Chair HS

Linear systems subject to constraints

Linear systems have been studied extensively and provide a good description of a system locally. However, if one wants to improve performance in a large region then nonlinearities can no longer be ignored. An autopilot for an airplane to keep the plane at a fixed heading, speed and height can be designed based on a linear model; an autopilot for take-off and landing cannot. One of the main focus areas in our research is to study specific nonlinear behavior. One type of nonlinearity that often gets introduced if you move beyond local control is constraints. The thrust of an engine is limited and cannot be made negative or too large. Also changes in thrust are limited and cannot be achieved too fast. For the simple autopilot with fixed heading, speed and height these issues can be taken care off in an ad-hoc fashion but in an autopilot for take-off these issues become dominant and can no longer be ignored. We are currently looking into systems with both input and state constraints. Again there are many open questions but currently our main objectives are stability, tracking and disturbance rejection. In this project the special structure of a linear system is used where constraints are the only nonlinearity occurring in the system.

In this setting a more or less complete controller design methodology needs to be developed. We have studied the problems of stabilization and tracking/regulation of linear systems subject to input saturation and/or subject to rate limits. Extensions to linear systems subject to state and input constraints are actively being developed. Regarding our future objectives, first of all we want to get a better understanding of the effects of rate-limits and state constraints in stability and regulation problems. Secondly, the problem of reducing the effect of disturbances will be studied. Currently this is only understood in the case of "matched" disturbances. In particular, we will investigate the effect of stochastic disturbances. We will also look into the question how disturbance rejection can be achieved in a Model Predictive Control framework.