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Sequential Alternating Least Squares for Solving High Dimensional Linear Hamilton-Jacobi-Bellman Equation

Stefansson, Elis and Leong, Yoke Peng (2016) Sequential Alternating Least Squares for Solving High Dimensional Linear Hamilton-Jacobi-Bellman Equation. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2016. IEEE , Piscataway, NJ, pp. 3757-3764. ISBN 978-1-5090-3762-9.

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This paper presents a technique to efficiently solve the Hamilton-Jacobi-Bellman (HJB) equation for a class of stochastic affine nonlinear dynamical systems in high dimensions. The HJB solution provides a globally optimal controller to the associated dynamical system. However, the curse of dimensionality, commonly found in robotic systems, prevents one from solving the HJB equation naively. This work avoids the curse by representing the linear HJB equation using tensor decomposition. An alternating least squares (ALS) based technique finds an approximate solution to the linear HJB equation. A straightforward implementation of the ALS algorithm results in ill-conditioned matrices that prevent approximation to a high order of accuracy. This work resolves the ill-conditioning issue by computing the solution sequentially and introducing boundary condition rescaling. Both of these additions reduce the condition number of matrices in the ALS-based algorithm. A MATLAB tool, Sequential Alternating Least Squares (SeALS), that implements the new method is developed. The performance of SeALS is illustrated using three engineering examples: an inverted pendulum, a Vertical Takeoff and Landing aircraft, and a quadcopter with state up to twelve.

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Additional Information:© 2016 IEEE. Date Added to IEEE Xplore: 01 December 2016. This work was supported by Caltech Summer Undergraduate Research Fellowship. The authors would like to thank Joel Burdick, John Doyle and Matanya Horowitz for useful feedback on this work.
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Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Record Number:CaltechAUTHORS:20161212-090349947
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Official Citation:E. Stefansson and Y. P. Leong, "Sequential alternating least squares for solving high dimensional linear Hamilton-Jacobi-Bellman equation," 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, South Korea, 2016, pp. 3757-3764. doi: 10.1109/IROS.2016.7759553
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72704
Deposited By: Ruth Sustaita
Deposited On:12 Dec 2016 18:35
Last Modified:03 Oct 2019 16:20

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