In this paper, the H2/H∞ control problem for a class of stochastic discrete-time linear systems with state-, control-, and external-disturbance-dependent noise or (x, u, v)-dependent noise involving multiple decision makers is investigated. It is shown that the conditions for the existence of a strategy are given by the solvability of cross-coupled stochastic algebraic Riccati equations (CSAREs). Some algorithms for solving these equations are discussed. Moreover, weakly-coupled large-scale stochastic systems are considered as an important application, and some illustrative examples are provided to demonstrate the effectiveness of the proposed decision strategies.

This paper addresses the discrete abstraction problem for stochastic nonlinear systems with continuous-valued state. The proposed solution is based on a function, called the bisimulation function, which provides a sufficient condition for the existence of a discrete abstraction for a given continuous system. We first introduce the bisimulation function and show how the function solves the problem. Next, a convex optimization based method for constructing a bisimulation function is presented. Finally, the proposed framework is demonstrated by a numerical simulation.

Based on the concept of sliding mode control, this paper investigates the upper bound covariance assignment with H∞ norm and variance constrained problem for bilinear stochastic systems. We find that the invariance property of sliding mode control ensures nullity of the matched bilinear term in the system on the sliding mode. Moreover, using the upper bound covariance control approach and combining the sliding phase and hitting phase of the system design, we will derive the control feedback gain matrix G, which is essential to the controller u(t) design, to achieve the performance requirements. Finally, a numerical example is given to illustrate the control effect of the proposed method.

Based on the concept of sliding mode control, we study the problem of steady state covariance assignment for bilinear stochastic systems. We find that the invariance property of sliding mode control ensures nullity of the matched bilinear term in the system on the sliding mode. By suitably using Ito calculus, the controller u(t) can be designed to force the feedback gain matrix G to achieve the goal of steady state covariance assignment. We also compare our method with other approaches via simulations.

Currently the long memory behavior is associated to stochastic processes. It can be modeled by different models such like the FARIMA processes, the k-factors GARMA processes or the fractal Brownian motion. On the other side, chaotic systems characterized by sensitivity to initial conditions and existence of an attractor are generally assumed to be close in their behavior to random white noise. Here we show why we can adjust a long memory process to well known chaotic systems defined in dimension one or in higher dimension. Using this new approach permits to characterize in another way the invariant measures associated to chaotic systems and to propose a way to make long term predictions: two properties which find applications in a lot of applied fields.

This paper proposes a new design method of nonlinear filtering and fixed-point smoothing algorithms in discrete-time stochastic systems. The observed value consists of nonlinearly modulated signal and additive white Gaussian observation noise. The filtering and fixed-point smoothing algorithms are designed based on the same idea as the extended Kalman filter derived based on the recursive least-squares Kalman filter in linear discrete-time stochastic systems. The proposed filter and fixed-point smoother necessitate the information of the autocovariance function of the signal, the variance of the observation noise, the nonlinear observation function and its differentiated one with respect to the signal. The estimation accuracy of the proposed extended filter is compared with the extended maximum a posteriori (MAP) filter theoretically. Also, the current estimators are compared in estimation accuracy with the extended MAP estimators, the extended Kalman estimators and the Kalman neuro computing method numerically.

This paper proposes a new design method of a nonlinear filtering algorithm in continuous-time stochastic systems. The observed value consists of nonlinearly modulated signal and additive white Gaussian observation noise. The filtering algorithm is designed based on the same idea as the extended Kalman filter is obtained from the recursive least-squares Kalman filter in linear continuous-time stochastic systems. The proposed filter necessitates the information of the autocovariance function of the signal, the variance of the observation noise, the nonlinear observation function and its differentiated one with respect to the signal. The proposed filter is compared in estimation accuracy with the MAP filter both theoretically and numerically.