Symbolic Computation and Control

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Symbolic Computation and Control consists of two interrelated parts. In the first part the basic techniques for the digital control of linear dynamical systems using feedback will be discussed. For such systems stability will be addressed as well as the technique of pole placement by state feedback to solve the regulation problem. This basic framework will be extended by introducing state observers in order to solve the regulation problem by output feedback. Next the course will focus on tracking problems. Here the aim is to have a system follow a trajectory, rather than just stabilize, which is achieved by extending the earlier set-up for output feedback. The first part of the course is concluded by a discussion on optimal control, which make use of a utility function to determine optimality, and which can widely be applied in practice. The second part of this course focusses on computational issues that are related to the field of systems and control. Using modern software packages such as Maple and Mathematica, the area of symbolic computation will be explored. It will be demonstrated how speed, efficiency and memory usage considerations often lead to surprising and fundamentally different algorithmic solutions in a symbolic or exact context. Examples of applications involve: stability of linear systems, model approximations. After completing this course students will be able to design state feedback and output feedback control laws for regulation and tracking problems. Students will be able to solve computation problems involving free parameters with adequate algorithms, avoiding pitfalls from approximate numerical computation.