This research studies a new control design methodology for uncertain dynamic systems, where the uncertainty is associated with the system's nonlinearity or time varying characteristics. The intent is to develop a controller which does not depend on any knowledge of the uncertainty except its possible bound. The control problem is formulated in a geometric manner where the uncertainty is described to lie within a hyperpolyhedron domain. And since uncertainty on system performance occurs at the corner points of the hyperpolyhedron, it is sufficient to study the system behavior by examining the polyhedron corner points. Computer dynamic programming techniques are used in searching for the solution. The research comprises two components, a practical design problem, and an analytical design problem. The analytical task examines the feasibility of using artificial neural networks to design and implement the control concept. The practical design task will demonstrate the practicality of the method for a flexible beam structure with piezoelectric sensors and actuators.
