arXiv subjects

Behrouz Touri

Publications and source records attributed to Behrouz Touri.

At least 37 records · Page 2Linked to original sources

arXiv2019

Control of Energy Storage in Home Energy Management Systems: Non-Simultaneous Charging and Discharging Guarantees

In this paper we provide non-simultaneous charging and discharging guarantees for a linear energy storage system (ESS) model for a model predictive control (MPC) based home energy management system (HEMS) algorithm. The HEMS optimally controls the residential load and residentially-owned power sources, such as photovoltaic (PV) power generation and energy storage, given residential customer preferences such as energy cost sensitivity and ESS lifetime. Under certain problem formulations with a linear ESS model, simultaneous charging and discharging can be observed as the optimal solution when there is high penetration of PV power. We present analysis for a proposed HEMS optimization formulation that ensures non-simultaneous ESS charging and discharging operation for a linear ESS model that captures both charging and discharging efficiency of the ESS. The energy storage system model behavior guarantees are shown for various electricity pricing schemes such as time of use (TOU) pricing and net metering. Simulation results demonstrating desirable ESS behavior are provided for each electricity pricing scheme.

math.OC↗

arXiv2018

A Signaling Game Approach to Databases Querying and Interaction

As most users do not precisely know the structure and/or the content of databases, their queries do not exactly reflect their information needs. The database management systems (DBMS) may interact with users and use their feedback on the returned results to learn the information needs behind their queries. Current query interfaces assume that users do not learn and modify the way way they express their information needs in form of queries during their interaction with the DBMS. Using a real-world interaction workload, we show that users learn and modify how to express their information needs during their interactions with the DBMS and their learning is accurately modeled by a well-known reinforcement learning mechanism. As current data interaction systems assume that users do not modify their strategies, they cannot discover the information needs behind users' queries effectively. We model the interaction between users and DBMS as a game with identical interest between two rational agents whose goal is to establish a common language for representing information needs in form of queries. We propose a reinforcement learning method that learns and answers the information needs behind queries and adapts to the changes in users' strategies and prove that it improves the effectiveness of answering queries stochastically speaking. We propose two efficient implementation of this method over large relational databases. Our extensive empirical studies over real-world query workloads indicate that our algorithms are efficient and effective.

cs.DB↗

arXiv2017

Global Games with Noisy Information Sharing

Global games form a subclass of games with incomplete information where a set of agents decide actions against a regime with an underlying fundamental $θ$ representing its power. Each agent has access to an independent noisy observation of $θ$. In order to capture the behavior of agents in a social network of information exchange we assume that agents share their observation in a noisy environment prior to making their decision. We show that global games with noisy sharing of information do not admit an intuitive type of threshold policy which only depends on agents' belief about the underlying $θ$. This is in contrast to the existing results on the threshold policy for the conventional set-up of global games. Motivated by this result, we investigate the existence of equilibrium strategies in a more general collection of threshold-type policies and show that such equilibrium strategies exist and are unique if the sharing of information happens over a sufficiently noisy environment.

cs.SI↗

arXiv2017

Push-sum on random graphs

In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion, which we term the directed infinite flow property, holds and the auxiliary states of agents are uniformly bounded away from zero infinitely often, we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states. Moreover, for a random sequence of graphs generated using a time-varying B-irreducible probability matrix, we establish convergence rates for the proposed push-sum algorithm.

math.OC↗

arXiv2017

The Reach-Avoid Problem for Constant-Rate Multi-Mode Systems

A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. Alur, Wojtczak, and Trivedi have shown that reachability problems for constant-rate multi-mode systems for open and convex safety sets can be solved in polynomial time. In this paper, we study the reachability problem for non-convex state spaces and show that this problem is in general undecidable. We recover decidability by making certain assumptions about the safety set. We present a new algorithm to solve this problem and compare its performance with the popular sampling based algorithm rapidly-exploring random tree (RRT) as implemented in the Open Motion Planning Library (OMPL).

cs.LO↗

arXiv2016

Non-Convex Distributed Optimization

We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. We generalize the results obtained previously to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function. Our analysis shows that this noised procedure converges at a rate of $O(1/t)$.

math.OC↗

arXiv2016

Almost-Sure Reachability in Stochastic Multi-Mode System

A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. We introduce and study a stochastic extension of a constant-rate multi-mode system where the dynamics is specified by mode-dependent compactly supported probability distributions over a set of constant rate vectors. Given a tolerance $\varepsilon > 0$, the almost-sure reachability problem for stochastic multi-mode systems is to decide the existence of a control strategy that steers the system almost-surely from an arbitrary start state to an $\varepsilon$-neighborhood of an arbitrary target state while staying inside a pre-specified safety set. We prove a necessary and sufficient condition to decide almost-sure reachability and, using this condition, we show that almost-sure reachability can be decided in polynomial time. Our algorithm can be used as a path-following algorithm in combination with any off-the-shelf path-planning algorithm to make a robot or an autonomous vehicle with noisy low-level controllers follow a given path with arbitrary precision.

math.OC↗

arXiv2016

On a conjecture of Godsil concerning controllable random graphs

It is conjectured by Godsil that the relative number of controllable graphs compared to the total number of simple graphs on n vertices approaches one as n tends to infinity. We prove that this conjecture is true. More generally, our methods show that the linear system formed from the pair (W, b) is controllable for a large class of Wigner random matrices W and deterministic vectors b. The proof relies on recent advances in Littlewood-Offord theory developed by Rudelson and Vershynin.

math.OC↗

arXiv2015

Controllability of random systems: Universality and minimal controllability

For a large class of random matrices $A$ and vectors $b$, we show that linear systems formed from the pair $(A,b)$ are controllable with high probability. Despite the fact that minimal controllability problems are, in general, NP-hard, we establish universality results for the minimal controllability of random systems. Our proof relies on the recent developments of Nguyen-Tao-Vu concerning gaps between eigenvalues of random matrices.

math.PR↗

arXiv2014

On Endogenous Random Consensus and Averaging Dynamics

Motivated by various random variations of Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging dynamics, i.e.\ an averaging dynamics whose evolution suffers from history dependent sources of randomness. We show that under general assumptions on the averaging dynamics, such dynamics is convergent almost surely. We also determine the limiting behavior of such dynamics and show such dynamics admit infinitely many time-varying Lyapunov functions.

math.OC↗

arXiv2013

Dynamics in atomic signaling games

We study an atomic signaling game under stochastic evolutionary dynamics. There is a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with high probability or mutate with low probability. We analyze the long-run distribution of states and show that, for sufficiently small mutation probability, its support is limited to efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a property that is due to the game having a potential structure with a potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we show that efficient languages eventually predominate the society while reproducing the empirical phenomenon of linguistic drift. The emergence of efficiency in the atomic case can be contrasted with results for non-atomic signaling games that establish the non-negligible possibility of convergence, under replicator dynamics, to states of unbounded efficiency loss.

math.PR↗

arXiv2013

Robust Distributed Averaging on Networks with Adversarial Intervention

We study the interaction between a network designer and an adversary over a dynamical network. The network consists of nodes performing continuous-time distributed averaging. The goal of the network designer is to assist the nodes reach consensus by changing the weights of a limited number of links in the network. Meanwhile, an adversary strategically disconnects a set of links to prevent the nodes from converging. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. We utilize Pontryagin's Maximum Principle (MP) to tackle both problems and derive the optimal strategies. Although the canonical equations provided by the MP are intractable, we provide an alternative characterization for the optimal strategies that highlights a connection with potential theory. Finally, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for this zero-sum game.

math.OC↗

arXiv2013

Robust Distributed Averaging in Networks

In this work, we consider two types of adversarial attacks on a network of nodes seeking to reach consensus. The first type involves an adversary that is capable of breaking a specific number of links at each time instant. In the second attack, the adversary is capable of corrupting the values of the nodes by adding a noise signal. In this latter case, we assume that the adversary is constrained by a power budget. We consider the optimization problem of the adversary and fully characterize its optimum strategy for each scenario.

math.OC↗

arXiv2013

Product of Random Stochastic Matrices

The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic associated with a given sequence of random (row-)stochastic matrices, we prove that the dynamics admits a class of time-varying Lyapunov functions, including a quadratic one. Then, we discuss a special class of stochastic matrices, a class $\Pstar$, which plays a central role in this work. We then introduce balanced chains and using some geometric properties of these chains, we characterize the stability of a subclass of balanced chains. As a special consequence of this stability result, we obtain an extension of a central result in the non-negative matrix theory stating that, for any aperiodic and irreducible row-stochastic matrix $A$, the limit $\lim_{k\to\infty}A^k$ exists and it is a rank one stochastic matrix. We show that a generalization of this result holds not only for sequences of stochastic matrices but also for independent random sequences of such matrices.

math.PR↗

arXiv2012

A General Framework for Distributed Vote Aggregation

We present a general model for opinion dynamics in a social network together with several possibilities for object selections at times when the agents are communicating. We study the limiting behavior of such a dynamics and show that this dynamics almost surely converges. We consider some special implications of the convergence result for gossip and top-$k$ selective gossip models. In particular, we provide an answer to the open problem of the convergence property of the top-$k$ selective gossip model, and show that the convergence holds in a much more general setting. Moreover, we propose an extension of the gossip and top-$k$ selective gossip models and provide some results for their limiting behavior.

cs.SI↗

arXiv2012

A Novel Distance-Based Approach to Constrained Rank Aggregation

We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking into account various issues arising in voting with side constraints. The side constraints of interest include non-uniform relevance of the top and the bottom of rankings (or equivalently, eliminating negative outliers in votes) and similarities between candidates (or equivalently, introducing diversity in the voting process). The proposed distance functions may be seen as weighted versions of the Kendall $τ$ distance and weighted versions of the Cayley distance. In addition to proposing the distance measures and providing the theoretical underpinnings for their applications, we also consider algorithmic aspects associated with distance-based aggregation processes. We focus on two methods. One method is based on approximating weighted distance measures by a generalized version of Spearman's footrule distance, and it has provable constant approximation guarantees. The second class of algorithms is based on a non-uniform Markov chain method inspired by PageRank, for which currently only heuristic guarantees are known. We illustrate the performance of the proposed algorithms for a number of distance measures for which the optimal solution may be easily computed.

cs.GT↗

arXiv2012

On Convergence Rate of Scalar Hegselmann-Krause Dynamics

In this work, we derive a new upper bound on the termination time of the Hegselmann-Krause model for opinion dynamics. Using a novel method, we show that the termination rate of this dynamics happens no longer than $O(n^3)$ which improves the best known upper bound of $O(n^4)$ by a factor of $n$ .

math.DS↗

arXiv2012

Nonuniform Vote Aggregation Algorithms

We consider the problem of non-uniform vote aggregation, and in particular, the algorithmic aspects associated with the aggregation process. For a novel class of weighted distance measures on votes, we present two different aggregation methods. The first algorithm is based on approximating the weighted distance measure by Spearman's footrule distance, with provable constant approximation guarantees. The second algorithm is based on a non-uniform Markov chain method inspired by PageRank, for which currently only heuristic guarantees are known. We illustrate the performance of the proposed algorithms on a number of distance measures for which the optimal solution may be easily computed.

cs.DS↗