Linear periodic controller design

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In systems control, the objective is to make a physical system (the plant) act in a desired manner through the use of an (automatic) controller, e.g. an autopilot (the controller) is used on an aircraft (the plant) to maintain speed, altitude and direction. The first step in control system design is to obtain a mathematical model of the plant, and then one designs a controller, described by a mathematical equation, which is typically implemented in software. This process is often difficult due to uncertainty in the plant model.Most controllers presently implemented are described by linear equations with fixed parameters, such as the well-known proportional-integral-differential (PID) compensator. As microprocessors become faster, it is becoming possible to implement (possibly complicated) nonlinear and/or time-varying controllers. The objective here is to develop advanced linear periodic controllers which provide enhanced tolerance to plant model uncertainty as well as good performance. We are considering three different contexts:(i) adaptive control, in which the plant parameters are unknown and possibly rapidly time-varying,(ii) robust control, in which the plant is poorly known, but the parameters are fixed, and(iii) control with delay, in which the plant model is well known but there is an uncertain delay in the feedback loop, such as when carrying out control over the Internet.This work has potential long-term benefits wherever control is used, from robotics to aerospace to industrial automation, and my former graduate students work in all of these areas.