Pontryagin's condition and its time stretching modification

2018 ◽  
Author(s):  
Greta Tsolakovna Chikrii
Keyword(s):  
Pontryagin’S Condition ◽  
Time Stretching

scholarly journals One Game Problem for Oscillatory Systems

2021 ◽  
pp. 5-15
Author(s):  
Greta Chikrii
Keyword(s):  
Differential Game ◽  
Direct Method ◽  
Game Problem ◽  
Oscillatory Systems ◽  
Terminal Set ◽  
Damped Oscillations ◽  
Pontryagin’S Condition ◽  
Linear Differential ◽  
Second Order Systems ◽  
Time Stretching

The paper concerns the linear differential game of approaching a cylindrical terminal set. We study the case when classic Pontryagin’s condition does not hold. Instead, the modified considerably weaker condition, dealing with the function of time stretching, is used. The latter allows expanding the range of problems susceptible to analytical solution by the way of passing to the game with delayed information. Investigation is carried out in the frames of Pontryagin’s First Direct method that provides hitting the terminal set by a trajectory of the conflict-controlled process at finite instant of time. In so doing, the pursuer’s control, realizing the game goal, is constructed on the basis of the Filippov-Castaing theorem on measurable choice. The outlined scheme is applied to solving the problem of pursuit for two different second-order systems, describing damped oscillations. For this game, we constructed the function of time stretching and deduced conditions on the game parameters, ensuring termination of the game at a finite instant of time, starting from arbitrary initial states and under all admissible controls of the evader. Keywords: differential game, time-variable information delay, Pontryagin’s condition, Aumann’s integral, principle of time stretching, Minkowski’ difference, damped oscillations.

Improved sigma-delta analog-to-digital converter using time-stretching technique

1999 ◽  
Author(s):  
Frederic Coppinger ◽  
V. Magoon ◽  
A. S. Bhushan ◽  
Bahram Jalali
Keyword(s):  
Analog To Digital Converter ◽  
Digital Converter ◽  
Sigma Delta ◽  
Analog To Digital ◽  
Time Stretching

Performance evaluation of measured time stretching approach for event timer

2021 ◽  
Author(s):  
Imants Pulkstenis ◽  
Anna Litvinenko ◽  
Viktors Kurtenoks ◽  
Vjaceslavs Lapkovskis
Keyword(s):  
Performance Evaluation ◽  
Measured Time ◽  
Event Timer ◽  
Time Stretching

Studies of the time-stretching of GRBs using the average curves of emissivity

1998 ◽  
Author(s):  
Maxim L. Litvak ◽  
Igor G. Mitrofanov ◽  
Michael S. Briggs ◽  
William S. Paciesas ◽  
Robert D. Preece ◽  
...  
Keyword(s):  
Time Stretching

Interactive Speech Skimming via Time-Stretched Audio Replay

2006 ◽  
pp. 355-361
Author(s):  
Wolfgang Hürst ◽  
Tbias Lauer
Keyword(s):  
Speech Signals ◽  
Specific Information ◽  
Limited Time ◽  
Time Compression ◽  
Network Bandwidth ◽  
Multimedia Contents ◽  
Time Scaling ◽  
Cartoon Character ◽  
Normal Speed ◽  
Time Stretching

Time stretching, sometimes also referred to as time scaling, is a term describing techniques for replaying speech signals faster (i.e., time compressed) or slower (i.e., time expanded) while preserving their characteristics, such as pitch and timbre. One example for such an approach is the SOLA (synchronous overlap and add) algorithm (Roucus & Wilgus, 1985), which is often used to avoid cartoon-character-like voices during faster replay. Many studies have been carried out in the past in order to evaluate the applicability and the usefulness of time stretching for different tasks in which users are dealing with recorded speech signals. One of the most obvious applications of time compression is speech skimming, which describes the actions involved in quickly going through a speech document in order to identify the overall topic or to locate some specific information. Since people can listen faster than they talk, time-compressed audio, within reasonable limits, can also make sense for normal listening, especially in view of He and Gupta (2001), who suggest that the future bottleneck for consuming multimedia contents will not be network bandwidth but people’s limited time. In their study, they found that an upper bound for sustainable speedup during continuous listening is at about 1.6 to 1.7 times the normal speed. This is consistent with other studies such as Galbraith, Ausman, Liu, and Kirby (2003) or Harrigan (2000), indicating preferred speedup ratios between 1.3 and 1.8. Amir, Ponceleon, Blanchard, Petkovic, Srinivasan, and Cohen (2000) found that, depending on the text and speaker, the best speed for comprehension can also be slower than normal, especially for unknown or difficult contents.

The time stretching of the average rise fronts and back slopes of different intensity groups of BATSE GRBs

1998 ◽  
Author(s):  
Maxim L. Litvak ◽  
Igor G. Mitrofanov ◽  
Michael S. Briggs ◽  
William S. Paciesas ◽  
Robert D. Preece ◽  
...  
Keyword(s):  
Average Rise ◽  
Time Stretching

Photonic time stretching of 102-GHz millimeter waves using 1.55-μm polymer electro-optic modulator

2000 ◽  
Author(s):  
Harold R. Fetterman ◽  
Daniel H. Chang ◽  
Hernan Erlig ◽  
Min-Cheol Oh ◽  
Cheng H. Zhang ◽  
...  
Keyword(s):  
Millimeter Waves ◽  
Electro Optic ◽  
Electro Optic Modulator ◽  
Time Stretching
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