H-infinity control of spatially distributed systems

Johannes Reinschke (CUED)

An input-output view of linear, time-invariant, spatially distributed systems is taken in which the system's input and output signals may depend on spatial variables as well as time or frequency. In this view, sensors and actuators (that is, their spatial distribution functions) are part of the (spatially distributed) controller, rather than being part of the plant, and the problem of optimal sensor and actuator placement is thus an integral part of an optimal controller design.

Two controller design procedures will be presented which both have the following as their main steps:

1. calculation of an approximate, finite-dimensional, nominal plant model;

2. error estimation;

3. synthesis of a spatially distributed controller achieving robust stability and robust performance, respectively.

In the talk, we will first give examples of linear, time-invariant, spatially distributed systems. This will lead us to identify (parameter-dependent) integral operators as suitable frequency-domain representations of such systems. We will then comment on the above-mentioned controller design steps, concluding with two numerical examples illustrating the two design procedures.

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