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 Publisher Website: 10.1109/CDC.2014.7039624
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Conference Paper: A maxplus based randomized algorithm for solving a class of HJB PDEs
Title  A maxplus based randomized algorithm for solving a class of HJB PDEs 

Authors  
Issue Date  2014 
Citation  Proceedings of the IEEE Conference on Decision and Control, 2014, v. 2015February, n. February, p. 15751580 How to Cite? 
Abstract  © 2014 IEEE. McEneaney introduced the curse of dimensionality free method for the special class of infinite horizon optimal control problems where the Hamiltonian is represented as a maximum of quadratic affine functions. This method is featured by its cubic complexity with respect to the state space dimension, but the number of basis functions is multiplied by the number of switches at each iteration, referred to as the 'curse of complexity'. In previous works, an SDPbased pruning technique was incorporated into the method in order to reduce the curse of complexity. Its efficiency was proved on many examples. In this paper we develop a new maxplus based randomized algorithm to solve the same class of infinite horizon optimal control problems. The major difference between the new algorithm and the previous SDPbased curse of dimensionality free method is that, instead of adding a large number of functions and then pruning the less useful ones, the new algorithm finds in cheap computation time (linear in the current number of basis functions), by a randomized procedure, useful quadratic functions and adds only those functions to the set of basis functions. Experimental results show that the maxplus randomized algorithm can reach the same precision order obtained by the SDPbased method with a speedup varying from 10 up to 100 and that the maximal precision order attainable by the new algorithm is much better than what can be done by the SDPbased algorithm in reasonable computation time. Besides, with the randomized algorithm we are now able to tackle switched problems with more number of switches, which will allow us to extend the algorithm to more general classes of optimal control problems. 
Persistent Identifier  http://hdl.handle.net/10722/219789 
ISSN 
DC Field  Value  Language 

dc.contributor.author  Qu, Zheng   
dc.date.accessioned  20150923T02:57:57Z   
dc.date.available  20150923T02:57:57Z   
dc.date.issued  2014   
dc.identifier.citation  Proceedings of the IEEE Conference on Decision and Control, 2014, v. 2015February, n. February, p. 15751580   
dc.identifier.issn  07431546   
dc.identifier.uri  http://hdl.handle.net/10722/219789   
dc.description.abstract  © 2014 IEEE. McEneaney introduced the curse of dimensionality free method for the special class of infinite horizon optimal control problems where the Hamiltonian is represented as a maximum of quadratic affine functions. This method is featured by its cubic complexity with respect to the state space dimension, but the number of basis functions is multiplied by the number of switches at each iteration, referred to as the 'curse of complexity'. In previous works, an SDPbased pruning technique was incorporated into the method in order to reduce the curse of complexity. Its efficiency was proved on many examples. In this paper we develop a new maxplus based randomized algorithm to solve the same class of infinite horizon optimal control problems. The major difference between the new algorithm and the previous SDPbased curse of dimensionality free method is that, instead of adding a large number of functions and then pruning the less useful ones, the new algorithm finds in cheap computation time (linear in the current number of basis functions), by a randomized procedure, useful quadratic functions and adds only those functions to the set of basis functions. Experimental results show that the maxplus randomized algorithm can reach the same precision order obtained by the SDPbased method with a speedup varying from 10 up to 100 and that the maximal precision order attainable by the new algorithm is much better than what can be done by the SDPbased algorithm in reasonable computation time. Besides, with the randomized algorithm we are now able to tackle switched problems with more number of switches, which will allow us to extend the algorithm to more general classes of optimal control problems.   
dc.language  eng   
dc.relation.ispartof  Proceedings of the IEEE Conference on Decision and Control   
dc.title  A maxplus based randomized algorithm for solving a class of HJB PDEs   
dc.type  Conference_Paper   
dc.description.nature  Link_to_subscribed_fulltext   
dc.identifier.doi  10.1109/CDC.2014.7039624   
dc.identifier.scopus  eid_2s2.084931829364   
dc.identifier.volume  2015February   
dc.identifier.issue  February   
dc.identifier.spage  1575   
dc.identifier.epage  1580   