Determination of Fire Control Policies via Approximate Dynamic Programming

Given the ubiquitous nature of both offensive and defensive missile systems, the catastrophe-causing potential they represent, and the limited resources available to countries for missile defense, optimizing the defensive response to a missile attack is a necessary endeavor. For a single salvo of offensive missiles launched at a set of targets, a missile defense system protecting those targets must decide how many interceptors to fire at each incoming missile. Since such missile engagements often involve the firing of more than one attack salvo, we develop a Markov decision process (MDP) model to examine the optimal fire control policy for the defender. Due to the computational intractability of using exact methods for all but the smallest problem instances, we utilize an approximate dynamic programming (ADP) approach to explore the efficacy of applying approximate methods to the problem. We obtain policy insights by analyzing subsets of the state space that reflect a range of possible defender interceptor inventories. Testing of four scenarios demonstrates that the ADP policy provides high-quality decisions for a majority of the state space, achieving a 7.74% mean optimality gap in the baseline scenario. Moreover, computational effort for the ADP algorithm requires only a few minutes versus 12 hours for the exact dynamic programming algorithm, providing a method to address more complex and realistically-sized instances

An Approximate Dynamic Programming Approach for Comparing Firing Solutions in a Networked Air Defense Environment

The United States Army currently employs a shoot-shoot-look firing policy for air defense. As the Army moves to a networked defense-in-depth strategy, this policy will not provide optimal results for managing interceptor inventories in a conflict to minimize the damage to defended assets. The objective for air and missile defense is to identify the firing policy for interceptor allocation that minimizes expected total cost of damage to defended assets. This dynamic weapon target assignment problem is formulated first as a Markov decision process (MDP) and then approximate dynamic programming (ADP) is used to solve problem instances based on a representative scenario. Least squares policy evaluation (LSPE) and least squares temporal difference (LSTD) algorithms are employed to determine the best approximate policies possible. An experimental design is conducted to investigate problem features such as conflict duration, attacker and defender weapon sophistication, and defended asset values. The LSPE and LSTD algorithm results are compared to two benchmark policies (e.g., firing one or two interceptors at each incoming tactical ballistic missile (TBM)). Results indicate that ADP policies outperform baseline polices when conflict duration is short and attacker weapons are sophisticated. Results also indicate that firing one interceptor at each TBM (regardless of inventory status) outperforms the tested ADP policies when conflict duration is long and attacker weapons are less sophisticated

Real-Time Heuristics and Metaheuristics for Static and Dynamic Weapon Target Assignments

The problem of targeting and engaging individual missiles (targets) with an arsenal of interceptors (weapons) is known as the weapon target assignment problem. This problem has been well-researched since the seminal work in 1958. There are two distinct categories of the weapon target assignment problem: static and dynamic. The static weapon target assignment problem considers a single instance in which a known number of incoming missiles is to be engaged with a finite number of interceptors. By contrast, the dynamic weapon target assignment problem considers either follow on engagement(s) should the first engagement(s) fail, a subsequent salvo of incoming missiles, or both. This research seeks to define and solve a realistic dynamic model. First, assignment heuristics and metaheuristics are developed to provide rapid near-optimal solutions to the static weapon target assignment. Next, a technique capable of determining how many of each interceptor type to reserve for a second salvo by means of approximate dynamic programming is developed. Lastly, a model that realistically considers erratic flight paths of incoming missiles and determines assignments and firing sequences of interceptors within a simulation to minimize the number of hits to a protected asset is developed. Additionally, the first contemporary survey of the weapon target assignment problem since 1985 is presented. Collectively, this work extends the research of missile defense into practical application more so than currently is found within the literature

A Game Theoretic Model for the Optimal Disposition of Integrated Air Defense System Assets

We examine the optimal allocation of Integrated Air Defense System (IADS) resources to protect a country\u27s assets, formulated as a Defender-Attacker-Defender three-stage sequential, perfect information, zero-sum game between two opponents. We formulate a trilevel nonlinear integer program for this Defender-Attacker-Defender model and seek a subgame perfect Nash equilibrium, for which neither the defender nor the attacker has an incentive to deviate from their respective strategies. Such a trilevel formulation is not solvable via conventional optimization software and an exhaustive enumeration of the game tree based on the discrete set of strategies is intractable for large problem sizes. As such, we test and evaluate variants of a tree pruning algorithm and a customized heuristic, which we benchmark against an exhaustive enumeration. Our tests demonstrate that the pruning strategy is not efficient enough to scale up to a larger problem. We then demonstrate the scalability of the heuristic to show that the model can be applied to a realistic size problem

Approximate Dynamic Programming for Military Resource Allocation

This research considers the optimal allocation of weapons to a collection of targets with the objective of maximizing the value of destroyed targets. The weapon-target assignment (WTA) problem is a classic non-linear combinatorial optimization problem with an extensive history in operations research literature. The dynamic weapon target assignment (DWTA) problem aims to assign weapons optimally over time using the information gained to improve the outcome of their engagements. This research investigates various formulations of the DWTA problem and develops algorithms for their solution. Finally, an embedded optimization problem is introduced in which optimization of the multi-stage DWTA is used to determine optimal weaponeering of aircraft. Approximate dynamic programming is applied to the various formulations of the WTA problem. Like many in the field of combinatorial optimization, the DWTA problem suffers from the curses of dimensionality and exact solutions are often computationally intractability. As such, approximations are developed which exploit the special structure of the problem and allow for efficient convergence to high-quality local optima. Finally, a genetic algorithm solution framework is developed to test the embedded optimization problem for aircraft weaponeering

OPTIMIZING VLS FIRING POLICY: AN ENUMERATION OF HETEROGENEOUS SEQUENCES TO INFORM EXPENDITURE

The U.S. Navy (USN) utilizes the Vertical Launch System (VLS) to store and launch both their offensive and defensive missiles. Since the number of VLS silos on a given ship is fixed, to maximize offensive capability the USN needs to minimize the number of interceptors required to combat incoming anti-surface missiles. Current firing policies may be overly conservative and expend too many interceptors per incoming threat, which results in a substantial fraction of VLS silos dedicated to defensive missiles. Decision makers need an analysis tool to explore the trade-off between missile consumption and probability of raid annihilation (PRA) for various firing policies and would also benefit from a prescriptive algorithm to help inform missile expenditure. This thesis provides a model to optimize VLS firing policy using a set of multiple interceptor types while accounting for range limitations, travel time, multi-interceptor salvos, battle damage assessment, and range dependent probability of kill. Additionally, the thesis derives analytical results for the optimal, lowest-cost allocation of interceptors in the single interceptor case, which, in turn, generates insight into how to structure sequential salvos.N81, Washington DCEnsign, United States NavyApproved for public release. Distribution is unlimited

The application of a viewpoints framework in the development of C4I systems

In the development of large distributed systems, both the detection and resolution of inconsistency in policy, requirements, and specifications pose major challenges. The purpose of this thesis is to examine the inconsistencies in policy, requirements, and specifications in the development of information/ Joint Command, Control, Communications, Computers, and Intelligence (C41) systems. In this thesis, we explore the application of a "viewpoints" framework to aid in the development of distributed information systems. A viewpoints framework methodology that was developed to aid in the development of distributed systems is the Reference Model of Open Distributed Processing (RM- ODP). This thesis is concerned with the application of the five viewpoints of RM-ODP and the translation of policy into requirements and specifications. In this thesis we use the Ballistic Missile Defense (BMD) system as a case study to explain how RM-ODP can be used to develop distributed information systems. We found that identifying inconsistencies regarding interoperability amongst the subsystems of BMD necessitated the use of multiple viewpoints and that firm conclusions could not be made until the system was viewed at the lower levels.http://archive.org/details/thepplicationofv109459326U.S. Navy (U.S.N.) author.Approved for public release; distribution is unlimited

A Survey on Weapon Target Allocation Models and Applications

In Command and Control (C2), Threat Evaluation (TE) and Weapon Target Allocation (WTA) are two key components. To build an automated system in this area after modeling Threat Evaluation and Weapon Target Allocation processes, solving these models and finding the optimal solution are further important issues. This setting demands instantaneous operational planning and decision making under inherent severe stress conditions. The associated responsibilities are usually divided among a number of operators and also computerized decision support systems that aid these operators during the decision making process. In this Chapter, the literature in the area of WTA system with the emphasis on the modeling and solving methods are surveyed

Satellite constellation design for mid-course ballistic missile intercept

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 223-228).This thesis will establish a conceptual approach to the design of constellations for satellite-based mid-course missile defense. The ballistic missile intercept problem leads to a new paradigm of coverage where interceptor "reachability" replaces line-of-sight coverage. Interceptors in this concept are limited in their time of flight and AV capabilities. Classical design approaches, based on ground coverage, are employed to provide a priori constellations for ballistic missile defense from a postulated North Korean attack. Both symmetric and asymmetric constellation types, designed for Earth coverage, provide bounds on the number of satellites required. A detailed parametric analysis is used to explore the constellation design space. Various constellation types are optimized to maximize missile defense coverage. Both genetic algorithms and gradient-based optimization techniques are employed. Satellite-based mid-course ballistic missile defense from a regional threat is achievable with as few as 21 satellites. Additional constellation intercept statistics, such as: the number of intercepts per missile, and interceptor closing velocities, are compiled to provide a lethality index. The effective capabilities of these constellations to defend CONUS, beyond the original regional threat, are also explored. It will be demonstrated that the constellations constructed in this work are capable of providing defense from an array of threatening states about the globe. This research illustrates how known design methods and astrodynamics techniques can be used to create new and viable methods of space-based missile defense.by Luke Michael Sauter.S.M