Mathematical optimization and robust control synthesis

Nowadays, performance requirements imposed on system control designs have become more and more complicated. For many problems, it is very hard or even impossible to obtain analytic solutions. In recent years, powerful numerical computational tools for solving mathematical programming/optimization problems have been developed. This makes it possible to formulate control design problems as mathematical programming problems and then solve them using numerical optimization techniques. In this thesis, we show that two classes of important robust control design problems can be tackled by employing some newly-emerged mathematical optimization techniques.; In the first part of the thesis, we present a methodology to address the general multiobjective (GMO) control problem involving the ℓ ₁ norm, $H2$ norm, $H\infty$ norm and time-domain constraint (TDC). We show that the auxiliary problem resulting after imposing a regularizing condition always admits an optimal solution. Suboptimal solutions with performance arbitrarily close to the optimal cost can be obtained by constructing two sequences of finite dimensional convex optimization problems whose objective values converge to the optimum from below and above. Numerical implementation of the proposed methodology is discussed and several numerical examples are presented to illustrate the effectiveness of the proposed methodology.; In the second part, we consider the integrated parameter and control (IPC) design problem where the system structure parameters enter the state-space representation of the system in a rational manner. Converging finite-dimensional sub-optimal problems are constructed and solved via a linear relaxation technique, whereby a global optimal solution to the IPC problem is computed within any given performance tolerance. Two numerical examples are provided.