Theoretical and algorithmic advances in multi-parametric optimization and control
File(s)
Author(s)
Oberdieck, Richard Henrich
Type
Thesis
Abstract
This thesis discusses recent advances in a variety of areas in multi-parametric programming
and explicit model predictive control (MPC). First, novel theoretical and algorithmic results
for multi-parametric quadratic and mixed-integer quadratic programming (mp-QP/mp-
MIQP) problems extend the current state-of-the-art: for mp-QP problems, it is shown that
its solution is given by a connected graph, based on which a novel solution procedure is
developed. Furthermore, several computational studies investigate the performance of different
mp-QP algorithms, and a new parallelization strategy is presented, together with an
application of mp-QP algorithms to multi-objective optimization. For mp-MIQP problems,
it is shown that it is possible to obtain the exact solution of a mp-MIQP problem without
resorting to the use of envelopes of solutions, whose computational performance is compared
in a computational study with different mp-MIQP algorithms. Then, the concept of robust
counterparts in robust explicit MPC for discrete-time linear systems is revisited and an elegant
reformulation enables the solution of closed-loop robust explicit MPC problems with
a series of projection operations. This approach is extended to hybrid systems, where the
same properties are proven to hold. Finally, a new approach towards unbounded and binary
parameters in multi-parametric programming is introduced, and several examples highlight
its potential.
and explicit model predictive control (MPC). First, novel theoretical and algorithmic results
for multi-parametric quadratic and mixed-integer quadratic programming (mp-QP/mp-
MIQP) problems extend the current state-of-the-art: for mp-QP problems, it is shown that
its solution is given by a connected graph, based on which a novel solution procedure is
developed. Furthermore, several computational studies investigate the performance of different
mp-QP algorithms, and a new parallelization strategy is presented, together with an
application of mp-QP algorithms to multi-objective optimization. For mp-MIQP problems,
it is shown that it is possible to obtain the exact solution of a mp-MIQP problem without
resorting to the use of envelopes of solutions, whose computational performance is compared
in a computational study with different mp-MIQP algorithms. Then, the concept of robust
counterparts in robust explicit MPC for discrete-time linear systems is revisited and an elegant
reformulation enables the solution of closed-loop robust explicit MPC problems with
a series of projection operations. This approach is extended to hybrid systems, where the
same properties are proven to hold. Finally, a new approach towards unbounded and binary
parameters in multi-parametric programming is introduced, and several examples highlight
its potential.
Version
Open Access
Date Issued
2016-09
Date Awarded
2017-02
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
License URL
Advisor
Pistikopoulos, Efstratios
Mantalaris, Sakis
Sponsor
European Commission
Engineering and Physical Sciences Research Council
Texas A & M University
Grant Number
OPTICO/G.A. No.280813, PIRSES, G.A. 294987
EP/M027856/1, EP/M028240/1, EP/I014640
Publisher Department
Chemical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)