Thesis title:	Event-Based Control Strategies Based on Differential Flatness
PhD Programme:	Information and Communication Technology
Supervisor:	Arvo Kaldmäe, Research Scientist
Offered by:	School of Information Technologies, Department of Software Science

Description
The PhD project is a part of a bigger project with the aim to develop a new modern method for controlling dynamical systems by combining the flatness-based feedforward control with the ideas of an event-based control. The property of differential flatness provides a very good control solution, but is sensitive to disturbances and model uncertainties. By combining it with an event-based control approach one can eliminate the negative aspects of the flatness-based control. Namely, the event generator reacts to model uncertainties and external disturbances and creates events, at which the flatness-based controller is updated with the data from the sensors. There are different theoretical and practical aspects that PhD candidate can study within the project.
The concept of differential flatness was introduced for control systems about 25 years ago and has become a very useful property. It is especially useful for tracking control, since for a flat control system it is relatively easy to construct a feedforward controller, such that the exact tracking is achieved. However, flatness and flatness-based control need an exact model to be effective, which is seldom achieved in practical applications.
Event-based control is a control method that closes the feedback loop only if an event indicates that it is necessary. This event can be, for example, that the output trajectory deviates from the desired trajectory too much. The main advantages of the event-based control are irregular sampling and reduced communication between system components, which can save energy. Therefore, it has much potential in the areas of resource-aware control and network-based control. The basic configuration of event-based control consists of the event generator, the controller and the control input generator. The event generator continuously compares the current system behavior and the desired behavior and generates events, when the differences become too large. The controller determines the control input at the event times, based on the information sent to it at these times. The control input generator (usually it is a simple zero-order hold) uses the values of the control input received from the controller to generate continuous-time input for the plant until the next event appears. The supervisor already constructed the event-based control strategy for differentially flat systems. The tasks for the PhD candidate are as follows: 1) generalize the ideas of flatness-based control to non-flat systems; 2) generalize the novel event-based control approach to non-flat systems; 3) prove the stability of the closed-loop system; 4) test and implement it on practical systems. Note that, depending on how difficult these tasks are to follow, one can add tasks or change them. For example, one can modify the control approach to deal with system constraints or to make it optimal in some sense.

Qualifications
Master’s degree in control theory, systems and control, applied mathematics or related fields.
The applicants should fulfill the following requirements:

• knowledge in Matlab
• excellent English language skills
• motivation to do theoretical research