Adaptive stabilization of unstable and nonminimum-phase stochastic systems

Abstract

The system under consideration is the discrete time stochastic system A( z) y n = zB( z) u n + w n driven by a martingale difference sequence { w n }, where A( z) are polynomilas in backward shift operator z with unknown coefficients and both A( z) and B( z) may be unstable. With the purpose of demonstrating theoretical possibility rather than designing a practically applicable control law, this paper constructs an adaptive control that stabilizes the system and simultaneously guarantees strong consistency of the least squares estimates for unknown coefficients.