Edgar Fuller

Lyapunov analysis of neural network stability in an adaptive flight control system

The paper presents the role of self-stabilization analysis in the design, verification and validation of the dynamics of an Adaptive Flight Control System (AFCS). Since the traditional self-stabilization approaches lack the flexibility to deal with the continuous adaptation of the neural network within the AFCS, the paper emphasizes an alternate self-stability analysis approach, namely Lyapunovs Second Method. A Lyapunov function for the neural network is constructed and used in presenting a formal mathematical proof that verifies the following claim: While learning from a fixed input manifold, the neural network is self-stabilizing in a Globally Asymptotically Stable manner. When dealing with variable data manifolds, we propose the need for a real-time stability monitor that can detect unstable state deviations. The test results based on the data collected from an F-15 flight simulator provide substantial heuristic evidence to support the idea of using a Lyapunov function to prove the self-stabilization properties of the neural network adaptation.

Adaptive control software: can we guarantee safety?

The appeal of including adaptive components in complex computational systems, such as flight control, is in their ability to cope with a changing environment. Continual changes induce uncertainty that limits the applicability of conventional verification and validation (V&V) techniques. In safety-critical applications, the mechanisms of change must be observed, diagnosed, accommodated and well understood prior to deployment. We present a nonconventional V&V approach suitable for online adaptive systems. We applied this approach to an adaptive flight control system that employs neural network learning for online adaptation. Presented methodology consists of a Novelty Detection technique and Online Stability Monitoring tools. The Novelty Detection technique is based on support vector data description that detects novel (abnormal) data patterns. The Online Stability Monitoring tools based on Lyapunovs stability theory detect unstable learning behavior in neural networks.

Using Genetic Algorithms for Tasking Teams of Raven UAVs

Control of multiple unmanned aerial vehicles is of importance given that so many have been deployed in the field. This work discusses how genetic algorithms (GA) have been applied to the cooperative tasking of the AeroVironment’s Raven unmanned aerial vehicle (UAV) engaged in an intelligence, reconnaissance, and surveillance (ISR) mission. Mission assumptions, development of the GA, the method used to test for convergence, and the outcome of preliminary testing are all discussed.

A Hierarchical Algorithm for Clustering Extremist Web Pages

Extremist political movements have proliferated on the web in recent years due to the advent of minimal publication costs coupled with near universal access, resulting in what appears to be an abundance of groups that hover on the fringe of many socially divisive issues. Whether white-supremacist, neo- Nazi, anti-abortion, black separatist, radical Christian, animal rights, or violent environmentalists, all have found a home (and voice) on the Web. These groups form social networks whose ties are predicated primarily on shared political goals. Little is known about these groups, their interconnections, their animosities, and most importantly, their growth and development and studies such as the Dark Web Project, while considering domestic extremists, have focused primarily on international terrorist groups. Yet here in the US, there has been a complex social dynamic unfolding as well. While left-wing radicalism declined throughout the 80s and 90s, right wing hate groups began to flourish. Today, the web offers a place for any brand of extremism, but little is understood about their current growth and development. While there is much to gain from in-depth studies of the content provided by these sites, there is also a surprising amount of information contained in their online network structure as manifested in links between and among these web sites. Our research follows the idea that much can be known about you by the company you keep. In this paper, we propose an approach to measure the intrinsic relationships (i.e., similarities) of a set of extremist web pages. In this model, the web presence of a group is thought of as a node in a social network and the links between these pages are the ties between groups. This approach takes the bi-directional hyperlink structure of web pages and, based on similarity scores, applies an effective multi-membership clustering algorithm known as the quasi clique merger method to cluster these web pages using a derived hierarchical tree. The experimental results show that this new similarity measurement and hierarchical clustering algorithm gives an improvement over traditional link based clustering methods.

An approach to v&v of embedded adaptive systems

Rigorous Verification and Validation (V& V) techniques are essential for high assurance systems. Lately, the performance of some of these systems is enhanced by embedded adaptive components in order to cope with environmental changes. Although the ability of adapting is appealing, it actually poses a problem in terms of V&V. Since uncertainties induced by environmental changes have a significant impact on system behavior, the applicability of conventional V& V techniques is limited. In safety-critical applications such as flight control system, the mechanisms of change must be observed, diagnosed, accommodated and well understood prior to deployment. In this paper, we propose a non-conventional V&V approach suitable for online adaptive systems. We apply our approach to an intelligent flight control system that employs a particular type of Neural Networks (NN) as the adaptive learning paradigm. Presented methodology consists of a novelty detection technique and online stability monitoring tools. The novelty detection technique is based on Support Vector Data Description that detects novel (abnormal) data patterns. The Online Stability Monitoring tools based on Lyapunovs Stability Theory detect unstable learning behavior in neural networks. Cases studies based on a high fidelity simulator of NASAs Intelligent Flight Control System demonstrate a successful application of the presented V&V methodology.

Monitoring techniques for an online neuro-adaptive controller

Abstract The appeal of biologically inspired soft computing systems such as neural networks in complex systems comes from their ability to cope with a changing environment. Unfortunately, adaptability induces uncertainty that limits the applicability of static analysis to such systems. This is particularly true for systems with multiple adaptive components or systems with multiple types of learning operation. This work builds a paradigm of dynamic analysis for a neuro-adaptive controller where different types of learning are to be employed for its online neural networks. We use support vector data description as the novelty detector to detect unforeseen patterns that may cause abrupt system functionality changes. It differentiates transients from failures based on the duration and degree of novelties. Further, for incremental learning, we utilize Lyapunov functions to assess real-time performance of the online neural networks. For quasi-online learning, we define a confidence measure, the validity index, to be associated with each network output. Our study on the NASA F-15 Intelligent Flight Control System demonstrates that our novelty detection tool effectively filters out transients and detects failures; and our light-weight monitoring techniques supply sufficient evidence for an insightful validation.

Lyapunov stability analysis of the quantization error for DCS neural networks

In this paper we show that the quantization error for Dynamic Cell Structures (DCS) Neural Networks (NN) as defined by Bruske and Sommer provides a measure of the Lyapunov stability of the weight centers of the neural net. We also show, however, that this error is insufficient in itself to verify that DCS neural networks provide stable topological representation of a given fixed input feature manifold. While it is true that DCS generates a topology preserving feature map, it is unclear when and under what circumstances DCS will have achieved an accurate representation. This is especially important in safety critical systems where it is necessary to understand when the topological representation is complete and accurate. The stability analysis here shows that there exists a Lyapunov function for the weight adaptation of the DCS NN system applied to a fixed feature manifold. The Lyapunov function works in parallel during DCS learning, and is able to provide a measure of the effective placement of neural units during the NNs approximation. It does not, however, guarantee the formation of an accurate representation of the feature manifold. Simulation studies from a selected CMU-Benchmark involving the use of the constructed Lyapunov function indicate the existence of a Globally Asymptotically Stable (GAS) state for the placement of neural units, but an example is given where the topology of the constructed network fails to mirror that of the input manifold even though the quantization error continues to decrease monotonically.

Signed Quasi-Clique Merger: A New Clustering Method for Signed Networks with Positive and Negative Edges

Signed networks with both positive and negative links have gained considerable attention over the past several years. Community detection is among the main challenges for signed network analysis. It aims to find mutually antagonistic groups such that entities within the same group have as many positive relationships as possible and entities between different groups have as many negative relationships as possible. Most existing algorithms for community detection in signed networks aim to provide a hard partition of the network where any node should belong to a single community. However, overlapping communities, where a node is allowed to belong to multiple communities, widely exist in many real-world networks. Another disadvantage of some existing algorithms is that the number of final clusters k should be an input of the clustering process. It may however be the case that we do not know k in advance. In this paper, to offer improvements to existing algorithms, we propose a new clustering method for signed networks, the Signed Quasi-clique Merger (SQCM) algorithm. This algorithm detects the meaningful clusters (i.e. subgraphs with high friendly density) from the networks directly, where the friendly density of a subgraph C=(V(C),E(C)) is defined as d(C)=2∑e∈E(C)w(e)|V(C)|(|V(C)|−1). We construct a hierarchically nested system to illustrate their inclusion relationships. The output of SQCM is a smaller hierarchical tree, which clearly highlights meaningful clusters. During the clustering process, we do not need to know the number of final clusters k in advance; the algorithm is able to detect it on its own. Another important feature of SQCM is overlapping clustering or multi-membership. Its effectiveness is demonstrated through rigorous experiments involving both benchmark and randomly generated signed networks.

Numerical Characterization of DNA Sequence Based on Dinucleotides

Sequence comparison is a primary technique for the analysis of DNA sequences. In order to make quantitative comparisons, one devises mathematical descriptors that capture the essence of the base composition and distribution of the sequence. Alignment methods and graphical techniques (where each sequence is represented by a curve in high-dimension Euclidean space) have been used popularly for a long time. In this contribution we will introduce a new nongraphical and nonalignment approach based on the frequencies of the dinucleotide XY in DNA sequences. The most important feature of this method is that it not only identifies adjacent XY pairs but also nonadjacent XY ones where X and Y are separated by some number of nucleotides. This methodology preserves information in DNA sequence that is ignored by other methods. We test our method on the coding regions of exon-1 of β–globin for 11 species, and the utility of this new method is demonstrated.

Stability monitoring and analysis of learning in an adaptive system

The ability to ensure reliable adaptation is important in safety-critical applications. Traditional software verification and validation techniques cannot account for the time-evolving nature of a system, making them inapplicable for adaptive computing system assurance. In this paper, we propose considering stability of adaptation as a heuristic measure of reliability. We present a stability monitoring technique that detects unstable learning behavior during online operation of adaptive systems. The stability monitoring relies upon Lyapunov-like functions that detect distinct states in learning that bifurcate away from stable behavior. Dempster-Shafer theory is used for combining stability estimates provided by the monitors into an easily interpretable stability belief function. The proposed analysis technique is evaluated using online learning experiments based on data generated by an actual adaptive flight control system. Results indicate that the stability monitoring successfully detects unstable learning conditions. Our approach is one of the first that can be used for the verification, validation and monitoring of adaptive computing applications.