The first problem is a feedback controller design based on the sampled-data H-infinity synthesis method, where the purpose is to achieve desired feedback characteristics such as robust stability, as well as robust tracking property. We derive a well-defined problem configuration and design procedure for both the fixed hold case and the generalized hold case. This part is a joint work with Prof. Shinji Hara.
In the second part of this talk, we consider a command shaping problem where the design parameter is the exogeneous command while the system is fixed. We optimize the piece-wise constant command to minimize the L2 norm of the tracking error, under constraints on values of control inputs and/or other related signals. The problem is then reduced into a convex optimization problem by relaxing the constraints into ones on finite time horizon.