Kalman—Type Filtering for Stochastic Systems with State—Dependent Noise and Markovian Jumps

2009 ◽  
Vol 42 (10) ◽  
pp. 1375-1380 ◽  
Author(s):  
A.–M. Stoica ◽  
V. Dragan ◽  
I. Yaesh
Keyword(s):  
Stochastic Systems ◽  
State Dependent

scholarly journals Nonlinear Finite-Horizon Regulation and Tracking for Systems with Incomplete State Information Using Differential State Dependent Riccati Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Ahmed Khamis ◽  
D. Subbaram Naidu ◽  
Ahmed M. Kamel
Keyword(s):  
Riccati Equation ◽  
Stochastic Systems ◽  
Finite Horizon ◽  
Guidance System ◽  
State Dependent ◽  
Wide Range ◽  
Linearized System ◽  
Estimation And Control ◽  
Regulation And Tracking ◽  
And Control

This paper presents an efficient online technique used for finite-horizon, nonlinear, stochastic, regulator, and tracking problems. This can be accomplished by the integration of the differential SDRE filter algorithm and the finite-horizon state dependent Riccati equation (SDRE) technique. Unlike the previous methods which deal with the linearized system, this technique provides finite-horizon estimation and control of the nonlinear stochastic systems. Further, the proposed technique is effective for a wide range of operating points. Simulation results of a missile guidance system are presented to illustrate the effectiveness of the proposed technique.

scholarly journals Stability of Multi-Dimensional Birth-and-Death Processes with State-Dependent 0-Homogeneous Jumps

2014 ◽  
Vol 46 (01) ◽  
pp. 59-75 ◽  
Author(s):  
Matthieu Jonckheere ◽  
Seva Shneer
Keyword(s):  
Stochastic Systems ◽  
Direct Proof ◽  
Geometric Interpretation ◽  
Stability Conditions ◽  
Birth And Death Processes ◽  
Piecewise Constant ◽  
State Dependent ◽  
The Stability ◽  
Deterministic Dynamical System ◽  
Simple Geometric Interpretation

We study the conditions for positive recurrence and transience of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a telecommunication wire-line or wireless network. First, using an associated deterministic dynamical system, we provide a generic method to construct a Lyapunov function when the drift is a smooth function on ℝN. This approach gives an elementary and direct proof of ergodicity. We also provide instability conditions. Our main contribution consists of showing how discontinuous drifts change the nature of the stability conditions and of providing generic sufficient stability conditions having a simple geometric interpretation. These conditions turn out to be necessary (outside a negligible set of the parameter space) for piecewise constant drifts in dimension two.

scholarly journals RobustH2/H∞Filter Design for a Class of Nonlinear Stochastic Systems with State-Dependent Noise

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Weihai Zhang ◽  
Bor-Sen Chen ◽  
Li Sheng ◽  
Ming Gao
Keyword(s):  
Stochastic Systems ◽  
Filter Design ◽  
Estimation Error ◽  
Design Procedure ◽  
Linear Matrix ◽  
Nonlinear Stochastic Systems ◽  
Worst Case ◽  
State Dependent ◽  
Exogenous Disturbance ◽  
Error Energy

This paper investigates the problem of robust filter design for a class of nonlinear stochastic systems with state-dependent noise. The state and measurement are corrupted by stochastic uncertain exogenous disturbance and the dynamic system is modeled by Itô-type stochastic differential equations. For this class of nonlinear stochastic systems, the robustH∞filter can be designed by solving linear matrix inequalities (LMIs). Moreover, a mixedH2/H∞filtering problem is also solved by minimizing the total estimation error energy when the worst-case disturbance is considered in the design procedure. A numerical example is provided to illustrate the effectiveness of the proposed method.

Numerical Methods for Monitoring Rare Events in Nonlinear Stochastic Systems

2021 ◽  
Vol 22 (6) ◽  
pp. 291-297
Author(s):  
A. A. Kabanov ◽  
S. A. Dubovik
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Large Deviations ◽  
Stochastic Systems ◽  
Rare Events ◽  
Rare Event ◽  
Stable State ◽  
The State ◽  
Nonlinear Stochastic Systems ◽  
State Dependent

In this article, we consider the development of numerical methods of large deviations analysis for rare events in nonlinear stochastic systems. The large deviations of the controlled process from a certain stable state are the basis for predicting the occurrenceof a critical situation (a rare event). The rare event forecasting problem is reduced to the Lagrange-Pontryagin optimal control problem.The presented approach for solving the Lagrange-Pontryagin problem differs from the approach used earlier for linear systems in that it uses feedback control. In the nonlinear case, approximate methods based on the representation of the system model in the state-space form with state-dependent coefficients (SDC) matrixes are used: the state-dependent Riccati equation (SDRE) and the asymptotic sequence of Riccati equations (ASRE). The considered optimal control problem allow us to obtain a numerical-analytical solutionthat is convenient for real-time implementation. Based on the developed methods of large deviations analysis, algorithms for estimating the probability of occurrence of a rare event in a dynamical systemare presented. The numerical applicability of the developed methods is shown by the example of the FitzHugh-Nagumo model for the analysis of switching between excitable modes. The simulation results revealed an additional problem related to the so-called parameterization problem of the SDC matrices. Since the use of different representations for SDC matrices gives different results in terms of the system trajectory, the choice of matrices is proposed to be carried out at each algorithm iteration so as to provide conditions for the solvability of the Lagrange-Pontryagin problem.

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