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This paper aims at familiarizing the reader with Stochastic Hybrid Systems (SHSs) and enabling her to use these systems to model and analyze Networked Control Systems (NCSs). Towards this goal, we introduce two different models of SHSs and a set of theoretical tools for their analysis. In parallel with the presentation of the mathematical models and results, we provide a few simple examples that illustrate the use of SHSs to models NCSs.

This research lays down a mathematical framework within which a system of interacting entities, such as a swarm robotic system, operating in a dynamic and uncertain environment can be analyzed for its properties such as stability, robustness, and emergent behavior. The framework, based upon stochastic differential equations and the Fokker-Planck formalism, allows the calculation of transient and steady state probability densities of the states of these systems. The framework has been applied to two scenarios related to swarm systems. The first scenario relates to a robotic swarm, the dynamics of which is inspired by ant foraging. The article develops a continuous time reaction-diffusion model based on Keller-Segel model of bactetrial chemotaxis and establishes a connection with the Fokker-Planck formalism. In addition, the authors also present a distributed control law in continuous time that combines gradient following for pheromone concentration as well as food scent with random motion seen in ants. The second scenario relates to a system of robots interacting via non-linear potentials and experiencing random excitations. The proposed framework allows calculation of probability density functions of states of the robots, such as positions and velocities, that helps analyze the stability of system and study its response to random excitations.

Solid state drives (SSDs) have seen wide deployment in mobiles, desktops, and data centers due to their high I/O performance and low energy consumption. As SSDs write data out-of-place, garbage collection (GC) is required to erase and reclaim space with invalid data. However, GC poses additional writes that hinder the I/O performance, while SSD blocks can only endure a finite number of erasures. Thus, there is a performance-durability tradeoff on the design space of GC. To characterize the optimal tradeoff, this paper formulates an analytical model that explores the full optimal design space of any GC algorithm. We first present a stochastic Markov chain model that captures the I/O dynamics of large-scale SSDs, and adapt the mean-field approach to derive the asymptotic steady-state performance. We further prove the model convergence and generalize the model for all types of workload. Inspired by this model, we propose a randomized greedy algorithm (RGA) that can operate along the optimal tradeoff curve with a tunable parameter. Using trace-driven simulation on DiskSim with SSD add-ons, we demonstrate how RGA can be parameterized to realize the performance-durability tradeoff.