Optimal Control of Port-Hamiltonian Systems: A Time-Continuous Learning Approach
Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse optimality property since each passivating state feedback controller is optimal with respect to some specific performance index. Due to the nonlinear port-Hamiltonian system structure, however, explicit (forward) methods f...
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creator | Kölsch, Lukas Soneira, Pol Jané Strehle, Felix Hohmann, Sören |
description | Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse
optimality property since each passivating state feedback controller is optimal
with respect to some specific performance index. Due to the nonlinear
port-Hamiltonian system structure, however, explicit (forward) methods for
optimal control of port-Hamiltonian systems require the generally intractable
analytical solution of the Hamilton-Jacobi-Bellman equation. Adaptive dynamic
programming methods provide a means to circumvent this issue. However, the few
existing approaches for port-Hamiltonian systems hinge on very specific
sub-classes of either performance indices or system dynamics or require the
intransparent guessing of stabilizing initial weights. In this paper, we
contribute towards closing this largely unexplored research area by proposing a
time-continuous adaptive feedback controller for the optimal control of general
time-continuous input-state-output port-Hamiltonian systems with respect to
general Lagrangian performance indices. Its control law implements an online
learning procedure which uses the Hamiltonian of the system as an initial value
function candidate. The time-continuous learning of the value function is
achieved by means of a certain Lagrange multiplier that allows to evaluate the
optimality of the current solution. In particular, constructive conditions for
stabilizing initial weights are stated and asymptotic stability of the
closed-loop equilibrium is proven. Our work is concluded by simulations for
exemplary linear and nonlinear optimization problems which demonstrate
asymptotic convergence of the controllers resulting from the proposed online
adaptation procedure. |
doi_str_mv | 10.48550/arxiv.2007.08645 |
format | Article |
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optimality property since each passivating state feedback controller is optimal
with respect to some specific performance index. Due to the nonlinear
port-Hamiltonian system structure, however, explicit (forward) methods for
optimal control of port-Hamiltonian systems require the generally intractable
analytical solution of the Hamilton-Jacobi-Bellman equation. Adaptive dynamic
programming methods provide a means to circumvent this issue. However, the few
existing approaches for port-Hamiltonian systems hinge on very specific
sub-classes of either performance indices or system dynamics or require the
intransparent guessing of stabilizing initial weights. In this paper, we
contribute towards closing this largely unexplored research area by proposing a
time-continuous adaptive feedback controller for the optimal control of general
time-continuous input-state-output port-Hamiltonian systems with respect to
general Lagrangian performance indices. Its control law implements an online
learning procedure which uses the Hamiltonian of the system as an initial value
function candidate. The time-continuous learning of the value function is
achieved by means of a certain Lagrange multiplier that allows to evaluate the
optimality of the current solution. In particular, constructive conditions for
stabilizing initial weights are stated and asymptotic stability of the
closed-loop equilibrium is proven. Our work is concluded by simulations for
exemplary linear and nonlinear optimization problems which demonstrate
asymptotic convergence of the controllers resulting from the proposed online
adaptation procedure.</description><identifier>DOI: 10.48550/arxiv.2007.08645</identifier><language>eng</language><subject>Computer Science - Systems and Control ; Mathematics - Optimization and Control</subject><creationdate>2020-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2007.08645$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2007.08645$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kölsch, Lukas</creatorcontrib><creatorcontrib>Soneira, Pol Jané</creatorcontrib><creatorcontrib>Strehle, Felix</creatorcontrib><creatorcontrib>Hohmann, Sören</creatorcontrib><title>Optimal Control of Port-Hamiltonian Systems: A Time-Continuous Learning Approach</title><description>Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse
optimality property since each passivating state feedback controller is optimal
with respect to some specific performance index. Due to the nonlinear
port-Hamiltonian system structure, however, explicit (forward) methods for
optimal control of port-Hamiltonian systems require the generally intractable
analytical solution of the Hamilton-Jacobi-Bellman equation. Adaptive dynamic
programming methods provide a means to circumvent this issue. However, the few
existing approaches for port-Hamiltonian systems hinge on very specific
sub-classes of either performance indices or system dynamics or require the
intransparent guessing of stabilizing initial weights. In this paper, we
contribute towards closing this largely unexplored research area by proposing a
time-continuous adaptive feedback controller for the optimal control of general
time-continuous input-state-output port-Hamiltonian systems with respect to
general Lagrangian performance indices. Its control law implements an online
learning procedure which uses the Hamiltonian of the system as an initial value
function candidate. The time-continuous learning of the value function is
achieved by means of a certain Lagrange multiplier that allows to evaluate the
optimality of the current solution. In particular, constructive conditions for
stabilizing initial weights are stated and asymptotic stability of the
closed-loop equilibrium is proven. Our work is concluded by simulations for
exemplary linear and nonlinear optimization problems which demonstrate
asymptotic convergence of the controllers resulting from the proposed online
adaptation procedure.</description><subject>Computer Science - Systems and Control</subject><subject>Mathematics - Optimization and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz81KxDAcBPBcPMjqA3gyL5CaNt_eSlFXKOzC9l7-qYkG2qSkXXHf3t3V0zAwDPwQeihpwbUQ9AnyT_guKkpVQbXk4hbtd_MaJhhxk-Ka04iTx_uUV7KFKYxrigEiPpyW1U3LM65xFyZHLtsQj-m44NZBjiF-4nqec4Lh6w7deBgXd_-fG9S9vnTNlrS7t_embglIJYgYpCi5-aDU2kp77wd27gwMN1pRK7iUWktFhWGlt6byoAxzRg7Ue2cryTbo8e_2SurnfEbkU3-h9Vca-wX4lkjP</recordid><startdate>20200716</startdate><enddate>20200716</enddate><creator>Kölsch, Lukas</creator><creator>Soneira, Pol Jané</creator><creator>Strehle, Felix</creator><creator>Hohmann, Sören</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20200716</creationdate><title>Optimal Control of Port-Hamiltonian Systems: A Time-Continuous Learning Approach</title><author>Kölsch, Lukas ; Soneira, Pol Jané ; Strehle, Felix ; Hohmann, Sören</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-5c65149d00bb28fffc35143a949870b5466886705931fb92fa793e96c0ffeb263</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer Science - Systems and Control</topic><topic>Mathematics - Optimization and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Kölsch, Lukas</creatorcontrib><creatorcontrib>Soneira, Pol Jané</creatorcontrib><creatorcontrib>Strehle, Felix</creatorcontrib><creatorcontrib>Hohmann, Sören</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kölsch, Lukas</au><au>Soneira, Pol Jané</au><au>Strehle, Felix</au><au>Hohmann, Sören</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal Control of Port-Hamiltonian Systems: A Time-Continuous Learning Approach</atitle><date>2020-07-16</date><risdate>2020</risdate><abstract>Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse
optimality property since each passivating state feedback controller is optimal
with respect to some specific performance index. Due to the nonlinear
port-Hamiltonian system structure, however, explicit (forward) methods for
optimal control of port-Hamiltonian systems require the generally intractable
analytical solution of the Hamilton-Jacobi-Bellman equation. Adaptive dynamic
programming methods provide a means to circumvent this issue. However, the few
existing approaches for port-Hamiltonian systems hinge on very specific
sub-classes of either performance indices or system dynamics or require the
intransparent guessing of stabilizing initial weights. In this paper, we
contribute towards closing this largely unexplored research area by proposing a
time-continuous adaptive feedback controller for the optimal control of general
time-continuous input-state-output port-Hamiltonian systems with respect to
general Lagrangian performance indices. Its control law implements an online
learning procedure which uses the Hamiltonian of the system as an initial value
function candidate. The time-continuous learning of the value function is
achieved by means of a certain Lagrange multiplier that allows to evaluate the
optimality of the current solution. In particular, constructive conditions for
stabilizing initial weights are stated and asymptotic stability of the
closed-loop equilibrium is proven. Our work is concluded by simulations for
exemplary linear and nonlinear optimization problems which demonstrate
asymptotic convergence of the controllers resulting from the proposed online
adaptation procedure.</abstract><doi>10.48550/arxiv.2007.08645</doi><oa>free_for_read</oa></addata></record> |
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subjects | Computer Science - Systems and Control Mathematics - Optimization and Control |
title | Optimal Control of Port-Hamiltonian Systems: A Time-Continuous Learning Approach |
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