Parallel solution of optimal control problems using the graphics processing unit

This paper presents an indirect method for solving optimal control problems (OCPs) using graphics processing unit (GPU). The OCPs considered here include control variable inequality constraints (CVICs), state variable inequality constraints (SVICs), and parameters. The necessary conditions of the mi...

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Vydáno v:Optimal control applications & methods Ročník 44; číslo 1; s. 2 - 22
Hlavní autoři: Yang, Chaoyi, Fabien, Brian C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Glasgow Wiley Subscription Services, Inc 01.01.2023
Témata:
Algorithms
boundary value problem
Boundary value problems
Central processing units
Continuation methods
CPUs
CUDA
Differential equations
GPU based parallel programming
Graphics processing units
index‐1 differential algebraic equation
multiple shooting method
Optimal control
Runge-Kutta method
slacked unconstrained penalty function method
ISSN:0143-2087, 1099-1514
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Shrnutí:This paper presents an indirect method for solving optimal control problems (OCPs) using graphics processing unit (GPU). The OCPs considered here include control variable inequality constraints (CVICs), state variable inequality constraints (SVICs), and parameters. The necessary conditions of the minimum for the OCPs are written as a boundary value problem with index‐1 differential algebraic equations (BVP‐DAEs). The complementarity conditions associated with those inequality constraints are approximated using Kanzow's smoothed Fisher‐Burmeister formula. The numerical solution for solving the BVP‐DAEs is based on the multiple shooting technique and the DAEs are solved using a single step linearly implicit Runge–Kutta (Rosenbrock–Wanner, ROW) method. A Newton's continuation method is performed to solve the BVP‐DAEs system and the descent direction is found by solving a sparse bordered almost block diagonal (BABD) linear system with a structured orthogonal factorization algorithm. Parallel computing techniques are used to accelerate the code which is implemented using Python and CUDA on GPU. Numerical examples are presented to illustrate the efficiency of the code. The GPU based parallel implementation is shown to be significantly faster than the implementation using central processing unit (CPU) alone.
Bibliografie:Funding information
National Science Foundation, Grant/Award Number: 1542228
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ISSN:0143-2087
1099-1514
DOI:10.1002/oca.2927