Adaptive control of stochastic bilinear systems

In this paper, the adaptive control problem is studied for discrete-time stochastic bilinear systems with correlated noises and unknown parameters. A new adaptive control scheme, which is the ELS-based adaptive tracker of the studied systems, is proposed according to the modified certainty equivalence principle. By using the algorithm, the given bounded reference signal can be tracked by the resulting closed-loop system´s output, the global stability of the designed adaptive tracking system is proved. And, the estimates of the unknown parameters are obtained with the strong consistency. The good tracking effect and parameter estimating performance of the proposed algorithm are presented in the two simulation examples.