A robustness analysis of stochastic adaptive pole placement controls

Stochastic adaptive control of a discrete-time system in the presence of unmodeled dynamics is considered. Unmodeled dynamics can consist of multiplicative as well as additive system uncertainty. The adaptive controller is based on the pole-placement method. For the identification of the nominal system parameters, a stochastic approximation algorithm with parameter projection and modified gain sequence is used. Minimum phase assumption for the nominal system is not required. The self-stabilization mechanism, inherent to adaptive control, is evaluated analytically. Global stability is obtained without requiring the persistency exciting condition to be satisfied. It is shown that the projection mechanism together with the simple modification of the gain sequence in the identification algorithm is sufficient to guarantee robust mean-square boundedness with respect to unmodeled dynamics