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Model Predictive Control Group






Control group

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Research Projects


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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