Theory and design of robust control systems

Project members: C.W. Scherer

Modern controller design techniques are based on models of a physical plant which are obtained using first principles or system identification. It is often possible to incorporate predictable changes of the physical plant into a model, such as variations in measurable parameters. In addition, one might as well encounter unpredictable or unmeasurable plant variations or system parts which are hard if impossible to be approximated by simple models. In order to cope with the latter effects, it is hence reasonable to base the controller design on a whole set of models which can be parameterized in a simple fashion. Combining both uncertainty structures, any realistic control design methodology should hence start with a parameterized family of model sets, the parameter capturing the measurable changes of the plant and the model sets representing unpredictable system variations. The design algorithm should lead to a parameterized or scheduled family of controllers which achieves not only one but a variety of design objectives for all elements in the model set.

Performance objectives are either specified in a qualitative manner (regulation, disturbance decoupling) or they can be quantified using system norms or gains (with the -norm and -norm as typical examples). For linear time invariant systems, it is by now well-established how to solve many of these problems independently. However, the theory of designing controllers achieving multiple objectives for one model or for a whole model set, the so-called robust multi-objective design, is still in its infancy.

The main goal of our research is to push further new developments in the area of robust multi-objective control and to combine the corresponding controller synthesis with scheduling techniques if the system varies with a measurable parameter.