Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Applying robust control theory to solve problems in bio-medical sciences: study of an apoptotic model

Biological models of an apoptotic process are studied using models describing a system of differential equations derived from reaction kinetics information. The mathematical model is re-formulated in a state-space robust control theory framework where parametric and dynamic uncertainty can be modelled to account for variations naturally occurring in biological processes. We propose to handle the nonlinearities using neural networks.

Regularization of descriptor systems

Implicit dynamic-algebraic equations, known in control theory as descriptor systems, arise naturally in many applications. Such systems may not be regular (often referred to as singular). In that case the equations may not have unique solutions for consistent initial conditions and arbitrary inputs and the system may not be controllable or observable. Many control systems can be regularized by proportional and/or derivative feedback.We present an overview of mathematical theory and numerical techniques for regularizing descriptor systems using feedback controls. The aim is to provide stable numerical techniques for analyzing and constructing regular control and state estimation systems and for ensuring that these systems are robust. State and output feedback designs for regularizing linear time-invariant systems are described, including methods for disturbance decoupling and mixed output problems. Extensions of these techniques to time-varying linear and nonlinear systems are discussed in the final section.

A testing and demonstration facility for PV systems and components

A test and demonstration facility for PV and PV hybrid systems and system components has been designed and installed at Dalarna University in Sweden. The facility allows studies of complete PV systems or single components in a range of 0.1-10 kW. The facility includes two grid-connected PV systems, a PV Hybrid off-grid system, three emulators and the necessary measurement and control equipment. Tests can be done manually or automatically through programmed test procedures controlled that will be implemented in Labview. The facility shall be used by researchers, professionals of the industry and engineering students.

Influence of hydraulics and control of thermal storage in solar assisted heat pump combisystems

This paper studies the influence of hydraulics and control of thermal storage in systems combined with solar thermal and heat pump for the production of warm water and space heating in dwellings. A reference air source heat pump system with flat plate collectors connected to a combistore was defined and modeled together with the IEA SHC Task 44 / HPP Annex 38 (T44A38) “Solar and Heat Pump Systems” boundary conditions of Strasbourg climate and SFH45 building. Three and four pipe connections as well as use of internal and external heat exchangers for DHW preparation were investigated as well as sensor height for charging of the DHW zone in the store. The temperature in this zone was varied to ensure the same DHW comfort was achieved in all cases. The results show that the four pipe connection results in 9% improvement in SPF compared to three pipe and that the external heat exchanger for DHW preparation leads to a 2% improvement compared to the reference case. Additionally the sensor height for charging the DHW zone of the store should not be too low, otherwise system performance is adversely affected

On Real-Time Monitoring And Control For Efficient Management Of Drinking Water Networks: Barcelona Case Study

Drinking water utilities in urban areas are focused on finding smart solutions facing new challenges in their real-time operation because of limited water resources, intensive energy requirements, a growing population, a costly and ageing infrastructure, increasingly stringent regulations, and increased attention towards the environmental impact of water use. Such challenges force water managers to monitor and control not only water supply and distribution, but also consumer demand. This paper presents and discusses novel methodologies and procedures towards an integrated water resource management system based on advanced ICT technologies of automation and telecommunications for largely improving the efficiency of drinking water networks (DWN) in terms of water use, energy consumption, water loss minimization, and water quality guarantees. In particular, the paper addresses the first results of the European project EFFINET (FP7-ICT2011-8-318556) devoted to the monitoring and control of the DWN in Barcelona (Spain). Results are split in two levels according to different management objectives: (i) the monitoring level is concerned with all the aspects involved in the observation of the current state of a system and the detection/diagnosis of abnormal situations. It is achieved through sensors and communications technology, together with mathematical models; (ii) the control level is concerned with computing the best suitable and admissible control strategies for network actuators as to optimize a given set of operational goals related to the performance of the overall system. This level covers the network control (optimal management of water and energy) and the demand management (smart metering, efficient supply). The consideration of the Barcelona DWN as the case study will allow to prove the general applicability of the proposed integrated ICT solutions and their effectiveness in the management of DWN, with considerable savings of electricity costs and reduced water loss while ensuring the high European standards of water quality to citizens.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Use of a semantically grained database system for distribution and control within design environments

This paper presents a technique to share the data stored in an object-oriented database aimed at designing environments. This technique shares data between two related databases, called the Original and Product databases, and is composed of three processes: data separation, evolution and integration. Whenever a block of data needs to be shared, it is spread into both databases, resulting in a block on the original database, and another into the Product database, with special links between them controlled by the Object Manager. These blocks do not need to be maintained identical during the evolution phase of the sharing process. Six types of links were defined, and by choosing one, the designer control the evolution and reintegration of the block in both databases. This process uses the composite object concept as the unit of control. The presented concepts can be applied to any data model with support to composite objects.

On Nonlinear Dynamics and Control of A Particular Portal Frame Foundation Model, Excited by a Non-Ideal Motor

The nonlinear dynamic response and a nonlinear control method of a particular portal frame foundation for an unbalanced rotating machine with limited power (non-ideal motor) are examined. Numerical simulations are performed for a set of control parameters (depending on the voltage of the motor) related to the static and dynamic characteristics of the motor. The interaction of the structure with the excitation source may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. A mathematical model having two degrees of freedom simplifies the non-ideal system. The study of controlling steady-state vibrations of the non-ideal system is based on the saturation phenomenon due to internal resonance.

A multiagent architecture for supervisory and control system

Supervising and controlling the many processes involved in petroleum production is both dangerous and complex. Herein, we propose a multiagent supervisory and control system for handle continuous processes like those in chemical and petroleum industries In its architeture, there are agents responsible for managing data production and analysis, and also the production equipments. Fuzzy controllers were used as control agents. The application of a fuzzy control system to managing an off-shore installation for petroleum production onto a submarine separation process is described. © 2008 IEEE.

Theory of constraints contributions to outbound logistics

Purpose: The purpose of this paper is to systematically describe the key practical contributions of the theory of constraints (TOC) to outbound (distribution) logistics. Design/methodology/approach: Based on theoretical research, this paper presents the main practical aspects of the approach suggested by TOC to outbound logistics and discusses the assumptions upon which it is based. Findings: This paper corroborates the thesis defended by TOC, according to which the current ways of managing outbound logistics, based mainly on sales forecasts lead to difficulties in handling trade-offs between logistics (stock and transportation) costs and stock-out levels. Research limitations/implications: The reported research is of a theoretical nature. Practical implications: TOC offers a proposal that is complementary in many aspects and very distinguishable in others about the way some key processes and elements of supply chain management (SCM) are managed, especially outbound logistics. Originality/value: Considering the dearth of papers dealing with the conceptual articulation and organization of this subject, the paper contributes to systematize the knowledge currently available about the contributions of the TOC to outbound logistics, highlighting the practical implications of applying TOC to outbound logistics. © Emerald Group Publishing Limited.

Use of myoelectric signals to command mobile entertainment robot by disabled children: Design and control architecture

Severely disabled children have little chance of environmental and social exploration and discovery. This lack of interaction and independency may lead to an idea that they are unable to do anything by themselves. In an attempt to help children in this situation, educational robotics can offer and aid, once it can provide them a certain degree of independency in the exploration of environment. The system developed in this work allows the child to transmit the commands to a robot through myoelectric and movement sensors. The sensors are placed on the child's body so they can obtain information from the body inclination and muscle contraction, thus allowing commanding, through a wireless communication, the mobile entertainment robot to carry out tasks such as play with objects and draw. In this paper, the details of the robot design and control architecture are presented and discussed. With this system, disabled children get a better cognitive development and social interaction, balancing in a certain way, the negative effects of their disabilities. © 2012 IEEE.

Latin American structuralism and economic theory

Includes bibliography