Correlation free forms for nonlinear stochastic systems

H∞ for Nonlinear Stochastic Systems

In this paper we develop a H∞ type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain prop...

Controllers for Nonlinear Systems Using Normal Forms

We describe a method of designing local nonlinear controllers for the purposes of stabilizing unstable fixed points (UFP’s) of nonlinear systems by using the methods of normal form theory [Wiggins, 1990; Guckenheimer & Holmes, 1983] to determine a coordinate transformation which makes the system “simpler”. In the transformed system we design a local linear controller to stabilize the desired UF...

Probabilistic Fault Diagnosis for Nonlinear Stochastic Systems

The paper focuses on fault detection and isolation (FDI) in stochastic nonlinear systems using Bayesian statistics. The main concept of this approach leans on a probabilistic model, which estimates the occurrences of faults by probabilities. The methodology consists in probabilistic mapping of the measured data into a fault variable, which acts as an indicator of considered modes of the systems...

Dynamics of Nonlinear Stochastic Systems

Stochastic Controllability of Nonlinear Systems

In the paper stochastic dynamical control systems described by nonlinear stationary ordinary differential state equations are considered. Using a generalized open mapping theorem, sufficient conditions for constrained local stochastic controllability in a given time interval are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed con...