Mathematics Works Inc.

Orchard Lake, MI, United States

Mathematics Works Inc.

Orchard Lake, MI, United States
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Rahnama A.,University of Notre Dame | Xia M.,Mathematics Works Inc. | Antsaklis P.J.,University of Notre Dame
2016 IEEE 55th Conference on Decision and Control, CDC 2016 | Year: 2016

In this paper, we show that dissipativity and passivity based control combined with event-triggered networked control systems (NCS) provide a powerful platform for designing cyber-physical systems (CPS). We propose QSR-dissipativity, passivity and finite-gain L2-stability conditions for an event-triggered NCS in cases where an input-output event-triggering sampler condition is located on the plant's output side, controller's output side, or both sides leading to a considerable decrease in communication load amongst sub-units in NCS. We show that the passivity and stability conditions depend on passivity levels for the plant and controller. Our results also illustrate the trade-off among passivity levels, stable performance, and system's dependence on the rate of communication between the plant and controller. © 2016 IEEE.


Zhang W.,Colorado State University | Yang L.,Colorado State University | Yang L.,CAS Institute of Automation | Cheng X.,CAS Institute of Automation | And 2 more authors.
IEEE Transactions on Vehicular Technology | Year: 2014

Rapid and accurate timing synchronization is a critical task in ultrawideband (UWB) systems. Yang and Giannakis introduced a promising algorithm, i.e., data-aided timing with dirty templates (TDT), which is known for low complexity and relaxed operation conditions in the presence of unknown time hopping and multipath channels. In this paper, we will explore the optimality of TDT. We develop a maximum-likelihood (ML) timing algorithm and obtain its optimum training sequence. It is shown that the optimum training sequence of the ML timing estimator coincides with that of the TDT algorithm. In addition, we prove that the ML algorithm can be simplified using this training sequence and that the simplified ML (SML) is equivalent to TDT. © 2013 IEEE.


Belludi N.,Cummins Inc. | Raymond J.,Cummins Inc. | Receveur J.,Cummins Inc. | Hosagrahara A.,Mathematics Works Inc.
SAE Technical Papers | Year: 2010

This paper presents the business purpose, software architecture, technology integration, and applications of the Cummins Vehicle Mission Simulation (VMS) software. VMS is the value-based analysis tool used by the marketing, sales, and product engineering functions to simulate vehicle missions quickly and to gauge, communicate, and improve the value proposition of Cummins engines to customers. VMS leverages the best of software architecture practices and proven technologies available today. It consists of a close integration of MATLAB and Simulink with Java, XML, and JDBC technologies. This Windows compatible application software uses stand-alone mathematical models compiled using Real Time Workshop. A built-in MySQL database contains product data for engines, driveline components, vehicles, and topographic routes. This paper outlines the database governance model that facilitates effective management, control, and distribution of engine and vehicle data across the enterprise. This paper also presents four case studies on the applications of VMS to augment Cummins engineering and sales competencies by helping customers understand vehicle performance, optimize vehicle configurations, improve fuel economy, and reduce greenhouse gas emissions. Copyright © 2010 SAE International.


Iruthayanathan N.,SSN College of Engineering | Srinivasan V.K.,SSN College of Engineering | Rajendran V.,Vels University | Palanimurugan R.,Mathematics Works Inc.
Computers and Electrical Engineering | Year: 2016

We consider turbo coded multi-carrier double space–time transmit diversity (DSTTD) system that employs orthogonal frequency division multiplexing (OFDM) for the transmission of acoustic signals in underwater communication, where acoustic interference and ambient noise are the major channel deficiencies. DSTTD employs two space–time block codes at the transmitter. At each receiver, we implement space–time Block-Nulling detection technique to increase throughput. We consider the iterative decoding algorithm at the receiver to alleviate the effects of ambient noise and acoustic interference. Further, we implement multi-carrier modulation technique to mitigate the effects of multipath propagation. We investigate the effects of eleven tap delay pertaining to shallow water channel model for the DSTTD-OFDM system. Our simulation results reveal that our considered system with Block-Nulling technique provides better bit error rates for lower signal-to-noise ratio when compared to a minimum mean square error detector-based system. Further, it achieves higher throughput with fewer computations at the receivers. © 2015 Elsevier Ltd


Shaar N.S.,Massachusetts Institute of Technology | Shaar N.S.,Mathematics Works Inc. | Barbastathis G.,Singapore Alliance for Research and Technology Center | Livermore C.,Northeastern University
Journal of Microelectromechanical Systems | Year: 2015

The design, implementation, and characterization of passively aligned reconfigurable three-dimensional (3-D) microelectromechanical systems via origami folding is presented. The process integrates into a two-mask pattern all of the features necessary for actuation, aligning, and latching segments into their correct positions under the influence of a single driving force with high tolerance to magnitude inaccuracy. Lorentz force folds the two-dimensional (2-D) elements out-of-plane. Their alignment is controlled by cascaded alignment features that create an initial interaction at coarse levels of alignment and deterministically drive the system to its as-designed final position. Reversible mechanical latches engage passively, preventing unfolding when the actuation force is released. The latches are designed to be able to be unlatched for future reconfiguration, either by returning to the unlatched state or by relatching into a second state. The proposed approach was demonstrated in an SU-8 corner cube connected by thin-film gold flexural hinges. The alignment mechanism is shown to correct for up to 11° of misalignment. The latches fasten and unfasten under forces of 13.1 and 12.5~\mu N, respectively. The average angle between folded segments of the final system is measured at 90.4° as compared with the design value of 90°, with a standard deviation of 0.6°. © 1992-2012 IEEE.


Jin C.T.,California Institute of Technology | Jin C.T.,University of Sydney | Jin C.T.,Computing and Audio Research Laboratory | Epain N.,Aix - Marseille University | And 4 more authors.
IEEE Transactions on Audio, Speech and Language Processing | Year: 2014

Spherical Microphone Arrays (SMAs) constitute a powerful tool for analyzing the spatial properties of sound fields. However, the performance of SMA-based signal processing algorithms ultimately depends on the physical characteristics of the array. In particular, the range of frequencies over which an SMA provide rich spatial information is conditioned by the size of the array, the angular position of the sensors and other factors. In this work, we investigate the design of SMAs offering a wider frequency range of operation than that offered by conventional designs. To achieve this goal, microphones are distributed both on and at a distance from the surface of a rigid spherical baffle. The contributions of the paper are as follows. First, we present a general framework for modeling SMAs whose sensors are located at different distances from the array center and calculating optimal filters for the decomposition of the sound field into spherical harmonic modes. Second, we present an optimization method to design multi-radius SMAs with an optimally wide frequency range of operation given the total number of sensors available and target spatial resolution. Lastly, based on the optimization results, we built a prototype dual-radius SMA with 64 microphones. We present measurement results for the prototype microphone array and compare these results with theory. © 2013 IEEE.


Mobasseri B.G.,Villanova University | Chakilam N.,Mathematics Works Inc. | Lynch R.S.,Naval Undersea Warfare Center
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2012

This paper reports on performance of a previously reported sonar watermarking algorithm in actual sea trials. Tests were conducted at the South Florida Ocean Measurement Facility in shallow water depths of 200m and a range of 7km subject to a 80dB propagation loss. The watermark was designed to match the acoustic channel simulated in the Sonar Simulation Toolset (SST), but no access to the actual acoustic channel was available prior to the test. Watermark detection was carried out over multiple ping cycles. For a 10-ping cycle, it was possible to achieve zero false alarm and a single miss at SWR=27dB. At SWR=30dB, zero false alarm was maintained but the miss rate increased to three. This experiment has reaffirmed the detectability of the watermark in actual sea deployment. © 2012 SPIE.


Ouedraogo L.,Iowa State University | Kumar R.,Mathematics Works Inc.
IEEE Transactions on Automation Science and Engineering | Year: 2014

FlexRay is a communication bus (and associated protocol) that supports transmission of time-triggered and event-triggered frames. A method for determining the worst-case response-time of FlexRay frames is proposed by Pop in 2008, and is formulated as iterative sequence of Integer Linear Programming (ILP) problems. As we show, the method of Pop is conservative (overestimates the response time). We propose a new ILP formulation that computes a precise value of the worst-case response time of FlexRay frames transmitted in the dynamic segment. Furthermore, our approach is non-iterative as it requires the solving of a single ILP for computing, respectively, the delay of full bus cycles and the delay of a partial (last) bus cycle. The proposed solution is also validated by applying it to a SAE benchmark and can be used for formally guaranteeing that no message will miss its deadline during system operation. © 2013 IEEE.


Jiang Yu.,Mathematics Works Inc. | Jiang Z.-P.,New York University
IEEE Transactions on Automatic Control | Year: 2015

This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB) equation to an optimization problem, which is solved via a new policy iteration method. The proposed method distinguishes from previously known nonlinear ADP methods in that the neural network approximation is avoided, giving rise to significant computational improvement. Instead of semiglobally or locally stabilizing, the resultant control policy is globally stabilizing for a general class of nonlinear polynomial systems. Furthermore, in the absence of the a priori knowledge of the system dynamics, an online learning method is devised to implement the proposed policy iteration technique by generalizing the current ADP theory. Finally, three numerical examples are provided to validate the effectiveness of the proposed method. © 1963-2012 IEEE.


Mckay B.,Mathematics Works Inc.
Electronic Products (Garden City, New York) | Year: 2011

Early verification with model-based design is necessary so that design problems are minimized and time-consuming hardware fixes are avoided. Early verification allows designers to quickly evaluate a variety of control strategies and optimize system behavior, identify errors early, before robot hardware is available, use simulation to test the full operating envelope, and reuse models for real-time testing. Model-based design allows designers to build a mathematical model of the control software and the physical robot, including mechanical, electrical, hydraulic, and other physical domains. These designs allow engineers to generate embedded code directly from the model to enable rapid prototyping and hardware-in-the-loop testing. In hardware-in-the-loop testing, the production controller hardware is tested against a real-time simulation of the physical robot.

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