A Stochastic Hybrid Approach to Decentralized Networked Control: Stochastic Network Delays and Poisson Pulsing Attacks

Abstract

By designing the decentralized time-regularized (Zeno-free) event-triggered strategies for the state-feedback control law, this paper considers the stochastic stabilization of a class of networked control systems, where two sources of randomness exist in multiple decentralized networks that operate asynchronously and independently: the communication channels are constrained by the stochastic network delays and also by Poisson pulsing denial-of-service (Pp-DoS) attacks. The time delay in the network denotes the length from a transmission instant to the corresponding update instant, and is supposed to be a continuous random variable subject to certain continuous probability distribution; while the attacks' cardinal number is a discrete random variable supposed to be subject to Poisson distribution, so the inter-attack time, i.e., the time between two consecutive attack instants, is subject to exponential distribution. The considered system is modeled as a stochastic hybrid formalism, where the randomness enters through the jump map into the reset value (the inter-attack time directly related) of each triggered strategy. By only sampling/transmitting state measurements when needed and simultaneously by taking the specific medium access protocols into account, the designed event-triggered strategies are synthesized in a state-based and decentralized form, which are robust (tolerable well) to stochastic network delays, under different tradeoff-conditions between the minimum inter-event times, maximum allowable delays (i.e., potentially tolerable delays) and the frequencies of attacks. Using stochastic hybrid tools to combine attack-active parts with attack-over parts, the designed triggered strategies, if designed well according to the actual system needs, can tolerate (be resilient to) the Pp-DoS attacks and stochastic network delays without jeopardizing the stability and Zeno-freeness.