Stochastic
MPC
Most industrial control systems are subject to constraints and
uncertainty, with uncertainty usually characterized in terms of
stochastic variables. Predictive control is well developed in terms of
handling constraints and bounded uncertainty but there is currently no
framework addressing problems involving stochastic objectives and
stochastic constraints. This project aims to achieve a full extension,
both in respect of constraints and objective, of model predictive
control (linear and nonlinear) to the stochastic case. Given the
omnipresence of uncertainties of a stochastic nature, the results are of
theoretical interest and will also have a significant impact in
practical applications. An objective of the project is to demonstrate
this through the study of (i) policy optimization in a sustainable
development problem addressing power generation, energy cost and
pollution; (ii) optimization of availability of power plant and grid
capacity within a competitive power generation market.
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Fast
on-line MPC optimization algorithms
To widen the applicability of nonlinear predictive control, this project
develops strategies that perform the required online optimization within
the exacting limits (e.g. several milliseconds) imposed by fast sampling
applications, while retaining guarantees of feasibility and closed-loop
stability. The project explores the potential benefits of
bilinearization techniques and of an augmented state-space formulation
of the prediction model incorporating the Euler-Lagrange co-state. The
work exploits the concept of feasible invariant sets, and also
introduces novel approaches through: (i) a differential description of
feasibility boundaries; (ii) an incremental approach to optimality;
(iii) MPC techniques developed for bilinear systems.
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Receding
horizon policy optimization for sustainable development
Policy optimization in sustainable development can be formulated as a
multi-objective problem involving power generation, transport,
agriculture, climate change, depletable and renewable resources. The aim
is to model the impacts of instruments (such as public spending on
R&D in different technologies) on measurable sustainability
indicators (such as energy costs and emissions of pollutants), and to
develop policies that maximize the likelihood of benefit while
minimizing risk. This project predicts the probabilities of risk and
benefit over a future horizon using stochastic models, and formulates
receding horizon control laws through the optimization of stochastic
objectives subject to stochastic constraints. The approach enables
methods to be developed for ensuring acceptable closed-loop performance
despite high levels of model uncertainty.
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Feedback
Linearization of Nonminimum Phase and Non-Involutive systems
Input-output feedback linearization allows for
techniques such as optimal control to be used to improve dynamic
behaviour of nonlinear systems. Linearization however is not
applicable to systems with unstable inverse dynamics, and this
necessitates the use of auxiliary synthetic outputs through which it is
possible to attain minimum phase characteristics. Control over dynamic
behaviour can then be exercised by matching plant outputs to synthetic
outputs. The objective of the project is the development of
rigorous extensions of these techniques to the case of constrained and
non-involutive systems, and for consideration of the discrete-time case.
The ultimate goal is the integration of such techniques into a
predictive control scheme.
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Invariant
sets and Model Predictive Control of nonlinear systems
Predictive control for linear systems is now a well-established
discipline providing a range of techniques with guaranteed stability,
feasibility and robustness. The extension of such techniques to
nonlinear models can lead to impracticable solutions due to the
nonconvexity of the relevant optimization and its excessive
computational burden. It is however possible to cast the
prediction problem in an autonomous framework which enables the
definition of computationally convenient ellipsoidal and/or polytopic
invariant sets that ensure future feasibility. This framework can be
used to develop predictive control algorithms with guaranteed stability
and robustness.
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