Robust Controller Synthesis for Linear Systems with Parameter Uncertainty Using Convex Optimization


A fundamental problem for Control Engineers is that of robust control synthesis for uncertain systems. Uncertainty in a dynamic system can be represented in a variety of ways. Very frequently, physical systems can be modeled by linear time-invariant dynamic equations involving physical parameters which are not known exactly, but rather have values that lie in known intervals. During the eighties, a great number of methods have been proposed for analysis of such systems, but these efforts have not led to the development of comprehensive and computationally efficient methods for robust controller synthesis. On the other hand, during the nineties, it has been shown that a very wide variety of control problems can be reduced to convex optimization problems involving Linear Matrix Inequalities (LMIs) and can be solved efficiently using powerful numerical techniques.

The aim of this research project is to develop an algorithm for robust control synthesis of linear SISO systems with parameter uncertainty using convex optimization. Since the problem, in the general case, is not convex, two different approaches will be adopted. In the first one, the conditions under which the whole problem can be reduced to a convex optimization problem will be studied. In the second approach, an algorithm will be developed to find iteratively a suboptimal or approximate solution to the nonconvex problem. The algorithm will be applied to a real system as well as an international benchmark.