Least Squares Identification and Adaptive Control of Stochastic High-Order Nonlinear Systems

This letter investigates the least-squares identification and adaptive control problem for stochastic high-order nonlinear systems. Noting that none of the existing adaptive designs on stochastic high-order nonlinear systems considers least-squares identification, the merits of our design are that all parameter estimates converge at similar rates, leading to more stable and predictable system behavior. Specifically, we first propose a novel least-squares identification method that uses an unfiltered regressor, then a new adaptive controller is designed to ensure that all system states converge to zero almost surely and that the closed-loop system is globally stable in probability. Moreover, by selecting appropriate estimator parameters, the convergence of the proposed estimator is ensured. Finally, two simulation examples, including Chua’s circuit system, are provided to validate the effectiveness of the proposed designs.