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| EPSRC Reference: |
EP/C014006/1 |
| Title: |
Stochastic model predictive control: theory and application to air-traffic control |
| Principal Investigator: |
Professor J Maciejowski |
| Other Investigators: |
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| Researcher Co-investigator: |
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| Project Partner: |
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| Department: |
Engineering |
| Organisation: |
University of Cambridge |
| Scheme: |
Standard Research |
| Starts: |
01 June 2005 |
Ends: |
31 May 2009 |
Value (£): |
275,004
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| EPSRC Research Topic Classifications: |
| Control Systems Engineering, Integration and Autonomy |
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| EPSRC Industrial Sector Classifications: |
| Aerospace, Defence and Marine |
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| Related Grants: |
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| Panel History: |
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Summary |
The proposed work addresses the problem of controlling uncertain complex systems through the predictive control approach with particular application to Air-Traffic Control.
The predictive approach to the control of uncertain dynamical systems consists of the following steps:
1) Use a model to predict the evolution of the system in response to possible control actions;
2) Use the resulting predictions to evaluate the best control action according to desired objectives;
3) Apply the selected control action and collect information on the actual evolution of the system, then loop to Step 1.
This strategy is very straightforward and has proved to be very effective in many applications. However, if the system is very complex and parts of it are not precisely known, a precise prediction model cannot be obtained. Prediction models that include some randomness in the evolution of the system can be used to simulate the effect uncertainties in the system. In these cases one has to make decisions in an uncertain scenario.
The objective of the proposed work is to find an efficient strategy for selecting control actions in the face of uncertainty. The key idea will be to simulate a large number of possible evolutions of the system, in order to evaluate the average effect of each control action, and then choose on the basis of these evaluations. This idea, usually denoted as "Monte Carlo" approach, can be used to solve very complex problems and, in general, can be very straightforward to implement. However, its efficiency, in terms of speed and accuracy in finding the solution, can vary considerably depending on the particular strategy that has been followed to implement it.
In this work, we will develop an efficient Monte Carlo strategy to the control of complex uncertain systems.
The application to Air-Traffic Control has been selected because air-traffic is an uncertain complex system. The effect of the wind on aircraft trajectories and imprecise knowledge of the behaviour of pilots in response to Air-Traffic Control instructions are examples of the uncertainty that affect air-traffic. In the current system the strategy is that Air-Traffic Control issues very conservative instructions in order to remain well on the safe side. However increasing levels of traffic are pushing the current system towards its limits, so that there is a strong need for more sophisticated, innovative, Air-Traffic Control strategies.
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| Final Report Summary |
This research addressed the problem of controlling uncertain complex systems through the predictive control approach with particular application to Air-Traffic Control. The predictive approach to the control of uncertain dynamical systems consists of the following steps:
1) Use a model to predict the evolution of the system in response to possible control actions;
2) Use the resulting predictions to evaluate the best control action according to desired objectives;
3) Apply the selected control action and collect information on the actual evolution of the system, then loop to Step 1.
This strategy is very straightforward and has proved to be very effective in many applications. However, if the system is very complex and parts of it are not precisely known, a precise prediction model cannot be obtained. Prediction models that include some randomness in the evolution of the system can be used to simulate the effect uncertainties in the system. In these cases one has to make decisions in an uncertain scenario.
The objective of the proposed work was to find an efficient strategy for selecting control actions in the face of uncertainty. The key idea was to simulate a large number of possible evolutions of the system, in order to evaluate the average effect of each control action, and then choose on the basis of these evaluations. This idea, usually denoted as "Monte Carlo" approach, can be used to solve very complex problems and, in general, can be very straightforward to implement. However, its efficiency, in terms of speed and accuracy in finding the solution, can vary considerably depending on the particular strategy that has been followed to implement it.
In this work, we pursued an efficient Monte Carlo strategy to the control of complex uncertain systems. We obtained novel results on the accuracy of "simulated annealing" optimisation methods when searching for optima over continuous domains, and we established the closed-loop stability of systems when controlled by stochastic model predictive controllers. In particular, we developed novel rigorous finite-time guaranteed bounds on the performance of
Markov chain Monte Carlo (MCMC) methods for optimization. This led to the first known
rigorous bounds on the accuracy and confidence of the solution found in finite-time by
MCMC optimization algorithms in the general case in which the optimization objective
is a stochastic performance criterion and the optimization variables take values in
continuous ranges. These results were initially presented at the annual conference on
Neural Information Processing Systems (NIPS) - one of the most selective
peer-reviewed conferences in Machine Learning - as a poster spotlight; only 10% of
submitted papers received poster spotlights. The extended version of this paper (arXiv:0906.1055v1) has been submitted for journal publication.
We progressed the development of stochastic models of air traffic and the preliminary formulation of innovative routing algorithms based on the optimization of a stochastic performance criterion with Markov chain Monte Carlo (MCMC) methods (published as a regular paper in the IEEE Transactions on Intelligent Transportation Systems).
We also established, by means of a simulation study and in collaboration with researchers at Eurocontrol, that stochastic modelling can be fruitfully combined with `worst-case' analysis in the context of Air-Traffic Control. The conservativeness of worst-case analysis can be mitigated, without allowing unsafe situations to arise.
The application to Air-Traffic Control was selected for this project because air-traffic is an uncertain complex system. The effect of the wind on aircraft trajectories and imprecise knowledge of the behaviour of pilots in response to Air-Traffic Control instructions are examples of the uncertainty that affect air-traffic.
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| Further Information: |
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| Organisation Website: |
http://www.cam.ac.uk |
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