4,424 research outputs found
Markov Decision Processes with Risk-Sensitive Criteria: An Overview
The paper provides an overview of the theory and applications of
risk-sensitive Markov decision processes. The term 'risk-sensitive' refers here
to the use of the Optimized Certainty Equivalent as a means to measure
expectation and risk. This comprises the well-known entropic risk measure and
Conditional Value-at-Risk. We restrict our considerations to stationary
problems with an infinite time horizon. Conditions are given under which
optimal policies exist and solution procedures are explained. We present both
the theory when the Optimized Certainty Equivalent is applied recursively as
well as the case where it is applied to the cumulated reward. Discounted as
well as non-discounted models are reviewe
A bi-level model of dynamic traffic signal control with continuum approximation
This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure
Input Design for System Identification via Convex Relaxation
This paper proposes a new framework for the optimization of excitation inputs
for system identification. The optimization problem considered is to maximize a
reduced Fisher information matrix in any of the classical D-, E-, or A-optimal
senses. In contrast to the majority of published work on this topic, we
consider the problem in the time domain and subject to constraints on the
amplitude of the input signal. This optimization problem is nonconvex. The main
result of the paper is a convex relaxation that gives an upper bound accurate
to within of the true maximum. A randomized algorithm is presented for
finding a feasible solution which, in a certain sense is expected to be at
least as informative as the globally optimal input signal. In the case
of a single constraint on input power, the proposed approach recovers the true
global optimum exactly. Extensions to situations with both power and amplitude
constraints on both inputs and outputs are given. A simple simulation example
illustrates the technique.Comment: Preprint submitted for journal publication, extended version of a
paper at 2010 IEEE Conference on Decision and Contro
Research in applied mathematics, numerical analysis, and computer science
Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers
A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance
This article presents a novel perspective along with a scalable methodology
to design a fault detection and isolation (FDI) filter for high dimensional
nonlinear systems. Previous approaches on FDI problems are either confined to
linear systems or they are only applicable to low dimensional dynamics with
specific structures. In contrast, shifting attention from the system dynamics
to the disturbance inputs, we propose a relaxed design perspective to train a
linear residual generator given some statistical information about the
disturbance patterns. That is, we propose an optimization-based approach to
robustify the filter with respect to finitely many signatures of the
nonlinearity. We then invoke recent results in randomized optimization to
provide theoretical guarantees for the performance of the proposed filer.
Finally, motivated by a cyber-physical attack emanating from the
vulnerabilities introduced by the interaction between IT infrastructure and
power system, we deploy the developed theoretical results to detect such an
intrusion before the functionality of the power system is disrupted
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