Optimal pilot decisions and flight trajectories in air combat

The thesis concerns the analysis and synthesis of pilot decision-making and the design of optimal flight trajectories. In the synthesis framework, the methodology of influence diagrams is applied for modeling and simulating the maneuvering decision process of the pilot in one-on-one air combat. The influence diagram representations describing the maneuvering decision in a one sided optimization setting and in a game setting are constructed. The synthesis of team decision-making in a multiplayer air combat is tackled by formulating a decision theoretical information prioritization approach based on a value function and interval analysis. It gives the team optimal sequence of tactical data that is transmitted between cooperating air units for improving the situation awareness of the friendly pilots in the best possible way. In the optimal trajectory planning framework, an approach towards the interactive automated solution of deterministic aircraft trajectory optimization problems is presented. It offers design principles for a trajectory optimization software that can be operated automatically by a nonexpert user. In addition, the representation of preferences and uncertainties in trajectory optimization is considered by developing a multistage influence diagram that describes a series of the maneuvering decisions in a one-on-one air combat setting. This influence diagram representation as well as the synthesis elaborations provide seminal ways to treat uncertainties in air combat modeling. The work on influence diagrams can also be seen as the extension of the methodology to dynamically evolving decision situations involving possibly multiple actors with conflicting objectives. From the practical point of view, all the synthesis models can be utilized in decision-making systems of air combat simulators. The information prioritization approach can also be implemented in an onboard data link system.reviewe

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

Counter Weapon Control

In this work, pursuit-evasion differential game theory is applied to the target defense scenario. The targets, attackers, and the defenders positional information is assumed to be known to the players. With positional information, a computational efficient method of strategy synthesis can be derived applying a differential game theory approach. We demonstrate that when non-optimal strategies are employed by one of the players, e.g. Line Of Sight guidance, the outcome will favor the players that employ the optimal strategy given by the solution of the pursuit-evasion differential game

Covariance Steering for Discrete-Time Linear-Quadratic Stochastic Dynamic Games

This paper addresses the problem of steering a discrete-time linear dynamical system from an initial Gaussian distribution to a final distribution in a game-theoretic setting. One of the two players strives to minimize a quadratic payoff, while at the same time tries to meet a given mean and covariance constraint at the final time-step. The other player maximizes the same payoff, but it is assumed to be indifferent to the terminal constraint. At first, the unconstrained version of the game is examined, and the necessary conditions for the existence of a saddle point are obtained. We then show that obtaining a solution for the one-sided constrained dynamic game is not guaranteed, and subsequently the players' best responses are analyzed. Finally, we propose to numerically solve the problem of steering the distribution under adversarial scenarios using the Jacobi iteration method. The problem of guiding a missile during the endgame is chosen to analyze the proposed approach. A numerical simulation corresponding to the case where the terminal distribution is not achieved is also included, and discuss the necessary conditions to meet the terminal constraint

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

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

Contributions To Pursuit-Evasion Game Theory.

This dissertation studies adversarial conflicts among a group of agents moving in the plane, possibly among obstacles, where some agents are pursuers and others are evaders. The goal of the pursuers is to capture the evaders, where capture requires a pursuer to be either co-located with an evader, or in close proximity. The goal of the evaders is to avoid capture. These scenarios, where different groups compete to accomplish conflicting goals, are referred to as pursuit-evasion games, and the agents are called players. Games featuring one pursuer and one evader are analyzed using dominance, where a point in the plane is said to be dominated by a player if that player is able to reach the point before the opposing players, regardless of the opposing players' actions. Two generalizations of the Apollonius circle are provided. One solves games with environments containing obstacles, and the other provides an alternative solution method for the Homicidal Chauffeur game. Optimal pursuit and evasion strategies based on dominance are provided. One benefit of dominance analysis is that it extends to games with many players. Two foundational games are studied; one features multiple pursuers against a single evader, and the other features a single pursuer against multiple evaders. Both are solved using dominance through a reduction to single pursuer, single evader games. Another game featuring competing teams of pursuers is introduced, where an evader cooperates with friendly pursuers to rendezvous before being captured by adversaries. Next, the assumption of complete and perfect information is relaxed, and uncertainties in player speeds, player positions, obstacle locations, and cost functions are studied. The sensitivity of the dominance boundary to perturbations in parameters is provided, and probabilistic dominance is introduced. The effect of information is studied by comparing solutions of games with perfect information to games with uncertainty. Finally, a pursuit law is developed that requires minimal information and highlights a limitation of dominance regions. These contributions extend pursuit-evasion game theory to a number of games that have not previously been solved, and in some cases, the solutions presented are more amenable to implementation than previous methods.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120650/1/dwoyler_1.pd

Reachable sets analysis in the cooperative control of pursuer vehicles

This thesis is concerned with the Pursuit-and-Evasion (PE) problem where the pursuer aims to minimize the time to capture the evader while the evader tries to prevent capture. In the problem, the evader has two advantages: a higher manoeuvrability and that the pursuer is uncertain about the evader's state. Cooperation among multiple pursuer vehicles can thus be used to overcome the evader’s advantages. The focus here is on the formulation and development of frameworks and algorithms for cooperation amongst pursuers, aiming at feasible implementation on real and autonomous vehicles. The thesis is split into Parts I and II. Part I considers the problem of capturing an evader of higher manoeuvrability in a deterministic PE game. The approach is the employment of Forward Reachable Set (FRS) analysis in the pursuers’ control. The analysis considers the coverage of the evader’s FRS, which is the set of reachable states at a future time, with the pursuer’s FRS and assumes that the chance of capturing the evader is dependent on the degree of the coverage. Using the union of multiple pursuers’ FRSs intuitively leads to more evader FRS coverage and this forms the mechanism of cooperation. A framework for cooperative control based on the FRS coverage, or FRS-based control, is proposed. Two control algorithms were developed within this framework. Part II additionally introduces the problem of evader state uncertainty due to noise and limited field-of-view of the pursuers’ sensors. A search-and-capture (SAC) problem is the result and a hybrid architecture, which includes multi-sensor estimation using the Particle Filter as well as FRS-based control, is proposed to accomplish the SAC task. The two control algorithms in Part I were tested in simulations against an optimal guidance algorithm. The results show that both algorithms yield a better performance in terms of time and miss distance. The results in Part II demonstrate the effectiveness of the hybrid architecture for the SAC task. The proposed frameworks and algorithms provide insights for the development of effective and more efficient control of pursuer vehicles and can be useful in the practical applications such as defence systems and civil law enforcement