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This paper introduces the idea of distributed gyricity, in which each volume element of a continuum possesses an infinitesimal quantity of stored angular momentum. The continuum is also assumed to be linear-elastic. Using operator notation, a partial differential equation is derived that governs the small displacements of this gyroelastic continuum. Gyroelastic vibration modes are derived and used as basis functions in terms of which the general motion can be expressed. A discretized approximation is also developed using the method of Rayleigh-Ritz. The paper concludes with a numerical example of gyroelastic modes.

A key challenge in evolving control systems for robots using neural networks is training tractability. Evolving monolithic fixed topology neural networks is shown to be intractable with limited supervision in high dimensional search spaces. Common strategies to overcome this limitation are to provide more supervision by encouraging particular solution strategies, manually decomposing the task and segmenting the search space and network. These strategies require a supervisor with domain knowledge and may not be feasible for difficult tasks where novel concepts are required. The alternate strategy is to use self-organized task decomposition to solve difficult tasks with limited supervision. The artificial neural tissue (ANT) approach presented here uses self-organized task decomposition to solve tasks. ANT inspired by neurobiology combines standard neural networks with a novel wireless signaling scheme modeling chemical diffusion of neurotransmitters. These chemicals are used to dynamically activate and inhibit wired network of neurons using a coarse-coding framework. Using only a global fitness function that does not encourage a predefined solution, modular networks of neurons are shown to self-organize and perform task decomposition. This approach solves the sign-following task found to be intractable with conventional fixed and variable topology networks. In this paper, key attributes of the ANT architecture that perform self-organized task decomposition are shown. The architecture is robust and scalable to number of neurons, synaptic connections, and initialization parameters.

We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that guarantees the quality of the network approximation. We show that a feedforward neural network can be trained on the vector-field representation of a given dynamical system using backpropagation, then recast it as a recurrent network that replicates the original system's dynamics. After detailing this algorithm and its relation to earlier approaches, we present numerical examples that demonstrate its capabilities. One of the distinguishing features of our approach is that both the original dynamical systems and the recurrent networks that simulate them operate in continuous time.

An optimal formulation is developed for the shape control of large flexible spacecraft possessing a distribution of control moment gyros. The structure is modeled as a continuum in mass, stiffness, and gyricity (stored angular momentum). A small, linear viscous damping term completes the dynamical description. The equation of motion is formulated in continuum form, and a brief eigenanalysis is presented that permits the modal equations of motion to be derived. The optimal control problem is treated using distributed-parameter concepts, and a modal expansion for the resulting Riccati operator reduces the problem to the solution of a matrix Riccati equation. Such an approach permits pointwise control moment gyros as well as the distributed analog to be handled with the same theory. By means of an example, the use of distributed gyricity is demonstrated to be very effective for shape control of large space structures. Moreover, the notion of a continuous distribution of gyricity is shown to be beneficial in modeling the dynamics and control of flexible spacecraft employing many control moment gyros.