Stochastic adaptive control: Conditions for the stability and convergence

The paper establishes simple sufficient conditions for the global stability and a.s. convergence for a stochastic adaptive control algorithm. At each discrete observation time the unknown parameters of the system are estimated using a recursive least squares estimator. A minimum variance control policy is implemented as if these estimates were the exact system parameters. The stability results do not rely on the positive real condition imposed by certain methods of analysis, algorithm monitoring or persistent excitation. The results are shown to apply to the Self Tuning Regulator and a stochastic adaptive controller. The theory can also be used for the robustness and stability analysis of more general adaptive control algorithms.