arXiv subjects

Jorge Cortes

Publications and source records attributed to Jorge Cortes.

At least 73 records · Page 4Linked to original sources

arXiv2018

Tutorial on dynamic average consensus: the problem, its applications, and the algorithms

This paper considers the problem of dynamic average consensus algorithm design for a group of communicating agents. This problem consists of designing a distributed algorithm that enables a group of agents with communication and computation capabilities to use local interactions to track the average of locally time-varying reference signals at each agent. The objective of this article is to provide an overview of the dynamic average consensus problem that serves as a comprehensive introduction to the problem definition, its applications, and the distributed methods available to solve them. Our primary intention, rather than providing a full account of all the available literature, is to introduce the reader, in a tutorial fashion, to the main ideas behind dynamic average consensus algorithms, the performance trade-offs considered in their design, and the requirements needed for their analysis and convergence guarantees.

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arXiv2018

On the detectability of transiting planets orbiting white dwarfs using LSST

White dwarfs are one of the few types of stellar objects for which we know almost nothing about the possible existence of companion planets. Recent evidence for metal contaminated atmospheres, circumstellar debris disks and transiting planetary debris all indicate that planets may be likely. However, white dwarf transit surveys are challenging due to the intrinsic faintness of such objects, the short timescale of the transits and the low transit probabilities due to their compact radii. The Large Synoptic Survey Telescope (LSST) offers a remedy to these problems as a deep, half-sky survey with fast exposures encompassing approximately 10 million white dwarfs with $r<24.5$ apparent magnitude. We simulate LSST photometric observations of 3.5 million white dwarfs over a ten-year period and calculate the detectability of companion planets with $P<10$ d via transits. We find typical detection rates in the range of $5 \times 10^{-6}$ to $4 \times 10^{-4}$ for Ceres-sized bodies to Earth-sized worlds, yielding $\sim 50$ to $4\,000$ detections for a 100% occurrence rate of each. For terrestrial planets in the continuously habitable zone, we find detection rates of $\sim 10^{-3}$ indicating that LSST would reveal hundreds of such worlds for occurrence rates in the range of 1% to 10%.

astro-ph.EP↗

arXiv2018

Double-layered distributed transient frequency control with regional coordination for power networks

This paper proposes a control strategy for power systems with a two-layer structure that achieves global stabilization and, at the same time, delimits the transient frequencies of targeted buses to a desired safe interval. The first layer is a model predictive control that, in a receding horizon fashion, optimally allocates the power resources while softly respecting transient frequency constraints. As the first layer control requires solving an optimization problem online, it only periodically samples the system state and updates its action. The second layer control, however, is implemented in real time, assisting the first layer to achieve frequency invariance and attractivity requirements.We show that the controllers designed at both layers are Lipschitz in the state. Furthermore, through network partition, they can be implemented in a distributed fashion, only requiring system information from neighboring partitions. Simulations on the IEEE 39-bus network illustrate our results.

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arXiv2018

Distributed Transient Frequency Control for Power Networks with Stability and Performance Guarantees

This paper proposes a distributed strategy regulated on a subset of individual buses in a power network described by the swing equations to achieve transient frequency control while preserving asymptotic stability. Transient frequency control refers to the ability to maintain the transient frequency of each bus of interest in a given safe region, provided it is initially in it, and ii) if it is initially not, then drive the frequency to converge to this region within a finite time, with a guaranteed convergence rate. Building on Lyapunov stability and set invariance theory, we formulate the stability and the transient frequency requirements as two separate constraints for the control input. Our design synthesizes a controller that satisfies both constraints simultaneously. The controller is distributed and Lipschitz, guaranteeing the existence and uniqueness of the trajectories of the closed-loop system. We further bound its magnitude and demonstrate its robustness against measurement inaccuracies. Simulations on the IEEE 39-bus power network illustrate our results.

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arXiv2018

Transient frequency control with regional cooperation for power networks

This paper proposes a centralized and a distributed sub-optimal control strategy to maintain in safe regions the real-time transient frequencies of a given collection of buses, and simultaneously preserve asymptotic stability of the entire network. In a receding horizon fashion, the centralized control input is obtained by iteratively solving an open-loop optimization aiming to minimize the aggregate control effort over controllers regulated on individual buses with transient frequency and stability constraints. Due to the non-convexity of the optimization, we propose a convexification technique by identifying a reference control input trajectory. We then extend the centralized control to a distributed scheme, where each subcontroller can only access the state information within a local region. Simulations on a IEEE-39 network illustrate our results.

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arXiv2018

Distributed transient frequency control in power networks

Modern power networks face increasing challenges in controlling their transient frequency behavior at acceptable levels due to low inertia and highly-dynamic units. This paper presents a distributed control strategy regulated on a subset of buses in a power network to maintain their transient frequencies in safe regions while preserving asymptotic stability of the overall system. Building on Lyapunov stability and set invariance theory, we formulate the transient frequency requirement and the asymptotic stability requirement as two separate constraints for the control input. Hereby, for each bus of interest, we synthesize a controller satisfying both constraints simultaneously. The controller is distributed and Lipschitz, guaranteeing the existence and uniqueness of the trajectories of the closed-loop system. Simulations on the IEEE 39-bus power network illustrate the results.

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arXiv2018

Virtual-Voltage Partition-Based Approach to Optimal Transmission Switching

This paper deals with optimal transmission switching (OTS) problems involving discrete binary decisions about network topology and non-convex power flow constraints. We adopt a semidefinite programming formulation for the OPF problem which, however, remains nonconvex due to the presence of discrete variables and bilinear products between the decision variables. To tackle the latter, we introduce a novel physically-inspired, virtual-voltage approximation that leads to provable lower and upper bounds on the solution of the original problem. To deal with the exponential complexity caused by the discrete variables, we introduce a graph partition-based algorithm which breaks the problem into several parallel mixed-integer subproblems of smaller size. Simulations demonstrate the high degree of accuracy and affordable computational requirements of our approach.

math.OC↗

arXiv2018

Event-triggered stabilization of disturbed linear systems over digital channels

We present an event-triggered control strategy for stabilizing a scalar, continuous-time, time-invariant, linear system over a digital communication channel having bounded delay, and in the presence of bounded system disturbance. We propose an encoding-decoding scheme, and determine lower bounds on the packet size and on the information transmission rate which are sufficient for stabilization. We show that for small values of the delay, the timing information implicit in the triggering events is enough to stabilize the system with any positive rate. In contrast, when the delay increases beyond a critical threshold, the timing information alone is not enough to stabilize the system and the transmission rate begins to increase. Finally, large values of the delay require transmission rates higher than what prescribed by the classic data-rate theorem. The results are numerically validated using a linearized model of an inverted pendulum.

math.OC↗

arXiv2017

Scheduled-Asynchronous Distributed Algorithm for Optimal Power Flow

Optimal power flow (OPF) problems are non-convex and large-scale optimization problems with important applications in power networks. This paper proposes the scheduled-asynchronous algorithm to solve a distributed semidefinite programming (SDP) formulation of the OPF problem. In this formulation, every agent seeks to solve a local optimization with its own cost function, physical constraints on its nodal power injection, voltage, and power flow of the lines it is connected to, and decision constraints on variables shared with neighbors to ensure consistency of the obtained solution. In the scheduled-asynchronous algorithm, every pair of connected nodes in the electrical network update their local variables in an alternating fashion. This strategy is asynchronous, in the sense that no clock synchronization is required, and relies on an orientation of the electrical network that prescribes the precise ordering of node updates. We establish the asymptotic convergence properties to the primal-dual optimizer when the orientation is acyclic. Given the dependence of the convergence rate on the network orientation, we also develop a distributed graph coloring algorithm that finds an orientation with diameter at most five for electrical networks with geometric degree distribution. Simulations illustrate our results on various IEEE bus test cases.

math.OC↗

arXiv2017

Time-triggering versus event-triggering control over communication channels

Time-triggered and event-triggered control strategies for stabilization of an unstable plant over a rate-limited communication channel subject to unknown, bounded delay are studied and compared. Event triggering carries implicit information, revealing the state of the plant. However, the delay in the communication channel causes information loss, as it makes the state information out of date. There is a critical delay value, when the loss of information due to the communication delay perfectly compensates the implicit information carried by the triggering events. This occurs when the maximum delay equals the inverse of the entropy rate of the plant. In this context, extensions of our previous results for event triggering strategies are presented for vector systems and are compared with the data-rate theorem for time-triggered control, that is extended here to a setting with unknown delay.

math.OC↗

arXiv2017

Event-triggered second-moment stabilization of linear systems under packet drops

This paper deals with the stabilization of linear systems with process noise under packet drops between the sensor and the controller. Our aim is to ensure exponential convergence of the second moment of the plant state to a given bound in finite time. Motivated by considerations about the efficient use of the available resources, we adopt an event-triggering approach to design the transmission policy. In our design, the sensor's decision to transmit or not the state to the controller is based on an online evaluation of the future satisfaction of the control objective. The resulting event-triggering policy is hence specifically tailored to the control objective. We formally establish that the proposed event-triggering policy meets the desired objective and quantify its efficiency by providing an upper bound on the fraction of expected number of transmissions in an infinite time interval. Simulations for scalar and vector systems illustrate the results.

math.OC↗

arXiv2017

Distributed control of vehicle strings under finite-time and safety specifications

This paper studies an optimal control problem for a string of vehicles with safety requirements and finite-time specifications on the approach time to a target region. Our problem formulation is motivated by scenarios involving autonomous vehicles circulating on arterial roads with intelligent management at traffic intersections. We propose a provably correct distributed control algorithm that ensures that the vehicles satisfy the finite-time specifications under speed limits, acceleration saturation, and safety requirements. The safety specifications are such that collisions can be avoided even in cases of communication failure. We also discuss how the proposed distributed algorithm can be integrated with an intelligent intersection manager to provide information about the feasible approach times of the vehicle string and a guaranteed bound of its time of occupancy of the intersection. Our simulation study illustrates the algorithm and its properties regarding approach time, occupancy time, and fuel and time cost.

math.OC↗

arXiv2017

The role of convexity on saddle-point dynamics: Lyapunov function and robustness

This paper studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and (projected) gradient ascent in variables corresponding to concavity. We examine the role that the local and/or global nature of the convexity-concavity properties of the saddle function plays in guaranteeing convergence and robustness of the dynamics. Under the assumption that the saddle function is twice continuously differentiable, we provide a novel characterization of the omega-limit set of the trajectories of this dynamics in terms of the diagonal blocks of the Hessian. Using this characterization, we establish global asymptotic convergence of the dynamics under local strong convexity-concavity of the saddle function. When strong convexity-concavity holds globally, we establish three results. First, we identify a Lyapunov function (that decreases strictly along the trajectory) for the projected saddle-point dynamics when the saddle function corresponds to the Lagrangian of a general constrained convex optimization problem. Second, for the particular case when the saddle function is the Lagrangian of an equality-constrained optimization problem, we show input-to-state stability of the saddle-point dynamics by providing an ISS Lyapunov function. Third, we use the latter result to design an opportunistic state-triggered implementation of the dynamics. Various examples illustrate our results.

math.OC↗

arXiv2017

Iterative bidding in electricity markets: rationality and robustness

This paper studies an electricity market consisting of an independent system operator (ISO) and a group of generators. The goal is to solve the DC optimal power flow (DC-OPF) problem: have the generators collectively meet the power demand while minimizing the aggregate generation cost and respecting line flow limits in the network. The ISO by itself cannot solve the DC-OPF problem as generators are strategic and do not share their cost functions. Instead, each generator submits to the ISO a bid, consisting of the price per unit of electricity at which it is willing to provide power. Based on the bids, the ISO decides how much production to allocate to each generator to minimize the total payment while meeting the load and satisfying the line limits. We provide a provably correct, decentralized iterative scheme, termed BID ADJUSTMENT ALGORITHM, for the resulting Bertrand competition game. Regarding convergence, we show that the algorithm takes the generators' bids to any desired neighborhood of the efficient Nash equilibrium at a linear convergence rate. As a consequence, the optimal production of the generators converges to the optimizer of the DC-OPF problem. Regarding robustness, we show that the algorithm is robust to affine perturbations in the bid adjustment scheme and that there is no incentive for any individual generator to deviate from the algorithm by using an alternative bid update scheme. We also establish the algorithm robustness to collusion, i.e., we show that, as long as each bus with generation has a generator following the strategy, there is no incentive for any group of generators to share information with the intent of tricking the system to obtain a higher payoff. Simulations illustrate our results.

math.OC↗

arXiv2016

Saddle-point dynamics: conditions for asymptotic stability of saddle points

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics (gradient-descent in the first variable and gradient-ascent in the second one). We identify a suite of complementary conditions under which the set of saddle points is asymptotically stable under the saddle-point dynamics. Our first set of results is based on the convexity-concavity of the function defining the saddle-point dynamics to establish the convergence guarantees. For functions that do not enjoy this feature, our second set of results relies on properties of the linearization of the dynamics, the function along the proximal normals to the saddle set, and the linearity of the function in one variable. We also provide global versions of the asymptotic convergence results. Various examples illustrate our discussion.

math.OC↗

arXiv2016

Event-Triggered Communication and Control for Multi-Agent Average Consensus

In this chapter we look at one of the canonical driving examples for multi-agent systems: average consensus. In this scenario, a group of agents seek to agree on the average of their initial states. Depending on the particular application, such states might correspond to sensor measurements, estimates about the position of a target, or some other data that needs to be fused. Due to its numerous applications in networked systems, many algorithmic solutions exist to the multi-agent average consensus problem; however, a majority of them rely on agents having continuous or periodic availability of information from other agents. Unfortunately, this assumption leads to inefficient implementations in terms of energy consumption, communication bandwidth, network congestion, and processor usage. Motivated by these observations, our main goal here is the design of provably correct distributed event-triggered strategies that autonomously decide when communication and control updates should occur so that the resulting asynchronous network executions still achieve average consensus.

math.OC↗

arXiv2016

Distributed coordination of DERs with storage for dynamic economic dispatch

This paper considers the dynamic economic dispatch problem for a group of distributed energy resources (DERs) with storage that communicate over a weight-balanced strongly connected digraph. The objective is to collectively meet a certain load profile over a finite time horizon while minimizing the aggregate cost. At each time slot, each DER decides on the amount of generated power, the amount sent to/drawn from the storage unit, and the amount injected into the grid to satisfy the load. Additional constraints include bounds on the amount of generated power, ramp constraints on the difference in generation across successive time slots, and bounds on the amount of power in storage. We synthesize a provably-correct distributed algorithm that solves the resulting finite-horizon optimization problem starting from any initial condition. Our design consists of two interconnected systems, one estimating the mismatch between the injection and the total load at each time slot, and another using this estimate to reduce the mismatch and optimize the total cost of generation while meeting the constraints.

math.OC↗

arXiv2015

Event-triggered control under time-varying rates and channel blackouts

This paper studies event-triggered stabilization of linear time-invariant systems over time-varying rate-limited communication channels. We explicitly account for the possibility of channel blackouts, i.e., intervals of time when the communication channel is unavailable for feedback. Assuming prior knowledge of the channel evolution, we study the data capacity, which is the maximum total number of bits that could be communicated over a given time interval, and provide an efficient real-time algorithm to lower bound it for a deterministic time-slotted model of channel evolution. Building on these results, we design an event-triggering strategy that guarantees Zeno-free, exponential stabilization at a desired convergence rate even in the presence of intermittent channel blackouts. The contributions are the notion of channel blackouts, the effective event-triggered control despite their occurrence, and the analysis and quantification of the data capacity for a class of time-varying continuous-time channels. Various simulations illustrate the results.

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