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Set-valued stochastic integrals and stochastic inclusions in a plane

Władysław Sosulski (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form z s , t φ s , t + 0 s 0 t F u , v ( z u , v ) d u d v + 0 s 0 t G u , v ( z u , v ) d w u , v

Set-valued Stratonovich integral

Anna Góralczyk, Jerzy Motyl (2006)

Discussiones Mathematicae Probability and Statistics

The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.

Some applications of Girsanov's theorem to the theory of stochastic differential inclusions

Micha Kisielewicz (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.

Stability analysis of high-order Hopfield-type neural networks based on a new impulsive differential inequality

Yang Liu, Rongjiang Yang, Jianquan Lu, Bo Wu, Xiushan Cai (2013)

International Journal of Applied Mathematics and Computer Science

This paper is devoted to studying the globally exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays. In the process of impulsive effect, nonlinear and delayed factors are simultaneously considered. A new impulsive differential inequality is derived based on the Lyapunov-Razumikhin method and some novel stability criteria are then given. These conditions, ensuring the global exponential stability, are simpler and less conservative than some of the previous...

Stochastic differential inclusions

Michał Kisielewicz (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The definition and some existence theorems for stochastic differential inclusions depending only on selections theorems are given.

Strong and weak solutions to stochastic inclusions

Michał Kisielewicz (1995)

Banach Center Publications

Existence of strong and weak solutions to stochastic inclusions x t - x s s t F τ ( x τ ) d τ + s t G τ ( x τ ) d w τ + s t n H τ , z ( x τ ) q ( d τ , d z ) and x t - x s s t F τ ( x τ ) d τ + s t G τ ( x τ ) d w τ + s t | z | 1 H τ , z ( x τ ) q ( d τ , d z ) + s t | z | > 1 H τ , z ( x τ ) p ( d τ , d z ) , where p and q are certain random measures, is considered.

Supervisory fault tolerant control with integrated fault detection and isolation: A switched system approach

Hao Yang, Bin Jiang, Vincent Cocquempot, Lingli Lu (2012)

International Journal of Applied Mathematics and Computer Science

This paper focuses on supervisory fault tolerant control design for a class of systems with faults ranging over a finite cover. The proposed framework is based on a switched system approach, and relies on a supervisory switching within a family of pre-computed candidate controllers without individual fault detection and isolation schemes. Each fault set can be accommodated either by one candidate controller or by a set of controllers under an appropriate switching law. Two aircraft examples are...

Switching control

Enrique Zuazua (2011)

Journal of the European Mathematical Society

We analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the dynamics of the system by switching from an actuator to the other in a systematic way so that, in each instant of time, only one actuator is active. We first address a finite-dimensional model and show that, under suitable rank conditions, switching control strategies exist and can be built in a systematic way. To do this we introduce a new variational principle building...

The covering semigroup of invariant control systems on Lie groups

Víctor Ayala, Eyüp Kizil (2016)

Kybernetika

It is well known that the class of invariant control systems is really relevant both from theoretical and practical point of view. This work was an attempt to connect an invariant systems on a Lie group G with its covering space. Furthermore, to obtain algebraic properties of this set. Let G be a Lie group with identity e and Σ 𝔤 a cone in the Lie algebra 𝔤 of G that satisfies the Lie algebra rank condition. We use a formalism developed by Sussmann, to obtain an algebraic structure on the covering...

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