Silvia Ferrari

Smooth function approximation using neural networks

An algebraic approach for representing multidimensional nonlinear functions by feedforward neural networks is presented. In this paper, the approach is implemented for the approximation of smooth batch data containing the functions input, output, and possibly, gradient information. The training set is associated to the network adjustable parameters by nonlinear weight equations. The cascade structure of these equations reveals that they can be treated as sets of linear systems. Hence, the training process and the network approximation properties can be investigated via linear algebra. Four algorithms are developed to achieve exact or approximate matching of input-output and/or gradient-based training sets. Their application to the design of forward and feedback neurocontrollers shows that algebraic training is characterized by faster execution speeds and better generalization properties than contemporary optimization techniques.

Online Adaptive Critic Flight Control

A nonlinear control system comprising a network of networks is taught by the use of a two-phase learning procedure realized through novel training techniques and an adaptive critic design. The neural network controller is trained algebraically, offline, by the observation that its gradients must equal corresponding linear gain matrices at chosen operating points. Online learning by a dual heuristic adaptive critic architecture optimizes performance incrementally over time by accounting for plant dynamics and nonlinear effects that are revealed during large, coupled motions. The method is implemented to control the six-degree-of-freedom simulation of a business jet aircraft over its full operating envelope. The result is a controller that improves its performance while unexpected conditions, such as unmodeled dynamics, parameter variations, and control failures, are experienced for the first time.

Information-Driven Sensor Path Planning by Approximate Cell Decomposition

A methodology is developed for planning the sensing strategy of a robotic sensor deployed for the purpose of classifying multiple fixed targets located in an obstacle-populated workspace. Existing path planning techniques are not directly applicable to robots whose primary objective is to gather sensor measurements using a bounded field of view (FOV). This paper develops a novel approximate cell-decomposition method in which obstacles, targets, sensors platform, and FOV are represented as closed and bounded subsets of an Euclidean workspace. The method constructs a connectivity graph with observation cells that is pruned and transformed into a decision tree from which an optimal sensing strategy can be computed. The effectiveness of the optimal sensing strategies obtained by this methodology is demonstrated through a mine-hunting application. Numerical experiments show that these strategies outperform shortest path, complete coverage, random, and grid search strategies, and are applicable to nonoverpass capable robots that must avoid targets as well as obstacles.

An adaptive critic global controller

A nonlinear control system comprising a network of networks is taught using a two-phase learning procedure realized through novel techniques for initialization, on-line training, and adaptive critic design. The neural networks are initialized algebraically by observing that the gradients of the networks must equal corresponding linear gain matrices at chosen operating points. On-line learning is based on a dual heuristic adaptive critic architecture that improves control for large, coupled motions by accounting for plant dynamics and nonlinear effects. The result is an adaptive controller that is as conservative as the linear designs and as effective as the global controller. The design method is implemented to control the full six-degree-of-freedom simulation of a business jet aircraft.

Constructing Bayesian networks for criminal profiling from limited data

The increased availability of information technologies has enabled law enforcement agencies to compile databases with detailed information about major felonies. Machine learning techniques can utilize these databases to produce decision-aid tools to support police investigations. This paper presents a methodology for obtaining a Bayesian network (BN) model of offender behavior from a database of cleared homicides. The BN can infer the characteristics of an unknown offender from the crime scene evidence, and help narrow the list of suspects in an unsolved homicide. Our research shows that 80% of offender characteristics are predicted correctly on average in new single-victim homicides, and when confidence levels are taken into account this accuracy increases to 95.6%.

Demining sensor modeling and feature-level fusion by Bayesian networks

A method for obtaining the Bayesian network (BN) representation of a sensors measurement process is developed so that the problems of sensor fusion and management can be approached from a unified point of view. Uncertainty, reliability, and causal information embedded in the sensor data are used to build the BN model of a sensor. The method is applied to model ground-penetrating radar, electromagnetic induction, and infrared sensors for humanitarian demining. Structural and parameter learning algorithms are employed to encode relationships among mine features, sensor measurements, and environmental conditions in the BN model. Inference is used to estimate target features in the presence of heterogeneous soil and varying environmental conditions. A multisensor fusion technique operating on BN models is developed to exploit the complementarity of the sensor measurements. Through the same approach, a BN classifier is obtained to estimate the target typology. The BN models and classifier also compute so-called confidence levels that quantify the uncertainty associated with the feature estimates and the classification decisions. The effectiveness of the approach is demonstrated by implementing these BN tools for the detection and classification of metal and plastic landmines that are characterized by different shape, size, depth, and metal content. Through BN fusion, the accuracy of the feature estimates is improved by up to 64% with respect to single-sensor measurements, and the number of objects that are both detected and classified is increased by up to 62%.

A Geometric Optimization Approach to Detecting and Intercepting Dynamic Targets Using a Mobile Sensor Network

A methodology is developed to deploy a mobile sensor network for the purpose of detecting and capturing mobile targets in the plane. The sensing-pursuit problem considered in this paper is analogous to the Marco Polo game, in which the pursuer must capture multiple mobile targets that are sensed intermittently, and with very limited information. In this paper, the mobile sensor network consists of a set of robotic sensors that must track and capture mobile targets based on the information obtained through cooperative detections. Since the sensors are installed on robotic platforms and have limited range, the geometry of the platforms and of the sensors field-of- view play a key role in obstacle avoidance and target detection. Thus, a new cell decomposition approach is presented to formulate the probability of detection and the cost of operating the robots based on the geometric properties of the network. Numerical simulations verify the validity and flexibility of our methodology.

Spike-based indirect training of a spiking neural network-controlled virtual insect

Spiking neural networks (SNNs) have been shown capable of replicating the spike patterns observed in biological neuronal networks, and of learning via biologically-plausible mechanisms, such as synaptic time-dependent plasticity (STDP). As result, they are commonly used to model cultured neural network, and memristor-based neuromorphic computer chips that aim at replicating the scalability and functionalities of biological circuitries. These examples of SNNs, however, do not allow for the direct manipulation of the synaptic strengths (or weights) as required by existing training algorithms. Therefore, this paper presents an indirect training algorithm that, instead, is designed to manipulate input spike trains (stimuli) that can be implemented by patterns of blue light, or controlled input voltages, to induce the desired synaptic weights changes via STDP. The approach is demonstrated by training an SNN to control a virtual insect that seeks to reach a target location in an obstacle populated environment, without any prior control or navigation knowledge. The simulation results illustrate the feasibility and efficiency of the proposed indirect training algorithm for a biologically-plausible sensorimotor system.

A Geometric Transversal Approach to Analyzing Track Coverage in Sensor Networks

This paper presents a new coverage formulation addressing the quality of service of sensor networks that cooperatively detect targets traversing a region of interest. The problem of track coverage consists of finding the positions of n sensors such that a Lebesgue measure on the set of tracks detected by at least k sensors is optimized. This paper studies the geometric properties of the network, addressing a deterministic track-coverage formulation and binary sensor models. It is shown that the tracks detected by a network of heterogeneous omnidirectional sensors are the geometric transversals of non-translates families of circles. A novel methodology based on cone theory is presented for representing and measuring sets of transversals in closed-form. Then, the solution of the track-coverage problem can be formulated as a nonlinear program (NLP). The numerical results show that this approach can improve track coverage by up to two orders of magnitude compared to grid and random deployments. Also, it can be used to reduce the number of sensors required to achieve a desired detection performance by up to 50%, and to optimally replenish or reposition existing sensor networks.

A Constrained Optimization Approach to Preserving Prior Knowledge During Incremental Training

In this paper, a supervised neural network training technique based on constrained optimization is developed for preserving prior knowledge of an input-output mapping during repeated incremental training sessions. The prior knowledge, referred to as long-term memory (LTM), is expressed in the form of equality constraints obtained by means of an algebraic training technique. Incremental training, which may be used to learn new short-term memories (STMs) online, is then formulated as an error minimization problem subject to equality constraints. The solution of this problem is simplified by implementing an adjoined error gradient that circumvents direct substitution and exploits classical backpropagation. A target application is neural network function approximation in adaptive critic designs. For illustrative purposes, constrained training is implemented to update an adaptive critic flight controller, while preserving prior knowledge of an established performance baseline that consists of classical gain-scheduled controllers. It is shown both analytically and numerically that the LTM is accurately preserved while the controller is repeatedly trained over time to assimilate new STMs.