Search

This paper studies linear quadratic (LQ) control of forward and backward stochastic difference system (FBSDS). There are two main contributions: first, the equivalent condition is obtained for the solvability of optimal control of FBSDS with multi-multiplicative noises under complete information and the analytic solution is also stated by the proposed Riccati equation. Second, the result of complete information is deduced to the situation of incomplete information, that is, the equivalent conditions of solvability and analytical solution are obtained based on Riccati equation. The main technique we use is to solve the forward–backward stochastic difference equations (FBSDEs) originated from maximum principle (MP). [ABSTRACT FROM AUTHOR]

In this paper, the generalized Lyapunov equation approach is used to study stochastic stabilization/detectability with state-multiplicative noise. Some practical test criteria for stochastic stabilization and detectability, such as stochastic Popov--Belevitch--Hautus Criterion for exact detectability, are obtained. Moreover, useful properties of the generalized Lyapunov equation are derived based on critical stability and exact detectability introduced in this paper. As applications, first, the stochastic linear quadratic regulator as well as the related generalized algebraic Riccati equation are discussed extensively. Second, the infinite horizon stochastic [H.sub.2]/[H.sub.[infinity]] control with state- and control-dependent noise is also investigated, which extends and improves the recently published results. Index Terms--Exact detectability, generalized algebraic Riccati equation (GARE), spectrum, stabilization, stochastic linear quadratic regulator, [H.sub.2]/[H.sub.[infinity]] control.

This paper considers the problem of robust channel estimation for direct-sequence code-division multiple-access (DS-CDMA) systems with time-varying multipath fading channels. Due to the lack of accurate knowledge of model dynamics and statistics of system noises, a polynomial H[infinity] channel estimator is developed by virtue of the Krein space theory. The estimator is calculated by performing a J-spectral factorization. In this paper, under some conditions, we obtain a closed-form solution to this J-spectral factorization, which greatly reduces the computational load of the estimator design. The simulation results show that the proposed H[infinity] estimator provides a robust estimation performance against various types of noises and modeling errors. Index Terms--Direct-sequence code-division multiple access (DS-CDMA), H[infinity] channel estimation, multipath fading channels, polynomial approach, robustness.

This brief is concerned with robust Kalman filtering for linear discrete-time systems with both instantaneous and single delayed measurements. The norm-bounded parameter uncertainties enter into the system matrix of the state space model. A new approach through the re-organization of measurements is proposed to improve the efficiency of computation. A sufficient condition for the existence of a robust Kalman filter is derived. The performance is clearly demonstrated through analytical results and simulation experiments. Index Terms--Discrete systems, Kalman filters, robustness, single delay.

This paper proposes and analyzes a new distributed power-control algorithm based on the theory of stochastic approximation. The power-control problem is first converted into a stochastic approximation problem in which the zero point of a specific function is determined. A distributed power-control algorithm is then derived and its convergence properties are analyzed using standard techniques. In the distributed algorithm, each user iteratively updates its power level by using estimates of the inverse of the signal-to-interference ratio (SIR) of its channel. No knowledge of the channel gains or state information of other users is required. Moreover, the algorithm is robust in the sense that it can handle errors in the bit-error rate estimates, and hence, can be used in practical scenarios. Convergence of the algorithm is analyzed in the almost-sure sense. Index Terms--Decentralized control, power control, stochastic approximation, time-varying systems.

This paper is concerned with the finite horizon [H.sub.[infinity]] full-information control for discrete-time systems with multiple control and exogenous input delays. We first establish a duality between the [H.sub.[infinity]] full-information control and the [H.sub.2] smoothing of a stochastic backward system in Krein space. Like the duality between the llinear quadratic regulation (LQR) of linear systems without delays and the Kalman filtering, the established duality allows us to address complicated multiple input delay problems in a simple way. Indeed, by applying innovation analysis and standard projection in Krein space, in this paper we derive conditions under which the [H.sub.[infinity]] full-information control is solvable. An explicit controller is constructed in terms of two standard Riccati difference equations of the same order as the original plant (ignoring the delays). As special cases, solutions to the [H.sub.[infinity]] state feedback control problem for systems with delays only in control inputs and the [H.sub.[infinity]] control with preview are obtained. An example is given to demonstrate the effectiveness of the proposed [H.sub.[infinity]] control design. Index Terms--Discrete-time system, [H.sub.[infinity]] control, multiple input delays, Riccati difference equation, smoothing estimation.