My main research interest is in the extension of numerical algorithms to solve the H-infinity optimization problems and its application to practical control-related optimization problems, which cannot be solved by the well-known LMI-based (or, equivalently, Ricatti-equation-based) approach. This talk is on the same line; this time I focus on optimal state estimation problems.

The state observer with the observer matrix (L) optimized in the H2 sense is well known as the Kalman filter. The H-infinity state observer comes with the H-infinity optimal, instead of H2 optimal, observer matrix. The idea of the H-infinity observer is not new; it can be derived in the similar way as the Kalman filter case.

There has not been, however, many applications of the H-infinity observers reported in the literature, mainly because its advantage over other (optimal) observers is not clear. In this talk, I propose a new "actually useful" application of the H-infinity optimization to observer design, along with the nonconvex optimization approach to solve the design problem. As an application example, it is applied to the fault detection filter design for vehicle control.

In the second part of the talk, I present the idea of mismatched state observers and the application of the H-infinity optimization to their design. The system matrices of mismatched observers do not necessarily coincide with those of the plant. This type of state observers is not new either; it is equivalent to the general- structure filters often used in the field of signal processing. This talk presents its novel application to control problems. As an application example, it is applied to the feedback linearization control of lateral motion of heavy-duty vehicles.