In general terms, control theory can be described
as the process of influencing the behaviour of a physical system to achieve
a desired goal, primarily through the use of feedback. It is important
in a diverse range of scientific and engineering disciplines including
such things as the design of robotic systems, the positioning of communication
satellites, the reduction of noise and vibration in structures, the control of
so-called smart materials, and the regulation of biological systems.
Current research includes the following topics:
Infinite dimensional systems arise in the control of systems modelled by
partial differential equations or delay differential equations. The goal
of the research is to investigate whether control systems with boundary
control and/or point sensing have desirable mathematical properties such
as being well-posed and stable. Results such as these are of practical
importance because they facilitate the design of controllers for these
Faculty: K. A. Morris
Active noise control:
The idea behind
such systems is to reduce the effect of acoustic disturbances. A
highly accurate one-dimensional electroacoustic model of an acoustic duct has been developed,
which will be used to explore the extent to which noise reduction is
possible in this case. This research is expected to provide
insight into achievable noise reduction in enclosures.
Faculty: S. P. Lipshitz, K. A. Morris
Control of smart materials:
smart materials, for example shape memory alloys, exhibit nonlinear hysteretic
behaviour, and thus represent a challenge as regards controller design.
The main goal of the research is to use the dissipativity of
these systems to design robust controllers.
Faculty: K. A. Morris
While most control systems are designed
and implemented using linear techniques, there are increasingly many cases in which the
nonlinearities of the system must be taken into account, for example in
the design of autonomous robots or in the automatic
control of spacecraft attitude. The design and
analysis of nonlinear control systems requires more sophisticated
mathematical tools than are typically used for linear systems.
Nonlinear control theory draws on a wide variety of topics, including
dynamical systems theory, geometric mechanics and differential geometry. Current research
involves questions of stability and detectability
for nonlinear systems, stabilization of mechanical systems by energy shaping and optimal control.
Faculty: D. E. Chang
Applications of control theory in biology:
The emerging field of systems biology involves the application of ideas from control theory to molecular biology. The research includes the construction of mathematical models of biological mechanisms and the reverse-engineering of processes of biological regulations.
Faculty: B. Ingalls
See also Controller Design, under Scientific Computation.