Stability, convergence, and performance of an adaptive controlalgorithm applied to a randomly varying system

摘要

The stability and performance of a stochastic adaptive controlnalgorithm applied to a randomly varying linear system is investigated.nUsing techniques from the theory of Markov chains, it is shown that lossnfunctions on the input-output process converge to their expectation withnrespect to an invariant probability. It is shown that the convergence isngeometric, establishing a form of stochastic exponential asymptoticnstability for the closed-loop system. Further results include centralnlimit theorems and the law of large numbers for the input-output andnparameter processes and near consistency and optimality in the casenwhere the disturbances are small