Stochastic Hybrid System Framework Research Articles

A Stochastic Hybrid Framework for Event-Triggered Nonlinear Control Systems With Stochastic Denial of Service Attacks

In this paper, the stability problem for event-triggered nonlinear control systems is addressed in the presence of stochastic denial of service (DoS) attacks on the communication network. Dynamic event-triggered control (DETC) and periodic event-triggered control (PETC) are considered under the stochastic attacks. The stochastic attacks are modeled by a stochastic hybrid timer and a logic variable which is used to identify whether the network is attacked or not. Then the entire closed-loop system can be modeled into the framework of stochastic hybrid systems. Uniform global asymptotic stability in probability is concluded for the resulting stochastic system by proving that the equilibrium set is uniformly globally stable in probability and each neighborhood of the equilibrium set is uniformly globally recurrent. A nonlinear system example is provided to illustrate the effectiveness of the proposed results.

Towards a Modelling Language for Distributed Control of Cyber-Physical Systems

Abstract In this paper we propose a multi-agent stochastic hybrid system framework with asynchronous communication for cyber-physical systems. The communication between agents is realized via some communication functionals that alter the rates of discrete transitions of stochastic agents. The control is then realized using the Fokker-Planck-Kolmogorov equation associated to the macroscopic behavior of the multi-agent system. The coordination is achieved when the multi-agent system lies in the steady-state regime associated to the invariant measures that characterize the limiting behaviors.

A stochastic hybrid systems model of common-cause failures of degrading components

Common-Cause Failures (CCFs) are an important threat to safety critical systems. Most existing CCF models assume that the component failure behavior does not vary over time. Such an assumption is often challenged in practice due to the influence of various degradation mechanisms, e.g., wear, corrosion, fatigue, etc. In this paper, we develop a new model for CCFs considering components degradation. The model is developed in the mathematical framework of Stochastic Hybrid Systems (SHS). The CCFs are modeled as random shock processes that affect a group of components simultaneously and the components degradation processes are modeled by stochastic differential equations derived from physics-of-failures. The benefit of using the SHS model for CCFs is that the developed model is analytically solvable. The system reliability can, then, also be solved analytically in closed form. The proposed CCF modelling framework is demonstrated by a numerical example of a three-unit redundant system and, then, applied to an Auxiliary Feedwater Pump (AFP) system of a Nuclear Power Plant (NPP). A comparison to the Binomial Failure Rate (BFR) model of literature shows that by considering the components degradation processes, the proposed model can accurately describe the CCF effect on the reliability of a system with degrading components.

Perturbation Analysis and Resource Contention Games in Multiclass Stochastic Flow Models

Abstract We present a stochastic hybrid system framework for Stochastic Flow Models (SFMs) with multiple classes and class-dependent performance objectives. Using Infinitesimal Perturbation Analysis (IPA) estimators for the derivatives of such objectives, we formulate and solve resource contention games that contrast system-centric and user-centric optimization in such SFMs.