Ben G. Fitzpatrick

Stochastic game approach to air operations

A command and control (C/sup 2/) problem for military air operations is addressed. Specifically, we consider C/sup 2/ problems for air vehicles against ground-based targets and defensive systems. The problem is viewed as a stochastic game. We restrict our attention to the C/sup 2/ level where the problem may consist of a few unmanned combat air vehicles (UCAVs) or aircraft (or possibly teams of vehicles), less than say, a half-dozen enemy surface-to-air missile air defense units (SAMs), a few enemy assets (viewed as targets from our standpoint), and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are mapped out and possible SAM sites that are unavoidably part of the situation are known. One may then employ a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged (if any), and by what series of air vehicle operations. We provide analysis, numerical implementation, and simulation for full state-feedback and measurement feedback control within this C/sup 2/ context. Sensitivity to parameter uncertainty is discussed. Some insight into the structure of optimal and near-optimal strategies for C/sup 2/ is obtained. The analysis is extended to the case of observations which may be affected by adversarial inputs. A heuristic based on risk-sensitive control is applied, and it is found that this produces improved results over more standard approaches.

SURVIVAL OF THE FITTEST IN A GENERALIZED LOGISTIC MODEL

In this paper we discuss the asymptotic behavior of a logistic model with distributed growth and mortality rates. In particular, we prove that the entire population becomes concentrated within the subpopulation with highest growth to mortality ratio, and converges to the equilibrium defined by this ratio. Finally, we present a numerical example illustrating the theoretical results.

CONTROL FOR UAV OPERATIONS UNDER IMPERFECT INFORMATION

We address Command and Control (C 2 ) problems for unmanned air vehicles (UAV’s) within the framework of stochastic games. The problem we consider involves one unit comprising a few UAV’s (typically in the range of two to ten) attacking a small number of targets. The targets are defended by surface-to-air missile (SAM) systems with missiles and associated search and track radars. The opponent may also employ decoy SAM radars. Our goal here is to develop a stochastic game formulation that can provide output feedback controls in the presence of uncertainty and partial information. We approach this goal by combining the estimator and controller via a modifled Certainy Equivalence Principle that weighs both the probability of each possible state and the potential cost such system state in a mathematically appropriate way, so as to determine a near optimal control.

Robustness and Performance of Adaptive Suppression of Unknown Periodic Disturbances

In recent years, a class of adaptive schemes has been developed for suppressing periodic disturbance signals with unknown frequencies, phases, and amplitudes. The stability and robustness of these schemes with respect to inevitable unmodeled dynamics and noise disturbances in the absence of persistently exciting signals has not been established despite successful simulation results and implementations. The purpose of this technical note is to propose a robust adaptive scheme for rejection of unknown periodic components of the disturbance and analyze its stability and performance properties. First, we consider the ideal case (non-adaptive) when complete information about the characteristics of the disturbance is available. We show that the rejection of periodic terms may lead to amplification of output noise and in some cases lead to a worse output performance. The way to avoid such undesirable noise amplification is to increase the size of the feedback control filter in order to have the flexibility to achieve rejection of the periodic disturbance terms while minimizing the effect of the noise on the output. The increased filter order leads to an over-parameterized scheme where persistence of excitation is no longer possible, and this shortcoming makes the use of robust adaptation essential. With this important insight in mind, the coefficients of the feedback filter whose size is over parameterized are adapted using a robust adaptive law. We show analytically that the proposed robust adaptive control scheme guarantees stability, performance and robustness with respect to unmodeled dynamics and bounded broadband noise disturbances. We use numerical simulations to demonstrate the results.

APPROXIMATION AND PARAMETER ESTIMATION PROBLEMS FOR ALGAL AGGREGATION MODELS

Aggregation processes are intrinsic to many biological phenomena including sedimentation and coagulation of algae during bloom periods. A fundamental but unresolved problem associated with aggregate processes is the determination of the “stickiness function,” a measure of the ability of particles to adhere to other particles. This leads to an inverse problem associated with a class of nonlinear integro-differential equations. The purpose of this article is to develop convergence theory for this algal coagulation model utilizing a spline-based collocation scheme within the context of the parameter identification problem.

Mixed Initiative Planning and Control Under Uncertainty

A hierarchical architecture is developed to provide closed-loop, mixed initiative planning and control for distributed force teams of unmanned air vehicles in an uncertain military operational environment. The hierarchical architecture derives from a rigorous decomposition of the problem that preserves systemlevel objectives while respecting local constraints and defines the interactions and information exchanges between decision-making nodes at each level. An intelligent adversary is addressed in planning and decision-making through coupling of uncertainty in state estimation and the risk associated with possible system states. The proposed hierarchical structure also accommodates human decision-makers and operators at any level within any planning and control function. This is made possible by the incorporation of humancentered design principles and human behavior representation models that enable human operators and machine automation to function as a cooperative team. Game-theoretic estimation and control techniques capture the actions of an intelligent adversary in order to improve performance under imperfect state knowledge. The problem decomposition and the use of experimentally derived heuristics make this approach computationally tractable. Computational cognitive process models capture expert human decision-making, thereby providing a foundation for bridging the gap between engineering estimation/optimization algorithms and naturalistic human machine interfaces (HSIs) that support effective mixed initiative monitoring, planning, and control in dynamic environments.

Forecasting the Effect of the Amethyst Initiative on College Drinking

BACKGROUND A number of college presidents have endorsed the Amethyst Initiative, a call to consider lowering the minimum legal drinking age (MLDA). Our objective is to forecast the effect of the Amethyst Initiative on college drinking. METHODS A system model of college drinking simulates MLDA changes through (i) a decrease in heavy episodic drinking (HED) because of the lower likelihood of students drinking in unsupervised settings where they model irresponsible drinking (misperception), and (ii) an increase in overall drinking among currently underage students because of increased social availability of alcohol (wetness). RESULTS For the proportion of HEDs on campus, effects of large decreases in misperception of responsible drinking behavior were more than offset by modest increases in wetness. CONCLUSIONS For the effect of lowering the MLDA, it appears that increases in social availability of alcohol have a stronger impact on drinking behavior than decreases in misperceptions.

Optimization and Control of Agent-Based Models in Biology: A Perspective

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Robust stability and performance of adaptive jitter supression in laser beam pointing

This paper studies the robustness and performance of an adaptive scheme for suppression of laser beam jitter in the presence of unmodeled dynamics in a continuous-time formulation. To demonstrate the level of performance that can be achieved in the case of known disturbances, at first we consider the ideal case (non-adaptive) when a complete information about characteristics of the noise-corrupted periodic disturbance is available. Then the adaptive case when the disturbance is unknown with time-varying characteristics is investigated. The results show under what conditions jitter suppression can be achieved and what parameters contribute to the performance of the adaptive control scheme. Numerical simulations are given to demonstrate the efficacy of the robust adaptive control law.

Robust noise attenuation under stochastic noises and worst-case unmodelled dynamics

This paper investigates noise attenuation problems for systems with unmodelled dynamics and unknown noise characteristics. A unique methodology is introduced that employs signal estimation in one phase, followed by control design for noise rejection. The methodology enjoys certain advantages in its simple control design process, accommodation of unmodelled dynamics, and non-conservative noise rejection performance. Under mild information on unmodelled dynamics, we first derive robust performance bounds on noise attenuation with respect to unmodelled dynamics without noise estimation errors. Then more general results are presented for systems that are subject to both stochastic signal estimation errors and unmodelled dynamics. Examples are also presented to demonstrate our findings.