Stochastic>tex<$H_2/H_infty $>/tex<Control WithState-Dependent Noise

Abstract

This paper discusses the stochastic 2 control problem with state-dependent noise. By means of the stabilization, exact observability and stochastic detectability of stochastic systems, the infinite horizon stochastic 2 control design is developed. For the finite horizon 2 control problem, our results generalize the corresponding deterministic ones to the stochastic models. Finally, the observer-based suboptimal stochastic 2 control is discussed in which the state variables cannot be measured directly, and a feasible design algorithm is proposed.Index Terms-Coupled Riccati equations, exact observability, state-dependent noise, stochastic detectability, stochastic 2 control.

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

“…control problem has a pair of solutions. Obviously, ðu à ; v Ã Þ is the Nash equilibrium strategies [7], such that J 1 ðu à ; v à ; x 0 ; iÞ 6 J 1 ðu à ; v; x 0 ; iÞ; J 2 ðu à ; v à ; x 0 ; iÞ 6 J 2 ðu; v à ; x 0 ; iÞ; i 2 N:…”

“…It has attracted much attention and has been widely applied to various fields, such as control theory (see [2,7,15,19], and reference therein), management science and economics [9], ecology [34], etc. Recent advances in stochastic LQ control problems have allowed us to expand the study on the Nash games for stochastic systems with state-and control-dependent noise (see [5,6,17,18]).…”

On the Information Transmission Ability of Nonlinear Stochastic Dynamic Networks

“…That is, the stochastic part of fluctuation is absorbed by with , where is a standard Wiener process [16][17][18] (Brownian motion) and the change of linear dynamic network by the random fluctuation source is denoted by .…”

“…In the conventional notation of engineering and system science, the linear stochastic dynamic network in (2) can be represented by the following Ito stochastic dynamic network [16]:…”

“…In accordance with system gain viewpoint, the ratio of output to input signal energy of a stochastic dynamic network is determined for all possible input signals. Then the maximum ratio is denoted as the information transmission ability, i.e., from the system (network) gain perspective [16][17][18][19][20]. This measure of information transmission ability is more dependent on the system characteristics of the studied dynamic network rather than the input signals.…”