Improved adaptive control of stochastic systems

The aim of the present paper is to show how the invariant embedding technique and fiducial approach may be used to solve the problem of improved adaptive controlling a discrete-time stochastic linear system in which the state transition matrix and the control driven matrix are unknown. This is the case when the certainty equivalence principle does not yield the admissible adaptive control laws for the present problem. The proposed approach does not require the arbitrary selection of priors as in the Bayesian approach. It makes it possible to simplify the problem of adaptive optimization of stochastic systems and, if the system noise and/or the measurement noise are Gaussian, to carry out the algorithm in closed form. The examples are given to illustrate the suggested methodology.