501 research outputs found
High performance implementation of MPC schemes for fast systems
In recent years, the number of applications of model predictive control (MPC) is rapidly
increasing due to the better control performance that it provides in comparison to
traditional control methods. However, the main limitation of MPC is the computational
e ort required for the online solution of an optimization problem. This shortcoming
restricts the use of MPC for real-time control of dynamic systems with high sampling
rates. This thesis aims to overcome this limitation by implementing high-performance
MPC solvers for real-time control of fast systems. Hence, one of the objectives of this
work is to take the advantage of the particular mathematical structures that MPC
schemes exhibit and use parallel computing to improve the computational e ciency.
Firstly, this thesis focuses on implementing e cient parallel solvers for linear MPC
(LMPC) problems, which are described by block-structured quadratic programming
(QP) problems. Speci cally, three parallel solvers are implemented: a primal-dual
interior-point method with Schur-complement decomposition, a quasi-Newton method
for solving the dual problem, and the operator splitting method based on the alternating
direction method of multipliers (ADMM). The implementation of all these solvers is
based on C++. The software package Eigen is used to implement the linear algebra
operations. The Open Message Passing Interface (Open MPI) library is used for the
communication between processors. Four case-studies are presented to demonstrate the
potential of the implementation. Hence, the implemented solvers have shown high
performance for tackling large-scale LMPC problems by providing the solutions in
computation times below milliseconds.
Secondly, the thesis addresses the solution of nonlinear MPC (NMPC) problems, which
are described by general optimal control problems (OCPs). More precisely,
implementations are done for the combined multiple-shooting and collocation (CMSC)
method using a parallelization scheme. The CMSC method transforms the OCP into a
nonlinear optimization problem (NLP) and de nes a set of underlying sub-problems for
computing the sensitivities and discretized state values within the NLP solver. These
underlying sub-problems are decoupled on the variables and thus, are solved in parallel.
For the implementation, the software package IPOPT is used to solve the resulting NLP
problems. The parallel solution of the sub-problems is performed based on MPI and
Eigen. The computational performance of the parallel CMSC solver is tested using case
studies for both OCPs and NMPC showing very promising results.
Finally, applications to autonomous navigation for the SUMMIT robot are presented.
Specially, reference tracking and obstacle avoidance problems are addressed using an
NMPC approach. Both simulation and experimental results are presented and compared
to a previous work on the SUMMIT, showing a much better computational e ciency
and control performance.Tesi
Custom optimization algorithms for efficient hardware implementation
The focus is on real-time optimal decision making with application in advanced control
systems. These computationally intensive schemes, which involve the repeated solution of
(convex) optimization problems within a sampling interval, require more efficient computational
methods than currently available for extending their application to highly dynamical
systems and setups with resource-constrained embedded computing platforms.
A range of techniques are proposed to exploit synergies between digital hardware, numerical
analysis and algorithm design. These techniques build on top of parameterisable
hardware code generation tools that generate VHDL code describing custom computing
architectures for interior-point methods and a range of first-order constrained optimization
methods. Since memory limitations are often important in embedded implementations we
develop a custom storage scheme for KKT matrices arising in interior-point methods for
control, which reduces memory requirements significantly and prevents I/O bandwidth
limitations from affecting the performance in our implementations. To take advantage of
the trend towards parallel computing architectures and to exploit the special characteristics
of our custom architectures we propose several high-level parallel optimal control
schemes that can reduce computation time. A novel optimization formulation was devised
for reducing the computational effort in solving certain problems independent of the computing
platform used. In order to be able to solve optimization problems in fixed-point
arithmetic, which is significantly more resource-efficient than floating-point, tailored linear
algebra algorithms were developed for solving the linear systems that form the computational
bottleneck in many optimization methods. These methods come with guarantees
for reliable operation. We also provide finite-precision error analysis for fixed-point implementations
of first-order methods that can be used to minimize the use of resources while
meeting accuracy specifications. The suggested techniques are demonstrated on several
practical examples, including a hardware-in-the-loop setup for optimization-based control
of a large airliner.Open Acces
Optimization Algorithms for Machine Learning Designed for Parallel and Distributed Environments
This thesis proposes several optimization methods that utilize parallel algorithms for large-scale machine learning problems. The overall theme is network-based machine learning algorithms; in particular, we consider two machine learning models: graphical models and neural networks. Graphical models are methods categorized under unsupervised machine learning, aiming at recovering conditional dependencies among random variables from observed samples of a multivariable distribution. Neural networks, on the other hand, are methods that learn an implicit approximation to underlying true nonlinear functions based on sample data and utilize that information to generalize to validation data. The goal of finding the best methods relies on an optimization problem tasked with training such models. Improvements in current methods of solving the optimization problem for graphical models are obtained by parallelization and the use of a new update and a new step-size selection rule in the coordinate descent algorithms designed for large-scale problems. For training deep neural networks, we consider the second-order optimization algorithms within trust-region-like optimization frameworks. Deep networks are represented using large-scale vectors of weights and are trained based on very large datasets. Hence, obtaining second-order information is very expensive for these networks. In this thesis, we undertake an extensive exploration of algorithms that use a small number of curvature evaluations and are hence faster than other existing methods
Quantum computing for finance
Quantum computers are expected to surpass the computational capabilities of
classical computers and have a transformative impact on numerous industry
sectors. We present a comprehensive summary of the state of the art of quantum
computing for financial applications, with particular emphasis on stochastic
modeling, optimization, and machine learning. This Review is aimed at
physicists, so it outlines the classical techniques used by the financial
industry and discusses the potential advantages and limitations of quantum
techniques. Finally, we look at the challenges that physicists could help
tackle
Multidisciplinary Design Optimization for Space Applications
Multidisciplinary Design Optimization (MDO) has been increasingly studied in aerospace engineering with the main purpose of reducing monetary and schedule costs. The traditional design approach of optimizing each discipline separately and manually iterating to achieve good solutions is substituted by exploiting the interactions between the disciplines and concurrently optimizing every subsystem. The target of the research was the development of a flexible software suite capable of concurrently optimizing the design of a rocket propellant launch vehicle for multiple objectives. The possibility of combining the advantages of global and local searches have been exploited in both the MDO architecture and in the selected and self developed optimization methodologies. Those have been compared according to computational efficiency and performance criteria. Results have been critically analyzed to identify the most suitable optimization approach for the targeted MDO problem
Image Reconstructions of Compressed Sensing MRI with Multichannel Data
Magnetic resonance imaging (MRI) provides high spatial resolution, high-quality of soft-tissue contrast, and multi-dimensional images. However, the speed of data acquisition limits potential applications. Compressed sensing (CS) theory allowing data being sampled at sub-Nyquist rate provides a possibility to accelerate the MRI scan time. Since most MRI scanners are currently equipped with multi-channel receiver systems, integrating CS with multi-channel systems can further shorten the scan time and also provide a better image quality. In this dissertation, we develop several techniques for integrating CS with parallel MRI.
First, we propose a method which extends the reweighted l1 minimization to the CS-MRI with multi-channel data. The individual channel images are recovered according to the reweighted l1 minimization algorithm. Then, the final image is combined by the sum-of-squares method. Computer simulations show that the new method can improve the reconstruction quality at a slightly increased computation cost.
Second, we propose a reconstruction approach using the ubiquitously available multi-core CPU to accelerate CS reconstructions of multiple channel data. CS reconstructions for phase array system using iterative l1 minimization are significantly time-consuming, where the computation complexity scales with the number of channels. The experimental results show that the reconstruction efficiency benefits significantly from parallelizing the CS reconstructions, and pipelining multi-channel data on multi-core processors. In our experiments, an additional speedup factor of 1.6 to 2.0 was achieved using the proposed method on a quad-core CPU.
Finally, we present an efficient reconstruction method for high-dimensional CS MRI with a GPU platform to shorten the time of iterative computations. Data managements as well as the iterative algorithm are properly designed to meet the way of SIMD (single instruction/multiple data) parallelizations. For three-dimension multi-channel data, all slices along frequency encoding direction and multiple channels are highly parallelized and simultaneously processed within GPU. Generally, the runtime on GPU only requires 2.3 seconds for reconstructing a simulated 4-channel data with a volume size of 256×256×32. Comparing to 67 seconds using CPU, it achieves 28 faster with the proposed method. The rapid reconstruction algorithms demonstrated in this work are expected to help bring high dimensional, multichannel parallel CS MRI closer to clinical applications
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