We propose to develop an Hoo optimization approach which will allow in addition to the customary frequency-domain specifications, explicit time-domain specifications. The latter specifications include shaping of the transient characteristics of the system by requiring that the step response lies in a given envelope, specifying that actuator signals do not exceed certain hard bounds in order to avoid saturation, etc. We refer to this approach as Constrained Hoo optimization. In the proposed approach the time-domain specifications are introduced as constraints onto the Hoo optimization. We expect to establish a decomposition of the latter problem to i) a finite dimensional convex optimization problem and ii) a standard Hoo optimization problem. This method will be capable of handling structured model uncertainty in as much the same way as Hoo optimization methods such as u-synthesis do. The approach will also inherit the algorithmic nature of Hoo optimization methods and systematically provide trade-offs between conflicting specifications, including specifications posed directly in the time-domain. It will be capable of revealing the achievable performance limits at a reasonable computational cost. We expect to establish that the controllers produced within this framework will have properties that guarantee effective degree reduction to the level of standard Hoo optimal controllers and specialized controller reduction schemes will be developed. In summary, our expected results should provide a general, systematic and practical approach for robust multivariable control system design with structured uncertainty, in which established measures of performance in the time-domain are incorporated explicitly, while the applicability of standard Hoo methods is retained in full. We believe that the proposed research offers a unique approach to the important subject of Robust Control of Constrained Systems.
