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Systems Optimization

It has been said that 80% of engineering design is optimization. The design of a new aircraft wing costs in excess of $2 billion, and involves the optimization of many variables subject to various constraints. Of course for such a task the optimization is carried out off-line with super computers working with various numerical methods, such as finite element methods or linear programming. Of course, wind tunnels and flight simulators are also used. The design of aircraft time tables are another example involving thousands of variables.

The trend in our research is towards on-line optimization, where an engineering system re-optimizes itself on a frequent or continual basis. For example, an oil refinery needs to re-optimize its various settings every few hours dependent on the market spot prices for different products. A robotic dextrous hand has to re-optimize its balancing forces dependent on the loads it carries and its manipulations of the load every few milliseconds. Such an optimization is not possible using classical control methodologies, but requires on-line optimization subject to the various friction inequality constraints.

A key feature derived in on-line optimzation, is that if the algorithm is interrupted or does not have enough time to calculate all the iterations than is desirable, the current best estimate provided should be at least feasible in the sense hat it satisfies the contraints. Algorithms which achieve this are termed interior point methods, and these contrast many optimization methods in the literature which approach optimality from outside the constraint set. Interior point methods have been successful in solving even the classical linear programming task, and are particularly attractive when the variable number is large, say in the thousands.

Of course, many problems in control theory, signal processing, learning systems, discrete-event systems, and robotic systems can be viewed as optimization. For control systems, the now classical linear quadratic Gaussian (LQG) methodology is really convex optimization leading to a unique global optimium control. More generally, risk-sensitive control methodology which allows the design to take into account robustness to model uncertainties, which leads to the so-called H-infinity control methodology at the one extreme, maximizing robustness to worst case uncertainty or disturbances, and the LQG methodology at the other.

Some of our work here has involved optimization on manifolds: think of cost contours on a sphere or doughnut. This work evolved out of studying gradient flows on manifolds, with particular attention to selecting the cost functions and the metric (direction of decent) so as to achieve optimization via dynamical sytems with attractive properties, see for example the book "Optimziation and Dynamical Systems", by U Helmke and J B Moore, Springer-Verlag, 1994.

Staff involved

Knut Hueper (NICTA)

Pei Yean Lee(NICTA)

Jonathan Manton

John Moore

Robert Orsi

Jochen Trumpf

Current PhD students

Desmond Chik

Hui-Bo Ji

Hendra Nurdin

Hao Shen

Yueshi Shen

Kaiyang Yang

Previous PhD students

Danchi Jiang

Pei-Yean Lee

Andrew Lim

Robert Mahony

Jane Perkins

See also Systems and Control