28 research outputs found
Application of Advanced Estimation Techniques to a Chemical Plant Model
The paper is aimed at comparing some of the most promising and novel advanced techniques for estimation by assessing their effectiveness on the chemical process benchmark. Global and distributed implementations of the extended Kalman filter are the key elements of the work. In addition, the paper is also aimed at describing and developing a recursive implementation of the autocovariance least square algorithm for the on-line updating of the tuning knobs of the filter, demonstrating its relevance in the performance monitoring of chemical processes
Policy Optimization of Finite-Horizon Kalman Filter with Unknown Noise Covariance
This paper is on learning the Kalman gain by policy optimization method.
Firstly, we reformulate the finite-horizon Kalman filter as a policy
optimization problem of the dual system. Secondly, we obtain the global linear
convergence of exact gradient descent method in the setting of known
parameters. Thirdly, the gradient estimation and stochastic gradient descent
method are proposed to solve the policy optimization problem, and further the
global linear convergence and sample complexity of stochastic gradient descent
are provided for the setting of unknown noise covariance matrices and known
model parameters
Computation of Input Disturbance Sets for Constrained Output Reachability
Linear models with additive unknown-but-bounded input disturbances are
extensively used to model uncertainty in robust control systems design.
Typically, the disturbance set is either assumed to be known a priori or
estimated from data through set-membership identification. However, the problem
of computing a suitable input disturbance set in case the set of possible
output values is assigned a priori has received relatively little attention.
This problem arises in many contexts, such as in supervisory control, actuator
design, decentralized control, and others. In this paper, we propose a method
to compute input disturbance sets (and the corresponding set of states) such
that the resulting set of outputs matches as closely as possible a given set of
outputs, while additionally satisfying strict (inner or outer) inclusion
constraints. We formulate the problem as an optimization problem by relying on
the concept of robust invariance. The effectiveness of the approach is
demonstrated in numerical examples that illustrate how to solve safe reference
set and input-constraint set computation problems
Meta-optimization of the Extended Kalman filter's parameters through the use of the Bias-Variance Equilibrium Point criterion
The extraction of information on land cover classes
using unsupervised methods has always been of relevance to the
remote sensing community. In this paper, a novel criterion is proposed,
which extracts the inherent information in an unsupervised
fashion from a time series. The criterion is used to fit a parametric
model to a time series, derive the corresponding covariance matrices
of the parameters for the model, and estimate the additive noise
on the time series. The proposed criterion uses both spatial and
temporal information when estimating the covariance matrices
and can be extended to incorporate spectral information. The
algorithm used to estimate the parameters for the model is the
extended Kalman filter (EKF). An unsupervised search algorithm,
specifically designed for this criterion, is proposed in conjunction
with the criterion that is used to rapidly and efficiently estimate the
variables. The search algorithm attempts to satisfy the criterion by
employing density adaptation to the current candidate system. The
application in this paper is the use of an EKF to model Moderate
Resolution Imaging Spectroradiometer time series with a triply
modulated cosine function as the underlying model. The results
show that the criterion improved the fit of the triply modulated
cosine function by an order of magnitude on the time series over
all seven spectral bands when compared with the other methods.
The state space variables derived from the EKF are then used for
both land cover classification and land cover change detection.
The method was evaluated in the Gauteng province of South
Africa where it was found to significantly improve on land cover
classification and change detection accuracies when compared
with other methods.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=36hb201
Control of fluid flows and other systems governed by partial differential-algebraic equations
The motion of fluids, such as air or water, is central to many engineering systems of significant
economic and environmental importance. Examples range from air/fuel mixing in combustion engines
to turbulence induced noise and fatigue on aircraft. Recent advances in novel sensor/actuator
technologies have raised the intriguing prospect of actively sensing and manipulating the motion
of the fluid within these systems, making them ripe for feedback control, provided a suitable control
model exists. Unfortunately, the models for many of these systems are described by nonlinear,
partial differential-algebraic equations for which few, if any, controller synthesis techniques exist.
In stark contrast, the majority of established control theory assumes plant models of finite (and
typically small) state dimension, expressed as a linear system of ordinary differential equations.
Therefore, this thesis explores the problem of how to apply the mainstream tools of control theory
to the class of systems described by partial differential-algebraic equations, that are either linear,
or for which a linear approximation is valid.
The problems of control system design for infinite-dimensional and algebraically constrained
systems are treated separately in this thesis. With respect to the former, a new method is presented
that enables the computation of a bound on the n-gap between a discretisation of a spatially distributed
plant, and the plant itself, by exploiting the convergence rate of the v-gap metric between
low-order models of successively finer spatial resolution. This bound informs the design, on loworder
models, of H[infinity] loop-shaping controllers that are guaranteed to robustly stabilise the actual
plant. An example is presented on a one-dimensional heat equation.
Controller/estimator synthesis is then discussed for finite-dimensional systems containing algebraic,
as well as differential equations. In the case of fluid flows, algebraic constraints typically
arise from incompressibility and the application of boundary conditions. A numerical algorithm is
presented, suitable for the semi-discrete linearised Navier-Stokes equations, that decouples the differential
and algebraic parts of the system, enabling application of standard control theory without
the need for velocity-vorticity type methods. This algorithm is demonstrated firstly on a simple
electrical circuit, and secondly on the highly non-trivial problem of flow-field estimation in the
transient growth region of a flat-plate boundary layer, using only wall shear measurements.
These separate strands are woven together in the penultimate chapter, where a transient energy
controller is designed for a channel-flow system, using wall mounted sensors and actuators