The convergence theorems for the stochastic approximation (SA) algorithm with expanding truncations are first presented, which the system identification methods discussed in the paper are essentially based on. Then, the recursive identification algorithms are respectively defined for the multivariate errors-in-variables systems, Hammerstein systems, and Wiener systems. All es- timates given in the paper are strongly consistent.

In this paper, we will investigate the maximum capability of adaptive feedback in stabilizing a basic class of discrete-time nonlinear systems with both multiple unknown parameters and bounded noises. We will present a complete proof of the polynomial criterion for feedback capability as stated in "Robust stability of discrete-time adaptive nonlinear control" (C. Li, L.-L. Xie. and L. Guo, IFAC World Congress, Prague, July 3-8, 2005), by providing both the necessity and sufficiency analyzes of the stabizability condition, which is determined by the growth rates of the system nonlinear dynamics only.

Over the last three decades, the certainty equivalence principle has been the fundamental paradigm in the design of adaptive control laws. It is well known, however, that for general control criterions the performance achieved through its use is strictly suboptimal. In order to overcome this difficulty, two different approaches have been proposed: i) the use of cost-biased parameter estimators; and ii) the injection of probing signals into the system so as to enforce consistency in the parameter estimate. This paper presents an overview of the cost-biased approach. New insight is achieved in this paper by the formalization of a general cost-biased principle named “Bet On the Best”-BOB. BOB may work in situations in which more standard implementations of the cost-biasing idea may fail to achieve optimality.

This paper is concerned with a stochastic optimal control problem where the controlled system is described by a forward–backward stochastic differential equation (FBSDE), while the forward state is constrained in a convex set at the terminal time. An equivalent backward control problem is introduced. By using Ekeland’s variational principle, a stochastic maximum principle is obtained. Applications to state constrained stochastic linear–quadratic control models and a recursive utility optimization problem are investigated.