14,526 research outputs found
Efficient Approaches for Enclosing the United Solution Set of the Interval Generalized Sylvester Matrix Equation
In this work, we investigate the interval generalized Sylvester matrix
equation and develop some
techniques for obtaining outer estimations for the so-called united solution
set of this interval system. First, we propose a modified variant of the
Krawczyk operator which causes reducing computational complexity to cubic,
compared to Kronecker product form. We then propose an iterative technique for
enclosing the solution set. These approaches are based on spectral
decompositions of the midpoints of , , and
and in both of them we suppose that the midpoints of and
are simultaneously diagonalizable as well as for the midpoints of
the matrices and . Some numerical experiments are given to
illustrate the performance of the proposed methods
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
A Structural Estimation and Interpretation of the New Keynesian Macro Model
We formulate and solve a Rational Expectations New Keynesian macro model that implies non-linear cross-equation restrictions on the dynamics of inflation, the output gap and the Federal funds rate. Our maximum likelihood estimation procedure fully imposes these restrictions and yields asymptotic and small sample distributions of the structural parameters. We show how the structural parameters shape the responses of the macro variables to the structural shocks. While the point estimates imply that the Fed has been stabilizing inflation fluctuations since 1980, our econometric analysis suggests considerable uncertainty regarding the stance of the Fed against inflation.
A Fuzzy-Logical Approach for Integrating Multi-Agent Estimators
This paper proposes a novel approach for integrating estimations from multiple agents. The approach is based on the fuzzy set theory. However, compared to existing fuzzy logical methods that use fuzzy if-then rules, this method is based on solving an over-determined fuzzy equation system. The result is either a global inconsistency message or the consistent core of the equation system. We demonstrate the approach with data from an actual case study undertaken by a German automotive manufacturer
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