Nonlinearities are present in all real physical systems. Typically a nonlinear system is modeled by an ordinary differential equation (ODE) dx/dt = f(x,u) where x is a vector of physical variables and u is the input.

Some current activities concern

Differential-algebraic systems

Models of physical systems are usually not directly in ODE form but contain a mixture of algebraic and differential equations. We investigate computational methods that do not require the model to be converted to ODE form. These include methods for optimal control, controllability analysis and model reduction.

Dynamics of rigid bodies

Many engineering systems involve control of rigid bodies, e.g. aircraft and industrial robots. The structure of the rigid body equations is well adpated to the use of Lyapunov and backstepping techniques. Also rigid body mechanics is a good test bed for many concepts in the analysis and design of control systems.

Algebraic Methods in Nonlinear Identification

Many systems can be modeled using polynomial equations in the physical variables and their derivatives. There are ways of systematically reducing such systems to standard forms (Ritt-Seidenberg algorithms) where questions like observability and identifiability can be easily studied. Recently these methods have been extended to discrete time problems.