ABSTRACT
In this chapter, problems of optimal isolation are considered for the case where the applied external disturbance is not completely known. The disturbance is assumed to belong to a specified class of possible disturbances. To allow for the uncertainty of information about the external disturbance, a game theory approach is used. The problem of optimal isolation is considered to be a “game with nature”. The “move” of the isolator designer is to choose the control law (isolator characteristic). This control law must use only the available (incomplete) information about the external disturbance. The “move” of nature is to generate the worst disturbance in response to the control law suggested by the designer. Under these conditions, the optimal isolator is that one which maximizes the isolation efficiency, provided that the worst disturbance is applied. This approach discriminates against the designer, in the sense that nature is assumed to be able to foresee the designer’s decision. The problem of optimal protection of a single-degree-of-freedom system against the disturbances subject to integral constraints is solved. The possibilities of the optimal isolation of successive instantaneous impulses are investigated for the case where the intensity and direction of each impulse, as well as the time intervals between them, are not completely known. In Chapter 8, dealing with numerical methods for limiting performance analyses, we will consider the case where the uncertainty in external disturbances is described by a “corridor” (envelope) to which these disturbances may belong.
