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.

This paper presents a novel constrained integration (CINT) method for solving initial boundary value partial differential equations (PDEs). The CINT method combines classical Galerkin methods with a constrained backpropogation training approach to obtain an artificial neural network representation of the PDE solution that approximately satisfies the boundary conditions at every integration step. The advantage of CINT over existing methods is that it is readily applicable to solving PDEs on irregular domains, and requires no special modification for domains with complex geometries. Furthermore, the CINT method provides a semi-analytical solution that is infinitely differentiable. In this paper the CINT method is demonstrated on two hyperbolic and one parabolic initial boundary value problems with a known analytical solutions that can be used for performance comparison. The numerical results show that, when compared to the most efficient finite element methods, the CINT method achieves significant improvements both in terms of computational time and accuracy

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, sensor's 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.

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.

This paper presents a novel optimal control problem, referred to as distributed optimal control, that is applicable to multiscale dynamical systems comprised of numerous interacting agents. The system performance is represented by an integral cost function of the macroscopic state that is optimized subject to a hyperbolic partial differential equation known as the advection equation. The microscopic control laws are derived from the optimal macroscopic description using a potential function approach. The optimality conditions of the distributed optimal control problem are first derived analytically and, then, demonstrated numerically through a multi-agent trajectory optimization problem