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On Complexity Certi...
On Complexity Certification of Active-Set QP Methods with Applications to Linear MPC
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- Arnström, Daniel, 1994- (författare)
- Linköpings universitet,Reglerteknik,Tekniska fakulteten
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- Axehill, Daniel, Associate Professor, 1978- (preses)
- Linköpings universitet,Reglerteknik,Tekniska fakulteten
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- Hansson, Anders, Professor, 1964- (preses)
- Linköpings universitet,Reglerteknik,Tekniska fakulteten
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- Johansson, Mikael, Professor (opponent)
- Avdelningen för reglerteknik, Kungliga Tekniska högskolan, Stockholm, Sverige
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(creator_code:org_t)
- ISBN 9789179296926
- Linköping : Linköping University Electronic Press, 2021
- Engelska 45 s.
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Serie: Linköping Studies in Science and Technology. Licentiate Thesis, 0280-7971 ; 1901
- Relaterad länk:
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Abstract
Ämnesord
Stäng
- 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).
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
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