A Comparison of the Embedding Method With Multiparametric Programming, Mixed-Integer Programming, Gradient-Descent, and Hybrid Minimum Principle-Based Methods

In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical nonlinear optimization, has not been extensively compared w...

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Vydáno v:	IEEE transactions on control systems technology Ročník 22; číslo 5; s. 1784 - 1800
Hlavní autoři:	Meyer, Richard T., Zefran, Milos, DeCarlo, Raymond A.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.09.2014 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Autonomous Boost converter Combinatorial analysis Complexity theory Embedded systems embedding method Integer programming Mathematical models Methods model predictive control multiparametric programming numerical optimization Optimal control Optimization Programming Robots switched optimal control Switched systems Switches model predictive control multiparametric programming switched optimal control embedding method Boost converter numerical optimization
ISSN:	1063-6536, 1558-0865
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Abstract	In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical nonlinear optimization, has not been extensively compared with alternative solution approaches. The goal of this paper is thus to compare the embedding approach with multiparametric programming, mixed-integer programming [mixed integer programming (MIP), commercial (CPLEX)], and gradient-descent-based methods in the context of five recently published examples: 1) a spring-mass system; 2) moving-target tracking for a mobile robot; 3) two-tank filling; dc-dc boost converter; and 5) skid-steered vehicle. A sixth example, an autonomous switched 11-region linear system, is used to compare a hybrid minimum principle method and traditional numerical programming. For a given performance index (PI) for each case, cost and solution times are presented. It is shown that there are numerical advantages of the embedding approach: lower PI cost (except in some instances when autonomous switches are present), generally faster solution time, and convergence to a solution when other methods may fail. In addition, the embedding method requires no ad hoc assumptions (e.g., predetermined mode sequences) or specialized control models. Theoretical advantages of the embedding approach over the other methods are also described; guaranteed existence of a solution under mild conditions, convexity of the embedded hybrid optimization problem (under the customary conditions on the PI), solvability with traditional techniques (e.g., sequential quadratic programming) avoiding the combinatorial complexity in the number of modes/discrete variables of MIP, applicability to affine nonlinear systems, and no need to explicitly assign discrete/mode variables to autonomous switches. Finally, common misconceptions regarding the embedding approach are addressed, including whether it uses an average value control model (no), whether it is necessary to tweak the algorithm to obtain bang-bang solutions (no), whether it requires infinite switching to implement embedded solution (no), and whether it has real-time capability (yes).
AbstractList	In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical nonlinear optimization, has not been extensively compared with alternative solution approaches. The goal of this paper is thus to compare the embedding approach with multiparametric programming, mixed-integer programming [mixed integer programming (MIP), commercial (CPLEX)], and gradient-descent-based methods in the context of five recently published examples: 1) a spring-mass system; 2) moving-target tracking for a mobile robot; 3) two-tank filling; dc-dc boost converter; and 5) skid-steered vehicle. A sixth example, an autonomous switched 11-region linear system, is used to compare a hybrid minimum principle method and traditional numerical programming. For a given performance index (PI) for each case, cost and solution times are presented. It is shown that there are numerical advantages of the embedding approach: lower PI cost (except in some instances when autonomous switches are present), generally faster solution time, and convergence to a solution when other methods may fail. In addition, the embedding method requires no ad hoc assumptions (e.g., predetermined mode sequences) or specialized control models. Theoretical advantages of the embedding approach over the other methods are also described; guaranteed existence of a solution under mild conditions, convexity of the embedded hybrid optimization problem (under the customary conditions on the PI), solvability with traditional techniques (e.g., sequential quadratic programming) avoiding the combinatorial complexity in the number of modes/discrete variables of MIP, applicability to affine nonlinear systems, and no need to explicitly assign discrete/mode variables to autonomous switches. Finally, common misconceptions regarding the embedding approach are addressed, including whether it uses an average value control model (no), whether it is necessary to tweak the algorithm to obtain bang-bang solutions (no), whether it requires infinite switching to implement embedded solution (no), and whether it has real-time capability (yes).
Author	Meyer, Richard T. Zefran, Milos DeCarlo, Raymond A.
Author_xml	– sequence: 1 givenname: Richard T. surname: Meyer fullname: Meyer, Richard T. email: rtmeyer@purdue.edu organization: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA – sequence: 2 givenname: Milos surname: Zefran fullname: Zefran, Milos email: mzefran@uic.edu organization: Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL, USA – sequence: 3 givenname: Raymond A. surname: DeCarlo fullname: DeCarlo, Raymond A. email: decarlo@ecn.purdue.edu organization: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA
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Cites_doi	10.1109/TIE.2008.2006951 10.1109/APEC.2009.4802805 10.1109/CDC.2003.1272479 10.1016/0005-1098(88)90027-1 10.1109/CDC.2010.5717263 10.1016/j.automatica.2005.04.017 10.1109/TCST.2012.2227964 10.1109/CDC.2010.5717264 10.1016/S0005-1098(01)00174-1 10.1016/j.nahs.2006.10.007 10.1016/j.automatica.2010.10.010 10.1002/asjc.553 10.1109/ACC.1999.786491 10.1109/CDC.1999.831404 10.1109/ROBOT.2007.363674 10.1007/978-3-540-24743-2_30 10.1016/S0005-1098(02)00308-4 10.1109/TAC.1981.1102596 10.1109/ROBOT.2010.5509356 10.1109/TCST.2009.2035306 10.1109/TAC.1983.1103294 10.1049/ip-cta:20050094 10.1109/TAC.2010.2047437 10.1109/COMPEL.2010.5562383 10.1109/ACC.2011.5991428 10.1109/ACC.2012.6314919 10.1109/CDC.2010.5717840 10.1016/S0005-1098(04)00223-7 10.1109/TAC.2006.878720 10.1109/TCST.2009.2017934 10.1109/APEC.2010.5433628
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References	ref13 ref35 ref12 ref34 ref37 ref14 ref30 ref11 ref10 ref32 wolsey (ref1) 1998 meyer (ref39) 2012 ref2 xu (ref31) 2000 ref17 ref16 ref38 (ref7) 2012 ref19 ref18 mayne (ref33) 2001 borrelli (ref8) 2013 bengea (ref25) 2011 žefran (ref42) 1997 ref23 ref26 ref20 ref22 ref21 ref43 borrelli (ref36) 2003 ref28 ref27 ref29 ref9 ref4 ref3 ref6 ref5 uthaichana (ref15) 2011; 2 ref40 neely (ref41) 2010 bengea (ref24) 2003; 5
References_xml	– ident: ref19 doi: 10.1109/TIE.2008.2006951 – ident: ref18 doi: 10.1109/APEC.2009.4802805 – ident: ref26 doi: 10.1109/CDC.2003.1272479 – start-page: 113 year: 1997 ident: ref42 article-title: Continuous motion plans for robotic systems with changing dynamic behavior publication-title: Robotic motion and manipulation – year: 1998 ident: ref1 publication-title: Integer Programming – ident: ref28 doi: 10.1016/0005-1098(88)90027-1 – ident: ref4 doi: 10.1109/CDC.2010.5717263 – ident: ref34 doi: 10.1016/j.automatica.2005.04.017 – ident: ref14 doi: 10.1109/TCST.2012.2227964 – ident: ref5 doi: 10.1109/CDC.2010.5717264 – start-page: 1 year: 2001 ident: ref33 article-title: Constrained optimal control publication-title: Proc Eur Control Conf Plenary Lecture – ident: ref35 doi: 10.1016/S0005-1098(01)00174-1 – ident: ref13 doi: 10.1016/j.nahs.2006.10.007 – ident: ref23 doi: 10.1016/j.automatica.2010.10.010 – start-page: 2683 year: 2000 ident: ref31 article-title: Optimal control of switched systems: New results and open problems publication-title: Proc Amer Control Conf – ident: ref27 doi: 10.1002/asjc.553 – ident: ref29 doi: 10.1109/ACC.1999.786491 – ident: ref30 doi: 10.1109/CDC.1999.831404 – ident: ref17 doi: 10.1109/ROBOT.2007.363674 – ident: ref6 doi: 10.1007/978-3-540-24743-2_30 – ident: ref37 doi: 10.1016/S0005-1098(02)00308-4 – ident: ref32 doi: 10.1109/TAC.1981.1102596 – year: 2012 ident: ref39 publication-title: MATLAB Toolbox for Hybrid Optimal Control – volume: 2 start-page: 96 year: 2011 ident: ref15 article-title: Hybrid optimal theory and predictive control for power management in hybrid electric vehicle publication-title: Applied Nonlinear Systems – ident: ref22 doi: 10.1109/ROBOT.2010.5509356 – ident: ref9 doi: 10.1109/TCST.2009.2035306 – ident: ref40 doi: 10.1109/TAC.1983.1103294 – year: 2003 ident: ref36 publication-title: Constrained optimal control of discrete-time linear hybrid systems – ident: ref10 doi: 10.1049/ip-cta:20050094 – volume: 5 start-page: 11 year: 2003 ident: ref24 article-title: Optimal control of a two-switched linear system publication-title: J Control Eng Appl Inf – ident: ref38 doi: 10.1109/TAC.2010.2047437 – ident: ref21 doi: 10.1109/COMPEL.2010.5562383 – year: 2013 ident: ref8 publication-title: Predictive Control for Linear and Hybrid Systems – year: 2010 ident: ref41 publication-title: Real-time hybrid model predictive control of switched DC-DC converters – ident: ref16 doi: 10.1109/ACC.2011.5991428 – ident: ref3 doi: 10.1109/ACC.2012.6314919 – ident: ref2 doi: 10.1109/CDC.2010.5717840 – start-page: 1 year: 2011 ident: ref25 publication-title: The Control Handbook Advanced Methods – ident: ref12 doi: 10.1016/S0005-1098(04)00223-7 – ident: ref11 doi: 10.1109/TAC.2006.878720 – ident: ref43 doi: 10.1109/TCST.2009.2017934 – year: 2012 ident: ref7 publication-title: IBM ILOG CPLEX Optimizer 12 3 – ident: ref20 doi: 10.1109/APEC.2010.5433628
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SubjectTerms	Algorithms Autonomous Boost converter Combinatorial analysis Complexity theory Embedded systems embedding method Integer programming Mathematical models Methods model predictive control multiparametric programming numerical optimization Optimal control Optimization Programming Robots switched optimal control Switched systems Switches
Title	A Comparison of the Embedding Method With Multiparametric Programming, Mixed-Integer Programming, Gradient-Descent, and Hybrid Minimum Principle-Based Methods
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