Discrete time optimal control with frequency constraints for non-smooth systems

We present a Pontryagin maximum principle for discrete time optimal control problems with (a) pointwise constraints on the control actions and the states, (b) frequency constraints on the control and the state trajectories, and (c) nonsmooth dynamical systems. Pointwise constraints on the states and the control actions represent desired and/or physical limitations on the states and the control values; such constraints are important and are widely present in the optimal control literature. Constraints of the type (b), while less standard in the literature, effectively serve the purpose of describing important spectral properties of inertial actuators and systems. The conjunction of constraints of the type (a) and (b) is a relatively new phenomenon in optimal control but are important for the synthesis control trajectories with a high degree of fidelity. The maximum principle established here provides first order necessary conditions for optimality that serve as a starting point for the synthesis of control trajectories corresponding to a large class of constrained motion planning problems that have high accuracy in a computationally tractable fashion. Moreover, the ability to handle a reasonably large class of nonsmooth dynamical systems that arise in practice ensures broad applicability our theory, and we include several illustrations of our results on standard problems

Speedes: A Case Study Of Space Operations

This thesis describes the application of parallel simulation techniques to represent the structured functional parallelism present within the Space Shuttle Operations Flow using the Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES), an object-oriented multi-computing architecture. SPEEDES is a unified parallel simulation environment, which allocates events over multiple processors to get simulation speed up. Its optimistic processing capability minimizes simulation lag time behind wall clock time, or multiples of real-time. SPEEDES accommodates an increase in process complexity with additional parallel computing nodes to allow sharing of processing loads. This thesis focuses on the process of translating a model of Space Shuttle Operations from a procedural oriented and single processor approach to one represented in a process-driven, object-oriented, and distributed processor approach. The processes are depicted by several classes created to represent the operations at the space center. The reference model used is the existing Space Shuttle Model created in ARENA by NASA and UCF in the year 2001. A systematic approach was used for this translation. A reduced version of the ARENA model was created, and then used as the SPEEDES prototype using C++. The prototype was systematically augmented to reflect the entire Space Shuttle Operations Flow. It was then verified, validated, and implemented

Efficient convolvers using the Polynomial Residue Number System technique

The problem of computing linear convolution is a very important one because with linear convolution we can mechanize digital filtering. The linear convolution of two N-point sequences can be computed by the cyclic convolution of the following 2N-point sequences. The original sequence padded with N zero’s each. The cyclic convolution of two N-point sequences requires multiplications and additions for its computation. A very efficient way of computing cyclic convolution of two sequences is by using the Polynomial Residue Number System (PRNS) technique. Using this technique the cyclic convolution of two N-point sequences can be computed using only N multiplications instead of N2 multiplications. This can be achieved based on some forward and inverse PRNS transformation mappings. These mappings rely on additions, subtractions and many scaling operations (multiplications by constants). The PRNS technique would lose a lot in value if these many scaling operations were difficultly implemented. In this thesis we will show how to calculate cyclic convolution of two sequences using the PRNS technique based on forward and inverse transformation mapping which rely on complement operations (negations), additions and rotation operations. These rotation operations do not require any computational hardware. Therefore the complicated hardware required for the scaling operations has now been substituted by rotators, which do not require any computational hardware

Conceptualization of Machine Learning in Economic Forecasting

Economic forecasting is a very important aspect that policymakers in the financial and corporate organization rely on because helps them to determine future events that might infringe some hardship on the economy and the citizens at large. However, the principal statistical pointers that are available to the public domain provide numerous reservations and doubts for their economics estimates as it is later released with frequent issues to major revisions and also it shows a great lag in decision making for an incoming event. To this effect, the expansion of the latest forecasting patterns was important to address the gaps. Hence, this paper examines the conceptualization of Machine learning in economic forecasting. To achieve this, the Italian economy was used as the dataset, and machine learning controlled tools were used as the method of analysis. The result obtained from this study shows that machine learning is a better model to use in economic forecasting for quick and reliable data to avert future events

Think aloud: Can eye tracking add value in detecting usability problems?

The protocols of Think Aloud and Eye Tracking, in their own unique way have proven to be great methods to understand users\u27 thought processes, and their mental models when interacting with interfaces. However the effectiveness of the combination of the two protocols in discovering usability problems has not been explored. This study aimed to discover if the addition of Eye Tracking data (fixations and scan movements) to the traditional protocol of Think Aloud can uncover more usability problems. Web users were split into three groups: Eye Tracking Only (ET), Think Aloud Only (TA), and Eye Tracking and Think Aloud Only (ET+TA). Participants in all conditions were asked to complete two tasks on two websites each. Along with questionnaires, eye movement data was collected for conditions with the Eye Tracking aspect and verbalizations were collected for conditions with the Think Aloud aspect. The analysis of the data showed that the total number of usability problems (not unique) identified by the participants in the `Eye Tracking and Think Aloud\u27 (ET + TA) condition was higher than the other two conditions. However, a Tukey HSD post-hoc test revealed that the differences between `ET + TA\u27 and the `Eye Tracking Only\u27 (ET) conditions was non-significant. The analysis also which resulted in non-significant differences between the conditions `Eye Tracking\u27 (ET) and `Eye Tracking and Think Aloud\u27 (ET + TA) led to inconclusive results on whether the Think Aloud method is disruptive or not. This may lead future researchers to develop robust practice sessions to help participants verbalize and create evaluation rules for eye movement data

Analytic solutions for reduced leading-edge noise aerofoils

This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a piecewise linear periodic leading edge. The Wiener-Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to allow analytical progress. A fully analytic solution is obtained in terms of a modal expansion for the far-field noise which is obtained by summing only a finite number of cuton modes, allowing very quick evaluation. The analytic solution is compared to experimental results for five test case leading-edge geometries. Good agreement is seen indicating the analytic model is capturing the key features of the interaction such as the destructive interference from the tip and root. In four of the five test cases the serrated edges show large reductions of noise compared to the straight edge at mid and high frequencies, however the square wave geometry is seen to be ineffective at noise reduction for high frequencies