A universal design procedure for adaptive control of nonminimum phase linear stochastic systems

A universal design procedure for adaptive control of possibly nonminimum phase linear stochastic systems is suggested in this paper. It is based on a class of weighted least squares (WLS) algorithms. The appealing feature of WLS is its self-convergence property, i.e., it converges to a certain random vector almost surely irrespective of the control law design. This “universal convergence” result combined with a method of random search can then be applied easily to construct a self-convergent and uniformly controllable estimated model, and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase ARMAX systems. As an application, we give a simple solution to the well-known stochastic adaptive pole-placement and LQG control problems in the paper