Percolation-like Scaling Exponents for Minimal Paths and Trees in the Stochastic Mean Field Model

In the mean field (or random link) model there are $n$ points and inter-point distances are independent random variables. For $0 < \ell < \infty$ and in the $n \to \infty$ limit, let $\delta(\ell) = 1/n \times$ (maximum number of steps in a path whose average step-length is $\leq \ell$). The function $\delta(\ell)$ is analogous to the percolation function in percolation theory: there is a critical value $\ell_* = e^{-1}$ at which $\delta(\cdot)$ becomes non-zero, and (presumably) a scaling exponent $\beta$ in the sense $\delta(\ell) \asymp (\ell - \ell_*)^\beta$. Recently developed probabilistic methodology (in some sense a rephrasing of the cavity method of Mezard-Parisi) provides a simple albeit non-rigorous way of writing down such functions in terms of solutions of fixed-point equations for probability distributions. Solving numerically gives convincing evidence that $\beta = 3$. A parallel study with trees instead of paths gives scaling exponent $\beta = 2$. The new exponents coincide with those found in a different context (comparing optimal and near-optimal solutions of mean-field TSP and MST) and reinforce the suggestion that these scaling exponents determine universality classes for optimization problems on random points.Comment: 19 page

Examples of Artificial Perceptions in Optical Character Recognition and Iris Recognition

This paper assumes the hypothesis that human learning is perception based, and consequently, the learning process and perceptions should not be represented and investigated independently or modeled in different simulation spaces. In order to keep the analogy between the artificial and human learning, the former is assumed here as being based on the artificial perception. Hence, instead of choosing to apply or develop a Computational Theory of (human) Perceptions, we choose to mirror the human perceptions in a numeric (computational) space as artificial perceptions and to analyze the interdependence between artificial learning and artificial perception in the same numeric space, using one of the simplest tools of Artificial Intelligence and Soft Computing, namely the perceptrons. As practical applications, we choose to work around two examples: Optical Character Recognition and Iris Recognition. In both cases a simple Turing test shows that artificial perceptions of the difference between two characters and between two irides are fuzzy, whereas the corresponding human perceptions are, in fact, crisp.Comment: 5th Int. Conf. on Soft Computing and Applications (Szeged, HU), 22-24 Aug 201

Modified Adaptive Control for Region 3 Operation in the Presence of Wind Turbine Structural Modes

Many challenges exist for the operation of wind turbines in an efficient manner that is reliable and avoids component fatigue and failure. Turbines operate in highly turbulent environments resulting in aerodynamic loads that can easily excite turbine structural modes, possibly causing component fatigue and failure. Wind turbine manufacturers are highly motivated to reduce component fatigue and failure that can lead to loss of revenue due to turbine down time and maintenance costs. The trend in wind turbine design is toward larger, more flexible turbines that are ideally suited to adaptive control methods due to the complexity and expense required to create accurate models of their dynamic characteristics. In this paper, we design an adaptive collective pitch controller for a high-fidelity simulation of a utility-scale, variable-speed horizontal axis wind turbine operating in Region 3. The objective of the adaptive pitch controller is to regulate generator speed, accommodate wind gusts, and reduce the excitation of structural modes in the wind turbine. The control objective is accomplished by collectively pitching the turbine blades. The adaptive collective pitch controller for Region 3 was compared in simulations with a baseline classical Proportional Integrator (PI) collective pitch controller. The adaptive controller will demonstrate the ability to regulate generator speed in Region 3, while accommodating gusts, and reducing the excitation of certain structural modes in the wind turbine

Augmented Adaptive Control of a Wind Turbine in the Presence of Structural Modes

Wind turbines operate in highly turbulent environments resulting in aerodynamic loads that can easily excite turbine structural modes, potentially causing component fatigue and failure. Two key technology drivers for turbine manufacturers are increasing turbine up time and reducing maintenance costs. Since the trend in wind turbine design is towards larger, more flexible turbines with lower frequency structural modes, manufacturers will want to develop methods to operate in the presence of these modes. Accurate models of the dynamic characteristics of new wind turbines are often not available due to the complexity and expense of the modeling task, making wind turbines ideally suited to adaptive control. In this paper, we develop theory for adaptive control with rejection of disturbances in the presence of modes that inhibit the controller. We use this method to design an adaptive collective pitch controller for a high-fidelity simulation of a utility-scale, variable-speed wind turbine operating in Region 3. The objective of the adaptive pitch controller is to regulate generator speed, accommodate wind gusts, and reduce the interference of certain structural modes in feedback. The control objective is accomplished by collectively pitching the turbine blades. The adaptive pitch controller for Region 3 is compared in simulations with a baseline classical Proportional Integrator (PI) collective pitch controller

Model reference control of distributed parameter systems: Application to the SCOLE problem

The model reference control of lumped linear systems and the model reference control of the distributed parameter system (DPS) are presented with their theory and Spacecraft Control Laboratory Experiment (SCOLE) applications

Packing While Traveling: Mixed Integer Programming for a Class of Nonlinear Knapsack Problems

Packing and vehicle routing problems play an important role in the area of supply chain management. In this paper, we introduce a non-linear knapsack problem that occurs when packing items along a fixed route and taking into account travel time. We investigate constrained and unconstrained versions of the problem and show that both are NP-hard. In order to solve the problems, we provide a pre-processing scheme as well as exact and approximate mixed integer programming (MIP) solutions. Our experimental results show the effectiveness of the MIP solutions and in particular point out that the approximate MIP approach often leads to near optimal results within far less computation time than the exact approach