Second-order bounds on the domain of attraction and the rate ofconvergence of nonlinear dynamical systems and neural networks

We present a method for analyzing the convergence properties of nonlinear dynamical systems yielding second-order bounds on the domain of attraction of an asymptotically stable equilibrium point and on the time of convergence in the estimated domain. We show that under certain conditions on the system, there exists an analytic solution to the corresponding optimization problem. The method is applied in analyzing the dynamics of a neural network model.     

Connectivity and performance tradeoffs in the cascade correlationlearning architecture

The cascade correlation is a very flexible, efficient and fast algorithm for supervised learning. It incrementally builds the network by adding hidden units one at a time, until the desired input/output mapping is achieved. It connects all the previously installed units to the new unit being added. Consequently, each new unit in effect adds a new layer and the fan-in of the hidden and output units keeps on increasing as more units get added. The resulting structure could be hard to implement in VLSI, because the connections are irregular and the fan-in is unbounded. Moreover, the depth or the propagation delay through the resulting network is directly proportional to the number of units and can be excessive. We have modified the algorithm to generate networks with restricted fan-in and small depth (propagation delay) by controlling the connectivity. Our results reveal that there is a tradeoff between connectivity and other performance attributes like depth, total number of independent parameters, and learning time.     

Neural network control of communications systems

Neural networks appear well suited to applications in the control of communications systems for two reasons: adaptivity and high speed. This paper describes application of neural networks to two problems, admission control and switch control, which exploit the adaptivity and speed property, respectively. The admission control problem is the selective admission of a set of calls from a number of inhomogeneous call classes, which may have widely differing characteristics as to their rate and variability of traffic, onto a network. It is usually unknown in advance which combinations of calls can be simultaneously accepted so as to ensure satisfactory performance. The approach adopted is that key network performance parameters are observed while carrying various combinations of calls, and their relationship is learned by a neural network structure. The network model chosen has the ability to interpolate or extrapolate from the past results and the ability to adapt to new and changing conditions. The switch control problem is the service policy used by a switch controller in transmitting packets. In a crossbar switch with input queueing, significant loss of throughput can occur when head-of-line service order is employed. A solution can be based on an algorithm which maximizes throughput. However since this solution is typically required in less than one microsecond, software implementation policy is infeasible. We will carry out an analysis of the benefits of such a policy, describe some existing proposed schemes for its implementation, and propose a further scheme that provides this submicrosecond optimization.     

A delta transform approach to loop gain-phase shaping design of robust digital control systems

This paper addresses the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete-time systems using the Δ-transform, a transform method that applies to both continuous-time and discrete-time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.     

Robust crossfeed design for hovering rotorcraft

Control law design for rotorcraft fly-by-wire systems normally attempts to decouple the angular responses using fixed-gain crossfeeds. This approach can lead to poor decoupling over the frequency range of pilot inputs and increase the load on the feedback loops. In order to improve the decoupling performance, dynamic crossfeeds should be adopted. Moreover, because of the large changes that occur in the aircraft dynamics due to small changes about the nominal design condition, especially for near-hovering flight, the crossfeed design must be ‘robust’. A new low-order matching method is presented here to design robust crossfeed compensators for multi-input, multi-output (MIMO) systems. The technique minimizes cross-coupling given an anticipated set of parameter variations for the range of flight conditions of concern. Results are presented in this paper of an analysis of the pitch/roll coupling of the UH-60 Black Hawk helicopter in near-hovering flight. A robust crossfeed is designed that shows significant improvement in decoupling perfomance and robustness over the fixed-gain or single point dynamic compensators. The design method and results are presented in an easily used graphical format that lends significant physical insight to the design procedure. This plant precompensation technique is an appropriate preliminary step to the design of robust feedback control laws for rotorcraft.     

An explicit finite difference method for finite-time observers

In this paper we present a numerical method for estimating the current state of a nonlinear control system. We use finite differences to discretize a modified version of the finite-time observer equations in James. The discretized equations are simple and easily programmed. The convergence and accuracy of the scheme is proved, and the scheme enjoys a number of important properties: availability of rate of convergence estimates, good robustness characteristics, and the ability to handle certain types of discontinuities in the observations. The major disadvantage is that the number of grid points required increases exponentially with the number of state dimensions.     

Low temperature wafer direct bonding

A pronounced increase of interface energy of room temperature bonded hydrophilic Si/Si, Si/SiO₂, and SiO₂/SiO ₂ wafers after storage in air at room temperature, 150°C for 10-400 h has been observed. The increased number of OH groups due to a reaction between water and the strained oxide and/or silicon at the interface at temperatures below 110°C and the formation of stronger siloxane bonds above 110°C appear to be the main mechanisms responsible for the increase in the interface energy. After prolonged storage, interface bubbles are detectable by an infrared camera at the Si/Si bonding seam. Desorbed hydrocarbons as well as hydrogen generated by a reaction of water with silicon appear to be the major contents in the bubbles. Design guidelines for low temperature wafer direct bonding technology are proposed     

The design, fabrication, and testing of corrugated silicon nitridediaphragms

Silicon nitride corrugated diaphragms of 2 mm×2 mm×1 μm have been fabricated with 8 circular corrugations, having depths of 4, 10, or 14 μm. The diaphragms with 4-μm-deep corrugations show a measured mechanical sensitivity (increase in the deflection over the increase in the applied pressure) which is 25 times larger than the mechanical sensitivity of flat diaphragms of equal size and thickness. Since this gain in sensitivity is due to reduction of the initial stress, the sensitivity can only increase in the case of diaphragms with initial stress. A simple analytical model has been proposed that takes the influence of initial tensile stress into account. The model predicts that the presence of corrugations increases the sensitivity of the diaphragms, because the initial diaphragm stress is reduced. The model also predicts that for corrugations with a larger depth the sensitivity decreases, because the bending stiffness of the corrugations then becomes dominant. These predictions have been confirmed by experiments. The application of corrugated diaphragms offers the possibility to control the sensitivity of thin diaphragms by geometrical parameters, thus eliminating the effect of variations in the initial stress, due to variations in the diaphragm deposition process and/or the influence of temperature changes and packaging stress     

Capacitive microphone with a surface micromachined backplate usingelectroplating technology

A technology for surface micromachining of free-standing metal microstructures using metal electrodeposition on a sacrificial photoresist layer has been applied to a condenser microphone. Electroplating technology has been used to implement a suspended and perforated 15-μm-thick microstructure in copper, which serves as backplate electrode in the condenser microphone. The 1.8×1.8 mm ² large microphone diaphragm is in monocrystalline silicon and is fabricated with anisotropic etching of the substrate wafer. The realized prototypes have a measured sensitivity of 1.4 mV/Pa using a bias voltage of 28 V. The bandwidth is limited by an anti-resonance at 14 kHz which is due to the semi-rigid backplate. The resonance behavior of the backplate structure has been analyzed with finite element modeling with results in good agreement with measured data