Decomposition and control of a class of nonlinear stochastic systems: theory and its application

2001 ◽  
Author(s):  
A.S.C. Sinha ◽  
S.E. Lyshevski
Keyword(s):  
Systems Theory ◽  
Stochastic Systems ◽  
Nonlinear Stochastic Systems ◽  
And Control

scholarly journals Feedback Stabilization for a Class of Nonlinear Stochastic Systems with State- and Control-Dependent Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yu-Hong Wang ◽  
Tianliang Zhang ◽  
Weihai Zhang
Keyword(s):  
State Feedback ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Global State ◽  
Nonlinear Stochastic Systems ◽  
Feedback Stabilizability ◽  
And Control

This paper mainly studies the state feedback stabilizability of a class of nonlinear stochastic systems with state- and control-dependent noise. Some sufficient conditions on local and global state feedback stabilizations are given in linear matrix inequalities (LMIs) and generalized algebraic Riccati equations (GAREs). Some obtained results improve the previous work.

scholarly journals A Review on Analysis and Synthesis of Nonlinear Stochastic Systems with Randomly Occurring Incomplete Information

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hongli Dong ◽  
Zidong Wang ◽  
Xuemin Chen ◽  
Huijun Gao
Keyword(s):  
Incomplete Information ◽  
Stochastic Systems ◽  
Future Research ◽  
Missing Measurements ◽  
Parameter Uncertainties ◽  
Nonlinear Stochastic Systems ◽  
Randomly Occurring Uncertainties ◽  
Analysis And Synthesis ◽  
System States ◽  
And Control

In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out.

Robust H∞ Control for Uncertain Nonlinear Stochastic Systems with Delayed State and Control

2011 ◽  
Vol 58-60 ◽  
pp. 685-690
Author(s):  
Cheng Wang ◽  
Yun Xu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Stochastic Systems ◽  
Stochastically Stable ◽  
Nonlinear Uncertain Systems ◽  
And Control

This paper considers the issue of robust H∞ control for a class of nonlinear uncertain systems with delayed states and control, and the feedback controller is designed. By constructing proper Lyapunov-krasovskii function, the resulting closed-loop system is stochastically stable for all admissible uncertainties, time-delays and nonlinearities, and satisfies a prescribed H∞ performance. Sufficient conditions for the system to be robustly stochastically asymptotically stable are derived, by using linear matrix inequalities and Lyapunov-krasovskii stability theory. The feedback controller is obtained by solving the linear matrix inequalities. Numerical example is provided to show the validity of the proposed approaches.

Improved Statistical Linearization for Analysis and Control of Nonlinear Stochastic Systems: Part II: Application to Control System Design

1981 ◽  
Vol 103 (1) ◽  
pp. 22-27 ◽  
Author(s):  
J. J. Beaman ◽  
J. K. Hedrick
Keyword(s):  
Stochastic Systems ◽  
Pole Placement ◽  
Linear Feedback ◽  
Statistical Linearization ◽  
Feedback Controllers ◽  
Nonlinear Stochastic Systems ◽  
Input Noise ◽  
Gaussian Method ◽  
And Control ◽  
Digital Simulations

Using the techniques of Gaussian statistical linearization and the extension given in Part I, this paper describes the synthesis of linear feedback controllers for nonlinear stochastic systems. The method used is that of pole placement of the statistically linearized “eigenvalues”. The technique is described in terms of a design example, a position servomechanism with backlash, it is shown that for this type of system the standard Gaussian method works well for large input noise levels but can lead to an unstable design for low input levels. The extended fourth cumulant method is satisfactory for both cases studied. The results of the analysis are compared to Monte Carlo digital simulations to test their accuracy.

Sign in / Sign up

Export Citation Format

Share Document