**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

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Many systems of practical importance can only be described by complex models. For example, vibrations and sound waves exhibit both time and space dependence and are hence modelled by partial differential equations. This means that the state variables that evolve on infinite-dimensional spaces. (This is contrast to systems with ordinary equation models where the state is in Rn.) Systems modelled by delay-differential equations also evolve on an infinite-dimensional space. The dynamics are complicated by the use of smart materials, such as piezo-electrics and shape memory alloys, which are of interest to control structures and acoustic systems. Their behaviour is hysteretic and highly nonlinear. Analysis and simulation of these systems is often not straightforward; the research in my group is focused on the even more challenging problem of designing controllers to alter the dynamics so as to achieve such goals as improved settling time and tracking of a reference signal.

Some controller and estimator design theory for infinite-dimensional systems is analogous to that for finite-dimensional systems, but the controller is now an operator that needs to be approximated to obtain an implementable finite-dimensional control law. The approximations that are used in simulation and controller design suffer from the deficiency that the control signal (and also disturbances) can affect higher modes which can lead to instability if the effect of the higher modes is not handled correctly.

For systems with time and space dependence, the location of the controller hardware can be selected. The choice of locations affects the performance and also the efficiency of the final controlled system. In many cases, the hardware can not be easily moved once installed. For example, piezo-electric patches are very diffiicult to remove once bonded to a structure. This motivates a mechatronic approach where the locations are included as part of the controller design process. We have been working on obtaining theoretical results for when such problems are well-posed, and also when approximations can be used to compute the controller and locations. Recent work has also been concerned with the development of algorithms suitable for large-scale approximating models.

Obtaining stabilizing controllers for systems with nonlinear partial differential equation models is a new area with many interesting problems. Few conditions even exist for when the stability of the linearized system predicts stability of the nonlinear system.

There are projects available for qualified graduate students. All accepted students will be fully funded. For more details, contact me.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land promised to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.