ADAPTIVE STABILIZATION OF UNSTABLE AND NONMINIMUM-PHASE STOCHASTIC-SYSTEMS

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) and B(z) are polynomials 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.