96,529 research outputs found
Non-linear projection to latent structures
PhD ThesisThis Thesis focuses on the study of multivariate statistical regression techniques which have
been used to produce non-linear empirical models of chemical processes, and on the
development of a novel approach to non-linear Projection to Latent Structures regression.
Empirical modelling relies on the availability of process data and sound empirical regression
techniques which can handle variable collinearities, measurement noise, unknown variable and
noise distributions and high data set dimensionality. Projection based techniques, such as
Principal Component Analysis (PCA) and Projection to Latent Structures (PLS), have been
shown to be appropriate for handling such data sets. The multivariate statistical projection based
techniques of PCA and linear PLS are described in detail, highlighting the benefits which can be
gained by using these approaches. However, many chemical processes exhibit severely nonlinear
behaviour and non-linear regression techniques are required to develop empirical models.
The derivation of an existing quadratic PLS algorithm is described in detail. The procedure for
updating the model parameters which is required by the quadratic PLS algorithms is explored
and modified. A new procedure for updating the model parameters is presented and is shown to
perform better the existing algorithm. The two procedures have been evaluated on the basis of
the performance of the corresponding quadratic PLS algorithms in modelling data generated
with a strongly non-linear mathematical function and data generated with a mechanistic model of
a benchmark pH neutralisation system. Finally a novel approach to non-linear PLS modelling is
then presented combining the general approximation properties of sigmoid neural networks and
radial basis function networks with the new weights updating procedure within the PLS
framework. These algorithms are shown to outperform existing neural network PLS algorithms
and the quadratic PLS approaches. The new neural network PLS algorithms have been evaluated
on the basis of their performance in modelling the same data used to compare the quadratic PLS
approaches.Strang Studentship
European project ESPRIT PROJECT 22281 (PROGNOSIS)
Centre for Process Analysis, Chemometrics
and Control
A Bayesian perspective on classical control
The connections between optimal control and Bayesian inference have long been
recognised, with the field of stochastic (optimal) control combining these
frameworks for the solution of partially observable control problems. In
particular, for the linear case with quadratic functions and Gaussian noise,
stochastic control has shown remarkable results in different fields, including
robotics, reinforcement learning and neuroscience, especially thanks to the
established duality of estimation and control processes. Following this idea we
recently introduced a formulation of PID control, one of the most popular
methods from classical control, based on active inference, a theory with roots
in variational Bayesian methods, and applications in the biological and neural
sciences. In this work, we highlight the advantages of our previous formulation
and introduce new and more general ways to tackle some existing problems in
current controller design procedures. In particular, we consider 1) a
gradient-based tuning rule for the parameters (or gains) of a PID controller,
2) an implementation of multiple degrees of freedom for independent responses
to different types of signals (e.g., two-degree-of-freedom PID), and 3) a novel
time-domain formalisation of the performance-robustness trade-off in terms of
tunable constraints (i.e., priors in a Bayesian model) of a single cost
functional, variational free energy.Comment: 8 pages, Accepted at IJCNN 202
Path integrals and symmetry breaking for optimal control theory
This paper considers linear-quadratic control of a non-linear dynamical
system subject to arbitrary cost. I show that for this class of stochastic
control problems the non-linear Hamilton-Jacobi-Bellman equation can be
transformed into a linear equation. The transformation is similar to the
transformation used to relate the classical Hamilton-Jacobi equation to the
Schr\"odinger equation. As a result of the linearity, the usual backward
computation can be replaced by a forward diffusion process, that can be
computed by stochastic integration or by the evaluation of a path integral. It
is shown, how in the deterministic limit the PMP formalism is recovered. The
significance of the path integral approach is that it forms the basis for a
number of efficient computational methods, such as MC sampling, the Laplace
approximation and the variational approximation. We show the effectiveness of
the first two methods in number of examples. Examples are given that show the
qualitative difference between stochastic and deterministic control and the
occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA
Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications *
We consider the optimal control problem for a linear conditional
McKean-Vlasov equation with quadratic cost functional. The coefficients of the
system and the weigh-ting matrices in the cost functional are allowed to be
adapted processes with respect to the common noise filtration. Semi closed-loop
strategies are introduced, and following the dynamic programming approach in
[32], we solve the problem and characterize time-consistent optimal control by
means of a system of decoupled backward stochastic Riccati differential
equations. We present several financial applications with explicit solutions,
and revisit in particular optimal tracking problems with price impact, and the
conditional mean-variance portfolio selection in incomplete market model.Comment: to appear in Probability, Uncertainty and Quantitative Ris
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