9,541 research outputs found
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
An extension to GUM methodology: degrees-of-freedom calculations for correlated multidimensional estimates
The Guide to the Expression of Uncertainty in Measurement advocates the use
of an 'effective number of degrees of freedom' for the calculation of an
interval of measurement uncertainty. However, it does not describe how this
number is to be calculated when (i) the measurand is a vector quantity or (ii)
when the errors in the estimates of the quantities defining the measurand (the
'input quantities') are not incurred independently. An appropriate analysis for
a vector-valued measurand has been described (Metrologia 39 (2002) 361-9), and
a method for a one-dimensional measurand with dependent errors has also been
given (Metrologia 44 (2007) 340-9). This paper builds on those analyses to
present a method for the situation where the problem is multidimensional and
involves correlated errors. The result is an explicit general procedure that
reduces to simpler procedures where appropriate. The example studied is from
the field of radio-frequency metrology, where measured quantities are often
complex-valued and can be regarded as vectors of two elements.Comment: 30 pages with 2 embedded figure
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