scholarly journals Automatic Synthesis of Piecewise Linear Quadratic Invariants for Programs

2015 ◽  
pp. 99-116 ◽  
Author(s):  
Assalé Adjé ◽  
Pierre-Loïc Garoche
Keyword(s):  
Piecewise Linear ◽  
Linear Quadratic ◽  
Automatic Synthesis ◽  
Quadratic Invariants

scholarly journals Seasonal sea ice prediction based on regional indices

2018 ◽  
Author(s):  
John E. Walsh ◽  
J. Scott Stewart ◽  
Florence Fetterer
Keyword(s):  
Sea Ice ◽  
Chukchi Sea ◽  
Numerical Models ◽  
Linear Trend ◽  
Piecewise Linear ◽  
Severity Index ◽  
The Arctic ◽  
Linear Quadratic ◽  
Predictive Skill ◽  
Arctic Ice

Abstract. Basic statistical metrics such as autocorrelations and across-region lag correlations of sea ice variations provide benchmarks for the assessments of forecast skill achieved by other methods such as more sophisticated statistical formulations, numerical models, and heuristic approaches. However, the strong negative trend of sea ice coverage in recent decades complicates the evaluation of statistical skill by inflating the correlation of interannual variations of pan-Arctic and regional ice extent. In this study we provide a quantitative evaluation of the contribution of the trend to the predictive skill of monthly and seasonal ice extent on the pan-Arctic and regional scales. We focus on the Beaufort Sea where the Barnett Severity Index provides a metric of historical variations in ice conditions over the summer shipping season. The variance about the trend line differs little among various methods of detrending (piecewise linear, quadratic, cubic, exponential). Application of the piecewise linear trend calculation indicates an acceleration of the trend during the 1990s in most of the Arctic subregions. The Barnett Severity Index as well as September pan-Arctic ice extent show significant statistical predictability out to several seasons when the data include the trend. However, this apparent skill largely vanishes when the data are detrended. No region shows significant correlation with the detrended September pan-Arctic ice extent at lead times greater than a month or two; the concurrent correlations are strongest with the East Siberian Sea. The Beaufort Sea’s ice extent as far back as July explains about 20 % of the variance of the Barnett Severity Index, which is primarily a September metric. The Chukchi Sea is the only other region showing a significant association with the Barnett Severity Index, although only at a lead time of a month or two.

scholarly journals Control Design and Validation for Floating Piston Electro-Pneumatic Gearbox Actuator

2020 ◽  
Vol 10 (10) ◽  
pp. 3514 ◽  
Author(s):  
Adam Szabo ◽  
Tamas Becsi ◽  
Peter Gaspar
Keyword(s):  
Piecewise Linear ◽  
Control Design ◽  
Continuous Control ◽  
Control Methods ◽  
Linear Quadratic ◽  
Modeling And Control ◽  
Control Frequency ◽  
Heavy Duty Vehicle ◽  
High Control ◽  
And Control

The paper presents the modeling and control design of a floating piston electro-pneumatic gearbox actuator and, moreover, the industrial validation of the controller system. As part of a heavy-duty vehicle, it needs to meet strict and contradictory requirements and units applying the system with different supply pressures in order to operate under various environmental conditions. Because of the high control frequency domain of the real system, post-modern control methods with high computational demands could not be used as they do not meet real-time requirements on automotive level. During the modeling phase, the essential simplifications are shown with the awareness of the trade-off between calculation speed and numerical accuracy to generate a multi-state piecewise-linear system. Two LTI control methods are introduced, i.e., a PD and an Linear-Quadratic Regulators (LQR) solution, in which the continuous control signals are transformed into discrete voltage solenoid commands for the valves. The validation of both the model and the control system are performed on a real physical implementation. The results show that both modeling and control design are suitable for the control tasks using floating piston cylinders and, moreover, these methods can be extended to electro-pneumatic cylinders with different layouts.

Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions

2013 ◽  
Vol 58 (1) ◽  
pp. 249-272 ◽  
Author(s):  
Bryan Gardiner ◽  
Khan Jakee ◽  
Yves Lucet
Keyword(s):  
Piecewise Linear ◽  
Linear Quadratic ◽  
Bivariate Functions

Fitting Functions to Data in High Dimensional Design Space

1999 ◽  
Author(s):  
Xiaoou Wang ◽  
Yingying Liu ◽  
Erik K. Antonsson
Keyword(s):  
Piecewise Linear ◽  
Region Of Interest ◽  
Multivariate Adaptive Regression Splines ◽  
High Dimensional ◽  
Linear Quadratic ◽  
Data Set ◽  
Data Points ◽  
Adaptive Regression ◽  
Representative Points ◽  
Adaptive Regression Splines

Abstract One approach to rapidly exploring large design spaces is to evaluate the performance of a small number of representative points in the space, then based on those points, construct an approximation to the response over a region of interest. Linear, piecewise linear, quadratic and multivariate adaptive regression splines (MARS) models are fit to an example 5-dimensional data set representative of information available in preliminary engineering design. When the number of data points representing a high-dimensional response is small, all of the approximation models appear to perform nearly equally.

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