A global optimization approach to scalar H2/H∞ control

Various approaches to the mixed H2/H_∞· control problem are proposed in the literature. The solution is often obtained by means of classical techniques (i.e. solving a Riccati problem) or by means of convex optimization procedures. With the aim to synthesize a fixed-structure controller for an uncertain plant, a global optimization approach to a single-input single-output (SISO) H₂/H_∞ problem is proposed. In particular, robust stability is guaranteed and a nominal quadratic performance index is minimized by solving an equivalent nonconvex semi-infinite optimization problem. The resulting design method is tested by synthesizing a PID controller for a plant with fractionary uncertainties and by verifying its performances through simulations.