Numerical Dynamic Programming on Parallel Computing Clusters: A 'MacGyver' Approach

2008 ◽  
Author(s):  
Florian Zainhofer
Keyword(s):  
Dynamic Programming ◽  
Parallel Computing ◽  
Numerical Dynamic Programming

scholarly journals A polyhedral approximation approach to concave numerical dynamic programming

2013 ◽  
Vol 37 (11) ◽  
pp. 2322-2335 ◽  
Author(s):  
Kenichi Fukushima ◽  
Yuichiro Waki
Keyword(s):  
Dynamic Programming ◽  
Polyhedral Approximation ◽  
Approximation Approach ◽  
Numerical Dynamic Programming

Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models

Econometrica ◽  
1998 ◽  
Vol 66 (2) ◽  
pp. 409 ◽  
Author(s):  
Manuel S. Santos ◽  
Jesus Vigo-Aguiar
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Economic Models ◽  
Programming Algorithm ◽  
Numerical Dynamic Programming

Automotive Transmission Clutch Fill Control Using a Customized Dynamic Programming Method

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Xingyong Song ◽  
Mohd Azrin Mohd Zulkefli ◽  
Zongxuan Sun ◽  
Hsu-Chiang Miao
Keyword(s):  
Dynamic Programming ◽  
Control Problem ◽  
Dynamic Model ◽  
Low Cost ◽  
Pressure Profile ◽  
Open Loop ◽  
Dynamic Programming Method ◽  
Flow Demand ◽  
Compact Design ◽  
Numerical Dynamic Programming

Clutch to clutch shift control technology, which is the key enabler for a compact and low cost transmission design, is important for both automatic and hybrid transmissions. To ensure a smooth clutch to clutch shift, precise synchronization between the on-coming and off-going clutches is critical. This further requires the on-coming clutch to be filled and ready for engagement at the predetermined time. Due to the compact design, currently there is no pressure sensor inside the clutch chamber, and therefore the clutch fill can only be controlled in an open loop fashion. The traditional clutch fill approach, by which the clutch fill input pressure command is manually calibrated, has a couple of limitations. First, the pressure profile is not optimized to reduce the peak flow demand during clutch fill. Moreover, it is not systematically designed to account for uncertainties in the system, such as variations of solenoid valve delay and parameters of the clutch assembly. In this paper, we present a systematic approach to evaluate the clutch fill dynamics and synthesize the optimal pressure profile. First, a clutch fill dynamic model, which captures the key dynamics in the clutch fill process, is constructed and analyzed. Second, the applicability of the conventional numerical dynamic programming (DP) method to the clutch fill control problem, which has a stiff dynamic model, is explored and shown to be ineffective. Thus, we proposed a customized DP method to obtain the optimal and robust pressure profile subject to specified constraints. The customized DP method not only reduces the computational burden significantly, but also improves the accuracy of the result by eliminating the interpolation errors. To validate the proposed method, a transmission clutch fixture has been designed and built in the laboratory. Both simulation and experimental results demonstrate that the proposed customized DP approach is effective, efficient and robust for solving the clutch fill optimal control problem.

Transmission Clutch Fill Control Using a Customized Dynamic Programming Method

2008 ◽  
Author(s):  
Xingyong Song ◽  
Mohd Azrin Mohd Zulkefli ◽  
Zongxuan Sun ◽  
Hsu-Chiang Miao
Keyword(s):  
Dynamic Programming ◽  
Control Problem ◽  
Systematic Approach ◽  
Traditional Approach ◽  
Pressure Profile ◽  
Dynamic Programming Method ◽  
Transmission Performance ◽  
Automotive Transmission ◽  
Flow Demand ◽  
Numerical Dynamic Programming

Clutch fill control is critical for automotive transmission performance and fuel economy, including both automatic and hybrid transmissions. The traditional approach, by which the clutch fill pressure command is manually calibrated, has a couple of limitations. First, the pressure profile is not optimized to reduce the peak clutch fill flow demand. Moreover, it is not systematically designed to account for uncertainties in the system, such as variations of solenoid valve time delay and parameters of the clutch assembly. In this paper, we present a systematic approach to evaluate the clutch fill dynamics and synthesize the optimal pressure profile. First, a clutch fill dynamic model is constructed and analyzed. Second, the applicability of the conventional numerical Dynamic Programming (DP) algorithm to the clutch fill control problem is explored and shown to be ineffective. Thus we developed a new customized DP method to obtain the optimal and robust pressure profile subject to specified constraints. After a series of simulations and case studies, the new customized DP approach is demonstrated to be effective, efficient, and robust for solving the clutch fill optimal control problem.

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