint by compensating the excessive total acceleration command. These three components are synthesized into a new guidance law, which involves three design parameter gains. Parameter study and numerical simulations are delivered to demonstrate the performance of the proposed repulsive function and guidance law. Finally, the guidance law simulations effectively achieve the zero terminal miss distance, while satisfying an evasive maneuver against intercept missile, considering impact angle, acceleration, and field-of-view limitation constraints simultaneously

Trajectory Optimisation of Long Range and Air-to-Air Tactical Flight Vehicles

This paper presents formulation and solution of long range flight vehicle and tactical air-to-air flight vehicle trajectory optimisation. The first case study is of a long range flight vehicle. Here an optimum steering program during powered phase has been evolved as control input for achieving maximum range with available propulsions in the presence of path and terminal constraints. The second case study is of a tactical flight vehicle for air-to-air application. Here a minimum flight time trajectory has been generated for covering a specified range pertaining to a specified air-to-air engagement by evolving pitch lateral acceleration as control input. Here also, there are many path and terminal constraints consisting of launch aircraft, pursuer, and evader. The studies have been carried out as part of system design activity of both flight vehicles. Both are real-life optimisation problems under several constraints. Through it is very difficult to solve such practical problems in flight dynamics using classical optimal control theory, it has been solved successfully using direct transcription method based on nonlinear programming. Rapid convergence has been achieved in four passes with minimum grids in first pass, to start with, and increasing the grids in subsequent passes. Solving such a real-life problem with proper convergence subjected to many constraints is claimed as novelty of present research.Defence Science Journal, Vol. 65, No. 2, March 2015, pp.107-118, DOI:http://dx.doi.org/10.14429/dsj.65.823

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