1,873 research outputs found
Stability for Receding-horizon Stochastic Model Predictive Control
A stochastic model predictive control (SMPC) approach is presented for
discrete-time linear systems with arbitrary time-invariant probabilistic
uncertainties and additive Gaussian process noise. Closed-loop stability of the
SMPC approach is established by appropriate selection of the cost function.
Polynomial chaos is used for uncertainty propagation through system dynamics.
The performance of the SMPC approach is demonstrated using the Van de Vusse
reactions.Comment: American Control Conference (ACC) 201
Algorithm Engineering in Robust Optimization
Robust optimization is a young and emerging field of research having received
a considerable increase of interest over the last decade. In this paper, we
argue that the the algorithm engineering methodology fits very well to the
field of robust optimization and yields a rewarding new perspective on both the
current state of research and open research directions.
To this end we go through the algorithm engineering cycle of design and
analysis of concepts, development and implementation of algorithms, and
theoretical and experimental evaluation. We show that many ideas of algorithm
engineering have already been applied in publications on robust optimization.
Most work on robust optimization is devoted to analysis of the concepts and the
development of algorithms, some papers deal with the evaluation of a particular
concept in case studies, and work on comparison of concepts just starts. What
is still a drawback in many papers on robustness is the missing link to include
the results of the experiments again in the design
Data-Driven Methods and Applications for Optimization under Uncertainty and Rare-Event Simulation
For most of decisions or system designs in practice, there exist chances of severe hazards or system failures that can be catastrophic. The occurrence of such hazards is usually uncertain, and hence it is important to measure and analyze the associated risks. As a powerful tool for estimating risks, rare-event simulation techniques are used to improve the efficiency of the estimation when the risk occurs with an extremely small probability. Furthermore, one can utilize the risk measurements to achieve better decisions or designs. This can be achieved by modeling the task into a chance constrained optimization problem, which optimizes an objective with a controlled risk level. However, recent problems in practice have become more data-driven and hence brought new challenges to the existing literature in these two domains. In this dissertation, we will discuss challenges and remedies in data-driven problems for rare-event simulation and chance constrained problems. We propose a robust optimization based framework for approaching chance constrained optimization problems under a data-driven setting. We also analyze the impact of tail uncertainty in data-driven rare-event simulation tasks.
On the other hand, due to recent breakthroughs in machine learning techniques, the development of intelligent physical systems, e.g. autonomous vehicles, have been actively investigated. Since these systems can cause catastrophes to public safety, the evaluation of their machine learning components and system performance is crucial. This dissertation will cover problems arising in the evaluation of such systems. We propose an importance sampling scheme for estimating rare events defined by machine learning predictors. Lastly, we discuss an application project in evaluating the safety of autonomous vehicle driving algorithms.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163270/1/zhyhuang_1.pd
A Practical Guide to Robust Optimization
Robust optimization is a young and active research field that has been mainly
developed in the last 15 years. Robust optimization is very useful for
practice, since it is tailored to the information at hand, and it leads to
computationally tractable formulations. It is therefore remarkable that
real-life applications of robust optimization are still lagging behind; there
is much more potential for real-life applications than has been exploited
hitherto. The aim of this paper is to help practitioners to understand robust
optimization and to successfully apply it in practice. We provide a brief
introduction to robust optimization, and also describe important do's and
don'ts for using it in practice. We use many small examples to illustrate our
discussions
Stability for Receding-horizon Stochastic Model Predictive Control
A stochastic model predictive control (SMPC) approach is presented for
discrete-time linear systems with arbitrary time-invariant probabilistic
uncertainties and additive Gaussian process noise. Closed-loop stability of the
SMPC approach is established by appropriate selection of the cost function.
Polynomial chaos is used for uncertainty propagation through system dynamics.
The performance of the SMPC approach is demonstrated using the Van de Vusse
reactions.Comment: American Control Conference (ACC) 201
Fault-Tolerant Shortest Paths - Beyond the Uniform Failure Model
The overwhelming majority of survivable (fault-tolerant) network design
models assume a uniform scenario set. Such a scenario set assumes that every
subset of the network resources (edges or vertices) of a given cardinality
comprises a scenario. While this approach yields problems with clean
combinatorial structure and good algorithms, it often fails to capture the true
nature of the scenario set coming from applications.
One natural refinement of the uniform model is obtained by partitioning the
set of resources into faulty and secure resources. The scenario set contains
every subset of at most faulty resources. This work studies the
Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest Path problem
in this failure model. We present complexity results alongside exact and
approximation algorithms for FTP. We emphasize the vast increase in the
complexity of the problem with respect to its uniform analogue, the
Edge-Disjoint Paths problem
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