James E. Steck

Simulations of quantum neural networks

We explore by simulation ways in which an array of quantum dot molecules could serve as a quantum neural computer. First, we show that a single quantum dot molecule evolving in real time can act as a recurrent temporal quantum neural network. Inputs are prepared by fixing the initial states of a quantum dot molecule, and outputs determined by reading its value at a given time T later. The nodes of the network are the instantaneous states of the molecule at successive time slices. The nodes interact indirectly through their mutual interaction with local and phononic modes of the substrate. These modes can be preferentially excited optically, and, therefore, controlled externally. The number of excitations can thus be used as trainable “weight” parameters for a neural network. This network is shown to perform classical logic gates. By preparing the input state as a superposition state, multiple inputs can be encoded as a single initial state. Second, we simulate the possibility of a spatial, rather than temporal, design, as a Hopfield net. The network consists of a regular array of quantum dot molecules on a suitable substrate. The molecules interact indirectly as before, and, now, with each other directly through Coulombic interactions. Both of the quantum networks have none of the “wiring problems” of traditional neural nets: the necessary connections are supplied by the physical system itself. Computation is performed by the intrinsic physics of the physical system. The long range character of the phononic interactions takes the net beyond traditional local connectionist structures. The hypothesized increase in complexity and power, in going to the quantum regime, is demonstrated. We train the quantum Hopfield net using simultaneous recurrent backpropagation.

Linear and neural network feedback for flight control decoupling

Some experts are of the opinion that the task of flight training can become far less labor-intensive if the pilot can directly control each of the state variables of the aircraft individually. Yet complete decoupling of the aircraft as a nonlinear system is a formidable problem. Such a task requires accurate aircraft state information and rapid computing. The difficulties are compounded when the dynamics or the aerodynamics of the aircraft fall in the highly nonlinear regimes. The authors demonstrate the potential for an artificial neural network in conjunction with a linear compensator to perform such a function. The authors show that the linear compensator is unable to control the aircraft in the absence of the neural network. A neural network can be trained to produce the large nonlinear portion of the control inputs; however, a hybrid combination of the neural network and the compensator based on the linearized equations of motion gives the best results. Furthermore, The authors demonstrate that such a hybrid system can tolerate a large amount of noise in the network input. Several examples are shown, with and without the linear compensator. Finally, the authors demonstrate generalization within the training domain through accurately predicting a case that was absent in the training domain.

Model Reference Adaptive Fight Control Adapted for General Aviation: Controller Gain Simulation and Preliminary Flight Testing On a Bonanza Fly-By-Wire Testbed

Model reference adaptive flight control (dynamic inverse with adaptation) methodology is adapted for use for a general aviation Hawker Beechcraft Bonanza fly-by-wire testbed. The control method is based on the work of Calise and the NASA Integrated Resilient Aircraft Control project. A derivation of the simplified inverse controller and adaptive elements is presented. The controller is a longitudinal flight controller that tracks pilot inputs of velocity and flight path angle. An L2 tracking error metric is used in a study to tune the outer controller loop gains by introducing artificial time delays in the control signals to determine the time delay margin. Results of this study are presented. Hardware in the loop control software ground testing followed by flight testing of this baseline controller have been completed. Flight test cards are presented in this paper as well as desktop simulation and flight test results.

Adaptive Feedback Control by Constrained Approximate Dynamic Programming

A constrained approximate dynamic programming (ADP) approach is presented for designing adaptive neural network (NN) controllers with closed-loop stability and performance guarantees. Prior knowledge of the linearized equations of motion is used to guarantee that the closed-loop system meets performance and stability objectives when the plant operates in a linear parameter-varying (LPV) regime. In the presence of unmodeled dynamics or failures, the NN controller adapts to optimize its performance online, whereas constrained ADP guarantees that the LPV baseline performance is preserved at all times. The effectiveness of an adaptive NN flight controller is demonstrated for simulated control failures, parameter variations, and near-stall dynamics.

Convergence of recurrent networks as contraction mappings

Three theorems are presented which establish an upper bound on the magnitude of the weights which guarantees convergence of the network to a stable unique fixed point. It is shown that the bound on the weights is inversely proportional to the product of the number of neurons in the network and the maximum slope of the neuron activation functions. The location of its fixed point is determined by the network architecture, weights, and the external input values. The proofs are constructive, consisting of representing the network as a contraction mapping and then applying the contraction mapping theorem from point set topology. The resulting sufficient conditions for network stability are shown to be general enough to allow the network to have nontrivial fixed points.<<ETX>>

Parallel implementation of a recursive least squares neural network training method on the Intel iPSC/2

An algorithm based on the Marquardt-Levenberg least-square optimization method has been shown by S. Kollias and D. Anastassiou (IEEE Trans. on Circuits Syst. vol.36, no.8, p.1092-101, Aug. 1989) to be a much more efficient training method than gradient descent, when applied to some small feedforward neural networks. Yet, for many applications, the increase in computational complexity of the method outweighs any gain in learning rate obtained over current training methods. However, the least-squares method can be more efficiently implemented on parallel architectures than standard methods. This is demonstrated by comparing computation times and learning rates for the least-squares method implemented on 1, 2, 4, 8, and 16 processors on an Intel iPSC/2 multicomputer. Two applications which demonstrate the faster real-time learning rate of the last-squares method over than of gradient descent are given

Robust Adaptive Control of a General Aviation Aircraft

In this paper, an application of newly developed modified state observer (MSO) based adaptive controller for the control of longitudinal dynamics of a general aviation (GA) aircraft is considered. The proposed controller structure uses nonlinear dynamic inversion to decouple the flight controls and to modify the handling qualities of the aircraft. The inversion error caused by modeling inaccuracies is compensated for by a real time robust adaptive control algorithm. The modeling inaccuracies can stem from the differences between the model used for the inversion controller and the actual aircraft which may have some impairment such as inadequate thrust delivery, improper functioning of the control surfaces or in-flight hardware failure. In all the cases the adaptive control algorithm should be able to rapidly adapt to the changing aircraft behavior and restore acceptable aircraft performance. In order to tackle this problem, the recently developed MSO methodology is employed which allows for fast adaptation without inducing any high frequency oscillations in the control signals. Simulations were carried out by introducing unanticipated failures in both trimmed and controlled flight conditions. Aeroelastic modes have also been included. This paper presents the results obtained and the analysis carried out.

Demonstration of the optimal control modification for general aviation: design and simulation

This paper presents the design and simulation of a model reference adaptive control system for general aviation, using the Optimal Control Modification (OCM). The controller is based on previous adaptive control research conducted at Wichita State University (WSU) and the National Aeronautics and Space Administration (NASA) Ames Research Center. The control system is designed for longitudinal control of a Beech Bonanza given pilot commands of pitch rate and airspeed. Three variations of the OCM adaptation are presented, utilizing 3 different parameterizations of the adaptive signal. The first is called OCM-Linear (OCM-L), where the adaptation output is linearly related to the aircraft states. The second variation is called OCM-Bias (OCM-B), which is only a bias adaptation output. The third is a combination of the previous two methods called OCM-Linear and Bias (OCMLB). The controllers are designed and simulated with a nonlinear aircraft model of the Beech Bonanza.

Neural network implementation using self-lensing media.

An all-optical implementation of a feed-forward artificial neural network is presented that uses self-lensing materials in which the index of refraction is irradiance dependent. Many of these types of material have ultrafast response times and permit both weighted connections and nonlinear neuron processing to be implemented with only thin material layers separated by free space. Both neuron processing and weighted interconnections emerge directly from the physical optics of the device. One creates virtual neurons and their connections simply by applying patterns of irradiance to thin layers of the nonlinear media. This is a result of a variation of the refractive-index profile of the self-lensing nonlinear media in response to the applied irradiance. An optical-backpropagation training method for this network is presented. The optical backpropagation is a training method that can be implemented potentially within the same optical device as the forward calculations, although several issues crucial to this po sibility remain to be addressed. Such a network was numerically simulated and trained to solve many benchmark classification problems, and some of these results are presented. To demonstrate the feasibility of building such a network, we also describe experimental work in the construction of an optical network trained to perform a logic XNOR function. This network, as a proof of concept, uses a relatively slow thermal nonlinear material with ~1-s response time.

Response and Recovery of an MRAC Advanced Flight Control System to Wake Vortex Encounters

A three-dimensional, twin-core wake vortex model is developed within the MATLAB/Simulink ® environment, and the effects of this disturbance on a 6 Degree-ofFreedom general aviation-based MRAC flight control system is studied. An envelope protection scheme is developed to augment the aircraft’s response to the disturbance, and three scenarios are tested to evaluate the controller’s performance in response to and recovery from the wake vortex. These scenarios include the controller responding with no pilot input, the controller responding with pilot input, and the pilot responding with no controller input. Pilot-in-the-loop testing and simulation runs are performed, and it is found that having the controller active greatly improves response and recovery performance during and after the wake vortex encounter.