Optimization and invariance of linear stationary control systems (Q1058495)

The survey deals with the relationship between optimization of linear stationary systems under stochastic external disturbances and nonrobustness or strict unrealizability of optimal controllers. The connection between stochastic optimization theory and invariance theory is discussed. It is shown that the well-known difficulties of invariance theory (instability or nonrobustness when attempts are made to achieve absolute invariance) have the same nature as the corresponding difficulties recently noticed in stochastic control theory. A measure of noninvariance is introduced to optimize the system with respect to the invariance property. Further, the connection with the problem of analytic design of controllers is described as well as the role of singular problems. A number of examples is given.