On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC

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Arnström, Daniel,1994-Linköpings universitet,Reglerteknik,Tekniska fakulteten (author)

On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC

BookEnglish2021

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Linköping :Linköping University Electronic Press,2021
45 s.
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LIBRIS-ID:oai:DiVA.org:liu-173716
ISBN:9789179296926
https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-173716URI
https://doi.org/10.3384/lic.diva-173716DOI

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Language:English
Summary in:English

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Subject category:lic swepub-publicationtype

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Linköping Studies in Science and Technology. Licentiate Thesis,0280-7971 ;1901

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In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these efficiently and to have good upper bounds on worst-case solution time. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving such QPs is active-set methods, where a sequence of linear systems of equations is solved. The primary contribution of this thesis is a method which determines which sequence of subproblems a popular class of such active-set algorithms need to solve, for every possible QP instance that might arise from a given linear MPC problem (i.e, for every possible state and reference signal). By knowing these sequences, worst-case bounds on how many iterations, floating-point operations and, ultimately, the maximum solution time, these active-set algorithms require to compute a solution can be determined, which is of importance when, e.g, linear MPC is used in safety-critical applications. After establishing this complexity certification method, its applicability is extended by showing how it can be used indirectly to certify the complexity of another, efficient, type of active-set QP algorithm which reformulates the QP as a nonnegative least-squares method. Finally, the proposed complexity certification method is extended further to situations when enhancements to the active-set algorithms are used, namely, when they are terminated early (to save computations) and when outer proximal-point iterations are performed (to improve numerical stability).

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Axehill, Daniel,Associate Professor,1978-Linköpings universitet,Reglerteknik,Tekniska fakulteten(Swepub:liu)danax42 (thesis advisor)
Hansson, Anders,Professor,1964-Linköpings universitet,Reglerteknik,Tekniska fakulteten(Swepub:liu)andha17 (thesis advisor)
Johansson, Mikael,ProfessorAvdelningen för reglerteknik, Kungliga Tekniska högskolan, Stockholm, Sverige (opponent)
Linköpings universitetReglerteknik (creator_code:org_t)

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