On Adaptive Stabilization of Time-Varying Stochastic Systems
Lei Guo · SIAM Journal on Control and Optimization · 1990
The basic stability issue of time-varying stochastic systems under adaptive control is studied. A difficulty arising from treating the stochastic case as compared to the deterministic case is the lack of an a priori upper bound on the sample paths of the random noise sequence. A projected gradient algorithm with small stepsize is used, avoiding possible large deviations of the estimates. It is shown that if the unknown parameters vary slowly in some sense, then an adaptive control law can be designed so that the closed-loop system is stable. Issues of performance and robustness are also discussed.