NDLI: Regression-based LP solver for chance-constrained finite horizon optimal control with nonconvex constraints

Content Provider	IEEE Xplore Digital Library
Author	Banerjee, A.G. Ono, M. Roy, N. Williams, B.C.
Copyright Year	2011
Description	Author affiliation: MIT, Cambridge, MA, USA (Banerjee, A.G.; Ono, M.; Roy, N.; Williams, B.C.)
Abstract	This paper presents a novel algorithm for finite-horizon optimal control problems subject to additive Gaussian-distributed stochastic disturbance and chance constraints that are defined over feasible, non-convex state spaces. Our previous work [1] proposed a branch and bound-based algorithm that can find a near-optimal solution by iteratively solving non-linear convex optimization problems, as well as their LP relaxations called Fixed Risk Relaxation (FRR) problems. The aim of this work is to significantly reduce the computation time of the previous algorithm so that it can be applied to practical problems, such as a path planning with multiple obstacles. Our approach is to use machine learning to efficiently estimate the objective function values of FRRs within an error bound that is fixed for a given problem domain and choice of model complexity. We exploit the fact that all the FRR problems associated with the branch-and-bound tree nodes are similar to each other, both in terms of the solutions as well as the objective function and constraint coefficients. A standard optimizer is first used to generate a training data set in the form of optimal FRR solutions. Matrix transformations and boosting trees are then applied to generate learning models; fast inference is performed at run-time for new but similar FRR problems that occur when the system dynamics and/or the environment changes slightly. By using this regression technique to estimate the lower bound of the cost function value, and subsequently solving the convex optimization problems exactly at the leaf nodes of the branch-and-bound tree, we achieve 10-35 times reduction in the computation time without compromising the optimality of the solution.
Sponsorship	Control Syst. Soc.
Starting Page	131
Ending Page	138
File Size	215350
Page Count	8
File Format	PDF
ISBN	9781457700804
ISSN	07431619
e-ISBN	9781457700811
DOI	10.1109/ACC.2011.5990937
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Optimization Optimal control Nickel Programming Training Regression tree analysis Path planning
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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