A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

On the Feasibility of Steering Swallowable Microsystem Capsules Using Computer-Aided Magnetic Levitation

Swallowable capsule endoscopy is used for non-invasive diagnosis of some gastrointestinal (GI) organs. However, control over the position of the capsule is a major unresolved issue. This study presents a design for steering the capsule based on magnetic levitation. The levitation is stabilized with the aid of a computer-aided feedback control system and diamagnetism. Peristaltic and gravitational forces to be overcome were calculated. A levitation setup was built to analyze the feasibility of using Hall Effect sensors to locate the in- vivo capsule. CAD software Maxwell 3D (Ansoft, Pittsburgh, PA) was used to determine the dimensions of the resistive electromagnets required for levitation and the feasibility of building them was examined. Comparison based on design complexity was made between positioning the patient supinely and upright.

Neural Control of Chaos and Aplications

Signal processing is an important topic in technological research today. In the areas of nonlinear dynamics search, the endeavor to control or order chaos is an issue that has received increasing attention over the last few years. Increasing interest in neural networks composed of simple processing elements (neurons) has led to widespread use of such networks to control dynamic systems learning. This paper presents backpropagation-based neural network architecture that can be used as a controller to stabilize unsteady periodic orbits. It also presents a neural network-based method for transferring the dynamics among attractors, leading to more efficient system control. The procedure can be applied to every point of the basin, no matter how far away from the attractor they are. Finally, this paper shows how two mixed chaotic signals can be controlled using a backpropagation neural network as a filter to separate and control both signals at the same time. The neural network provides more effective control, overcoming the problems that arise with control feedback methods. Control is more effective because it can be applied to the system at any point, even if it is moving away from the target state, which prevents waiting times. Also control can be applied even if there is little information about the system and remains stable longer even in the presence of random dynamic noise.

Simultaneous Control of Chaotic Systems Using RBF Networks

Chaos control is a concept that recently acquiring more attention among the research community, concerning the fields of engineering, physics, chemistry, biology and mathematic. This paper presents a method to simultaneous control of deterministic chaos in several nonlinear dynamical systems. A radial basis function networks (RBFNs) has been used to control chaotic trajectories in the equilibrium points. Such neural network improves results, avoiding those problems that appear in other control methods, being also efficient dealing with a relatively small random dynamical noise.