Système de transition d'états

En informatique théorique, un système de transition d'états est une forme de machine abstraite utilisée pour modéliser un ou des calcul(s). Un système de transition d'états est constitué d'un ensemble d'états et d'un ensemble de transitions d'un état à un autre, qui peuvent être étiquetées ; une même étiquette peut apparaître sur plusieurs transitions. Si l'ensemble des étiquettes est un singleton, on peut omettre l'étiquetage. Les systèmes d'états-transitions sont des graphes orientés. Définitions formelles Système de transition d'états non étiqueté Un système de transition d'états non étiqueté est un couple (S, \rightarrow), où S est l'ensemble des états et \rightarrow \subseteq S \times S est la relation de transition. Si p et q sont deux états, (p, q) \in \rightarrow signifie qu'il existe une transition de p à q, et on l'écrit p \rightarrow q

Scalable scheduling of energy control systems

Xuan Truong Nghiem

Peak power consumption is a universal problem across energy control systems in electrical grids, buildings, and industrial automation where the uncoordinated operation of multiple controllers result in temporally correlated electricity demand surges (or peaks). While there exist several different approaches to balance power consumption by load shifting and load shedding, they operate on coarse grained time scales and do not help in de-correlating energy sinks. The Energy System Scheduling Problem is particularly hard due to its binary control variables. Its complexity grows exponentially with the scale of the system, making it impossible to handle systems with more than a few variables. We developed a scalable approach for fine-grained scheduling of energy control systems that novelly combines techniques from control theory and computer science. The original system with binary control variables are approximated by an averaged system whose inputs are the utilization values of the binary inputs within a given period. The error between the two systems can be bounded, which allows us to derive a safety constraint for the averaged system so that the original system's safety is guaranteed. To further reduce the complexity of the scheduling problem, we abstract the averaged system by a simple single-state single-input dynamical system whose control input is the upper-bound of the total demand of the system. This model abstraction is achieved by extending the concept of simulation relations between transition systems to allow for input constraints between the systems. We developed conditions to test for simulation relations as well as algorithms to compute such a model abstraction. As a consequence, we only need to solve a small linear program to compute an optimal bound of the total demand. The total demand is then broken down, by solving a linear program much smaller than the original program, to individual utilization values of the subsystems, whose actual schedule is then obtained by a low-level scheduling algorithm. Numerical simulations in Matlab show the effectiveness and scalability of our approach.

IEEE Press2015

Self-organization of spatial solitons

Demetri Psaltis, Ye Pu

We present experimental results on the transverse modulation instability of an elliptical beam propagating in a bulk nonlinear Kerr medium, and the formation and self-organization of spatial solitons. We have observed the emergence of order, self organization and a transition to an unstable state. Order emerges through the formation of spatial solitons in a periodic array. If the initial period of the array is unstable the solitons will tend to self-organize into a larger (more stable) period. Finally the system transitions to a disordered state where most of the solitons disappear and the beam profile becomes unstable to small changes in the input energy. © 2005 Optical Society of America.

2005

Scalable scheduling of energy control systems

Xuan Truong Nghiem

IEEE Press2015