Root locus of fractional linear systems

In this paper an algorithm for the calculation of the root locus of fractional linear systems is presented. The proposed algorithm takes advantage of present day computational resources and processes directly the characteristic equation, avoiding the limitations revealed by standard methods. The results demonstrate the good performance for different types of expressions.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

Efficient schedulability tests for real-time embedded systems with urgent routines

Task scheduling is one of the key mechanisms to ensure timeliness in embedded real-time systems. Such systems have often the need to execute not only application tasks but also some urgent routines (e.g. error-detection actions, consistency checkers, interrupt handlers) with minimum latency. Although fixed-priority schedulers such as Rate-Monotonic (RM) are in line with this need, they usually make a low processor utilization available to the system. Moreover, this availability usually decreases with the number of considered tasks. If dynamic-priority schedulers such as Earliest Deadline First (EDF) are applied instead, high system utilization can be guaranteed but the minimum latency for executing urgent routines may not be ensured. In this paper we describe a scheduling model according to which urgent routines are executed at the highest priority level and all other system tasks are scheduled by EDF. We show that the guaranteed processor utilization for the assumed scheduling model is at least as high as the one provided by RM for two tasks, namely 2(2√−1). Seven polynomial time tests for checking the system timeliness are derived and proved correct. The proposed tests are compared against each other and to an exact but exponential running time test.

Intra-Task Device Scheduling for Real-Time Embedded Systems

An ever increasing need for extra functionality in a single embedded system demands for extra Input/Output (I/O) devices, which are usually connected externally and are expensive in terms of energy consumption. To reduce their energy consumption, these devices are equipped with power saving mechanisms. While I/O device scheduling for real-time (RT) systems with such power saving features has been studied in the past, the use of energy resources by these scheduling algorithms may be improved. Technology enhancements in the semiconductor industry have allowed the hardware vendors to reduce the device transition and energy overheads. The decrease in overhead of sleep transitions has opened new opportunities to further reduce the device energy consumption. In this research effort, we propose an intra-task device scheduling algorithm for real-time systems that wakes up a device on demand and reduces its active time while ensuring system schedulability. This intra-task device scheduling algorithm is extended for devices with multiple sleep states to further minimise the overall device energy consumption of the system. The proposed algorithms have less complexity when compared to the conservative inter-task device scheduling algorithms. The system model used relaxes some of the assumptions commonly made in the state-of-the-art that restrict their practical relevance. Apart from the aforementioned advantages, the proposed algorithms are shown to demonstrate the substantial energy savings.

Logic-based schedulability analysis for compositional hard real-time embedded systems

Over the past decades several approaches for schedulability analysis have been proposed for both uni-processor and multi-processor real-time systems. Although different techniques are employed, very little has been put forward in using formal specifications, with the consequent possibility for mis-interpretations or ambiguities in the problem statement. Using a logic based approach to schedulability analysis in the design of hard real-time systems eases the synthesis of correct-by-construction procedures for both static and dynamic verification processes. In this paper we propose a novel approach to schedulability analysis based on a timed temporal logic with time durations. Our approach subsumes classical methods for uni-processor scheduling analysis over compositional resource models by providing the developer with counter-examples, and by ruling out schedules that cause unsafe violations on the system. We also provide an example showing the effectiveness of our proposal.

Measuring end-to-end delay in real-time auralisation systems

One of the major challenges in the development of an immersive system is handling the delay between the tracking of the user’s head position and the updated projection of a 3D image or auralised sound, also called end-to-end delay. Excessive end-to-end delay can result in the general decrement of the “feeling of presence”, the occurrence of motion sickness and poor performance in perception-action tasks. These latencies must be known in order to provide insights on the technological (hardware/software optimization) or psychophysical (recalibration sessions) strategies to deal with them. Our goal was to develop a new measurement method of end-to-end delay that is both precise and easily replicated. We used a Head and Torso simulator (HATS) as an auditory signal sensor, a fast response photo-sensor to detect a visual stimulus response from a Motion Capture System, and a voltage input trigger as real-time event. The HATS was mounted in a turntable which allowed us to precisely change the 3D sound relative to the head position. When the virtual sound source was at 90º azimuth, the correspondent HRTF would set all the intensity values to zero, at the same time a trigger would register the real-time event of turning the HATS 90º azimuth. Furthermore, with the HATS turned 90º to the left, the motion capture marker visualization would fell exactly in the photo-sensor receptor. This method allowed us to precisely measure the delay from tracking to displaying. Moreover, our results show that the method of tracking, its tracking frequency, and the rendering of the sound reflections are the main predictors of end-to-end delay.

Evaluation of the determinism of the actuator sensor interface (ASI) on programmable logic controllers (PLC), personal computers (PC) and real-time operating systems (RTOS)

The purpose of this study was to evaluate the determinism of the AS-lnterface network and the 3 main families of control systems, which may use it, namely PLC, PC and RTOS. During the course of this study the PROFIBUS and Ethernet field level networks were also considered in order to ensure that they would not introduce unacceptable latencies into the overall control system. This research demonstrated that an incorrectly configured Ethernet network introduces unacceptable variable duration latencies into the control system, thus care must be exercised if the determinism of a control system is not to be compromised. This study introduces a new concept of using statistics and process capability metrics in the form of CPk values, to specify how suitable a control system is for a given control task. The PLC systems, which were tested, demonstrated extremely deterministic responses, but when a large number of iterations were introduced in the user program, the mean control system latency was much too great for an AS-I network. Thus the PLC was found to be unsuitable for an AS-I network if a large, complex user program Is required. The PC systems, which were tested were non-deterministic and had latencies of variable duration. These latencies became extremely exaggerated when a graphing ActiveX was included in the control application. These PC systems also exhibited a non-normal frequency distribution of control system latencies, and as such are unsuitable for implementation with an AS-I network. The RTOS system, which was tested, overcame the problems identified with the PLC systems and produced an extremely deterministic response, even when a large number of iterations were introduced in the user program. The RTOS system, which was tested, is capable of providing a suitable deterministic control system response, even when an extremely large, complex user program is required.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

The Limits of Discrete Time Repeated Games:Some Notes and Comments

This paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes.

Impulse response recovery of linear systems through weighted cumulant slice

Identifiability of the so-called ω-slice algorithm is proven for ARMA linear systems. Although proofs were developed in the past for the simpler cases of MA and AR models, they were not extendible to general exponential linear systems. The results presented in this paper demonstrate a unique feature of the ω-slice method, which is unbiasedness and consistency when order is overdetermined, regardless of the IIR or FIR nature of the underlying system, and numerical robustness.

Solving large sparse linear systems over the field GF(2)

Nowadays problem of solving sparse linear systems over the field GF(2) remain as a challenge. The popular approach is to improve existing methods such as the block Lanczos method (the Montgomery method) and the Wiedemann-Coppersmith method. Both these methods are considered in the thesis in details: there are their modifications and computational estimation for each process. It demonstrates the most complicated parts of these methods and gives the idea how to improve computations in software point of view. The research provides the implementation of accelerated binary matrix operations computer library which helps to make the progress steps in the Montgomery and in the Wiedemann-Coppersmith methods faster.

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.