Performance limits in adaptive control

Minimum variance control of difference equation systems with time-varying stochastic parameters are studied. The optimal control law is derived under the assumption that all previous but not the current parameter values are known. This is used to give performance limits for dual control. In particular, it is shown that too much parameter uncertainty may cause the system to be unstable in the mean-square sense, whatever control law is used. Furthermore, it is shown that the optimal system may show a behavior that makes it difficult to test suboptimal control laws using simulation studies.