# Optimal and robust control (ORR)

This advanced course will be focused on design methods for optimal and robust control. Major emphasis will be put on practical computational skills and realistically complex problem assignments.

The unifying concept is that of minimization of some *optimization criterion*. The properties of the resulting controller depend upon which criterion is minimized. Minimizing the popular integral-of-square-of criterion (known as LQ-optimal regulation) seeks a trade-off between a regulation error and a control effort. The modern theory introduces the concept of a *system norm*. Minimizing the H_{2} norm leads to the classical LQ/LQG control but offers some generalizations. Minimizing H_{∞} norm gives a controller which is robust (insensitive) to inacurracies in the mathematical model of the system. μ-synthesis is then an extension of H_{∞} methodology for systems with structured uncertainty. Hence robust control can be viewed as an offspring of the powerful paradigm of optimal control.

The above mentioned optimization problems can be solved either offline or online. In the latter case this calls for invoking some nonlinear programming solver once every sampling period. The optimization is then performed over some finite (prediction) horizon. This is the so-called model predictive control (MPC), which gains more and popularity in industry.

Also included in this course will be methods for time optimal and suboptimal control, which have already been found useful in applications with stringent timing requirements. Semidefinite optimization and linear matrix inequalities will also be introduced in this course as these constitute a very flexible framework both for analysis and for numerical computation in robust control. Finally, computational methods for reduction of model and controller order will be covered in the course.