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 function's 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.

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.

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This paper addresses the need for surveillance of fugitive methane emissions over broad geographical regions. Most existing techniques suffer from being either extensive (but qualitative) or quantitative (but intensive with poor scalability). A total of two novel advancements are made here. First, a recursive Bayesian method is presented for probabilistically characterizing fugitive point-sources from mobile sensor data. This approach is made possible by a new cross-plume integrated dispersion formulation that overcomes much of the need for time-averaging concentration data. The method is tested here against a limited data set of controlled methane release and shown to perform well. We then present an information-theoretic approach to plan the paths of the sensor-equipped vehicle, where the path is chosen so as to maximize expected reduction in integrated target source rate uncertainty in the region, subject to given starting and ending positions and prevailing meteorological conditions. The information-driven sensor path planning algorithm is tested and shown to provide robust results across a wide range of conditions. An overall system concept is presented for optionally piggybacking of these techniques onto normal industry maintenance operations using sensor-equipped work trucks.

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Much of our real-life decision making is bounded by uncertain information, limitations in cognitive resources, and a lack of time to allocate to the decision process. It is thought that humans overcome these limitations through satisficing, fast but "good-enough" heuristic decision making that prioritizes some sources of information (cues) while ignoring others. However, the decision-making strategies we adopt under uncertainty and time pressure, for example during emergencies that demand split-second choices, are presently unknown. To characterize these decision strategies quantitatively, the present study examined how people solve a novel multicue probabilistic classification task under varying time pressure, by tracking shifts in decision strategies using variational Bayesian inference. We found that under low time pressure, participants correctly weighted and integrated all available cues to arrive at near-optimal decisions. With increasingly demanding, subsecond time pressures, however, participants systematically discounted a subset of the cue information by dropping the least informative cue(s) from their decision making process. Thus, the human cognitive apparatus copes with uncertainty and severe time pressure by adopting a "drop-the-worst" cue decision making strategy that minimizes cognitive time and effort investment while preserving the consideration of the most diagnostic cue information, thus maintaining "good-enough" accuracy. This advance in our understanding of satisficing strategies could form the basis of predicting human choices in high time pressure scenarios.

This paper presents a constrained backpropagation (CPROP) methodology for solving nonlinear elliptic and parabolic partial differential equations (PDEs) adaptively, subject to changes in the PDE parameters or external forcing. Unlike existing methods based on penalty functions or Lagrange multipliers, CPROP solves the constrained optimization problem associated with training a neural network to approximate the PDE solution by means of direct elimination. As a result, CPROP reduces the dimensionality of the optimization problem, while satisfying the equality constraints associated with the boundary and initial conditions exactly, at every iteration of the algorithm. The effectiveness of this method is demonstrated through several examples, including nonlinear elliptic and parabolic PDEs with changing parameters and nonhomogeneous terms.

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