Internal model adaptive control

The problem of servomechanism control of unknown multi-input, multi-output linear systems with stochastic disturbances is addressed here. In deterministic framework Internal Model Principle gives linear stationary controller structures which are robust (or structurally stable) with respect to uncertainty in system parameters, and allow asymptotic tracking of non-decaying reference signals in presence of non-decaying disturbances. An appropriate stochastic framework that reflects important characteristics of realistic disturbances for this robust servomechanism problem is obtained by introducing a jump process in the disturbances. Discrete-time adaptive control schemes based upon this framework are developed so that stopping of adaption results in a robust servomechanism. For a stochastic approximation type update it is shown that strict positive realness of a certain operator associated with a prediction form of the system is sufficient for global convergence of the resulting self-tuning scheme with probability one. The resulting control gives asymptotically optimal control performance.