Control Theory

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:
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 systems.

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:
So-called 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
Nonlinear systems:
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.