Approximate Dynamic Programming with Applications
(2008) In PhD Theses TFRT1082. Abstract
 This thesis studies approximate optimal control of nonlinear systems. Particular attention is given to global solutions and to the computation of approximately optimal feedback controllers. The solution to an optimal control problem is characterized by the optimal value function. For a large class of problems the optimal value function must satisfy a HamiltonJacobiBellman type equation. Two common methods for solving such equations are policy iteration and value iteration. Both these methods are studied in this thesis.
An approximate policy iteration algorithm is presented for both the continuous and discrete time settings. It is shown that the sequence produced by this algorithm converges monotonically towards the optimal value... (More)  This thesis studies approximate optimal control of nonlinear systems. Particular attention is given to global solutions and to the computation of approximately optimal feedback controllers. The solution to an optimal control problem is characterized by the optimal value function. For a large class of problems the optimal value function must satisfy a HamiltonJacobiBellman type equation. Two common methods for solving such equations are policy iteration and value iteration. Both these methods are studied in this thesis.
An approximate policy iteration algorithm is presented for both the continuous and discrete time settings. It is shown that the sequence produced by this algorithm converges monotonically towards the optimal value function. A multivariate polynomial relaxation algorithm is proposed for linearly constrained discrete time optimal control problems with convex cost. Relaxed value iteration is studied for constrained linear systems with convex piecewise linear cost. It is shown how an explicit piecewise linear control law can be computed and how the resulting lookup table can be reduced efficiently.
The online implementation of receding horizon controllers, even for linear systems, is usually restricted to systems with slow dynamics. One reason for this is that the delay between measurement and actuation introduced by computing the control signal online can severely degrade systems with fast dynamics. A method to improve robustness against such delays and other uncertainties is presented. A case study on the control of DCDC converters is given. Feasibility of a Relaxed Dynamic Programming algorithm is verified by synthesizing controllers for both a stepdown converter and a stepup converter. The control performance is evaluated both in simulations and in real experiments. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1023673
 author
 Wernrud, Andreas ^{LU}
 supervisor

 Anders Rantzer ^{LU}
 opponent

 Professor Parrilo, Pablo, Massachusetts Institute of Technology (MIT)
 organization
 publishing date
 2008
 type
 Thesis
 publication status
 published
 subject
 in
 PhD Theses
 volume
 TFRT1082
 publisher
 Department of Automatic Control, Lund Institute of Technology, Lund University
 defense location
 Room M:A, the Mbuilding, Ole Römers väg 1, Lund University Faculty of Engineering
 defense date
 20080229 10:15
 ISSN
 02805316
 language
 English
 LU publication?
 yes
 id
 bd85f9a702b843ad95c6f3b1962a296d (old id 1023673)
 date added to LUP
 20080205 10:24:48
 date last changed
 20181121 20:25:25
@phdthesis{bd85f9a702b843ad95c6f3b1962a296d, abstract = {This thesis studies approximate optimal control of nonlinear systems. Particular attention is given to global solutions and to the computation of approximately optimal feedback controllers. The solution to an optimal control problem is characterized by the optimal value function. For a large class of problems the optimal value function must satisfy a HamiltonJacobiBellman type equation. Two common methods for solving such equations are policy iteration and value iteration. Both these methods are studied in this thesis.<br/><br/>An approximate policy iteration algorithm is presented for both the continuous and discrete time settings. It is shown that the sequence produced by this algorithm converges monotonically towards the optimal value function. A multivariate polynomial relaxation algorithm is proposed for linearly constrained discrete time optimal control problems with convex cost. Relaxed value iteration is studied for constrained linear systems with convex piecewise linear cost. It is shown how an explicit piecewise linear control law can be computed and how the resulting lookup table can be reduced efficiently.<br/><br/>The online implementation of receding horizon controllers, even for linear systems, is usually restricted to systems with slow dynamics. One reason for this is that the delay between measurement and actuation introduced by computing the control signal online can severely degrade systems with fast dynamics. A method to improve robustness against such delays and other uncertainties is presented. A case study on the control of DCDC converters is given. Feasibility of a Relaxed Dynamic Programming algorithm is verified by synthesizing controllers for both a stepdown converter and a stepup converter. The control performance is evaluated both in simulations and in real experiments.}, author = {Wernrud, Andreas}, issn = {02805316}, language = {eng}, publisher = {Department of Automatic Control, Lund Institute of Technology, Lund University}, school = {Lund University}, series = {PhD Theses}, title = {Approximate Dynamic Programming with Applications}, volume = {TFRT1082}, year = {2008}, }