# Your search: "author:"Cortes, Jorge""

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## Scholarly Works (26 results)

This paper presents a continuous-time coverage algorithm based on the singu- lar perturbations method. The algorithm generates a control for a network of autonomous agents. The algorithm is distributed in the sense that the agents need only information about their neighbors. The singular perturbation method is applied as a means to update the control at a faster time scale to approach performance of a centralized approach. The paper concludes with results from simulations and experiment.

Electric power systems safety is a fundamental aspect of the operation and management of the grid. In order to maintain safety, the power system is operated around a nominal frequency. In fact, large frequency fluctuations can trigger generator relay-protection mechanisms and load shedding, which may further jeopardize network integrity, leading to cascading failures. Without appropriate estimations on the possible consequences resulting from contingency, operational architectures, and control safeguards in place, the likelihood of such events is not negligible, given that the high penetration of non-rotational renewable resources provides less inertia, possibly inducing higher frequency excursions. These observations motivate us in this thesis to develop approximation and control schemes to efficiently estimate the transient-state evolution subject to disturbances and contingencies and further actively mitigate undesired transient frequency deviations.

This thesis first develops methods to efficiently compute the set of disturbances on a power network that do not tip the frequency of each bus and the power flow in each transmission line beyond their respective bounds. For a linearized power network model, we propose a sampling method to provide superset and subset approximations with a desired accuracy of the set of feasible disturbances. We also introduce an error metric to measure the approximation gap and design an algorithm that is able to reduce its value without impacting the complexity of the resulting set approximations.

As a natural follow-up to our on approximating feasible disturbances, we seek to further regulate transient frequency via novel control schemes. With regard to this, this thesis proposes three control strategies that all achieve local stabilization of power networks characterized by nonlinear swing equations and, at the same time, delimit the transient frequencies of targeted buses to a desired safe interval. To handle the coordination of large numbers of resources in an adaptive and scalable fashion, all three controllers can be implemented in an either partially or fully distributed fashion. Specifically, we synthesize the first transient frequency controller by having it satisfy a transient frequency constraint and an asymptotic stability constraint. Benefitting from its structural simplicity, the controller can be implemented in a distributed fashion by merely allowing each controlled bus physically measure the states of neighbors. To reduce the control effort, the second MPC-based controller enables control command cooperation by communication; however, the coordination is limited within a designed range, and the control algorithm is only partially distributed, potentially non-Lipschitz, and not as computationally efficient. The third controller successfully addresses all these issues via a bilayered structure and information exchange with up to 2-hop neighbors.

Many natural and man-made systems, ranging from the

nervous system to power and transportation grids to societies, exhibit

dynamic behaviors that evolve over a sparse and complex network.

This networked aspect raises significant challenges and opportunities for the identification, analysis, and control of such dynamic behaviors. While some of these challenges emanate from the networked aspect \emph{per se} (such as the sparsity of connections between system components and the interplay between nodal \emph{communication} and network dynamics), various challenges arise from the specific application areas (such as privacy concerns in cyber-physical systems or the need for \emph{scalable} algorithm designs due to the large size of various biological and engineered networks). On the other hand, networked systems provide significant opportunities and allow for performance and robustness levels that are far beyond reach for centralized systems, with examples ranging from the Internet (of Things) to the smart grid and the brain. This dissertation aims to address several of these challenges and harness these opportunities.

The dissertation is divided into three parts. In the first part, we study privacy concerns whose resolution is vital for the utility of networked cyber-physical systems. We study the problems of average consensus and convex optimization as two principal distributed computations occurring over networks and design algorithm with rigorous privacy guarantees that provide a \emph{best achievable} tradeoff between network utility and privacy. In the second part, we analyze networks with resource constraints. More specifically, we study three problems of stabilization under communication (bandwidth and latency) limitations in sensing and actuation, optimal time-varying control scheduling problem under limited number of actuators and control energy, and the structure identification problem of under-sensed networks (i.e., networks with latent nodes). Finally in the last part, we focus on the intersection of networked dynamical systems and neuroscience and draw connections between brain network dynamics and two extensively studied but yet not fully understood neuro-cognitive phenomena: goal-driven selective attention and neural oscillations. Using a novel axiomatic approach, we establish these connections in the form of necessary and/or sufficient conditions on the network structure that match the network output trajectories with experimentally observed brain activity.

Autonomous unmanned vehicles (UxVs) can be useful in many scenarios

including disaster relief, production and manufacturing, as well as

carrying out Naval missions such as surveillance, mapping of unknown

regions and pursuit of other hostile vehicles. When considering

these scenarios, one of the most difficult challenges is determining

which actions or tasks the vehicles should take in order to most

efficiently satisfy the objectives. This challenge becomes more

difficult with the inclusion of multiple vehicles, because the

action and state space scale exponentially with the number of

agents. Many planning algorithms suffer from the curse of

dimensionality as more agents are included, sampling for

suitable actions in the joint action space becomes infeasible within

a reasonable amount of time. To enable autonomy, methods that can be

applied to a variety of scenarios are invaluable because they reduce

human involvement and time.

Recently, advances in technology enable algorithms that require more

computational power to be effective but work in broader

frameworks. We offer three main approaches to multi-agent planning

which are all inspired by model-based reinforcement learning.

First, we address the curse of dimensionality and investigate how to

spatially reduce the state space of massive environments where

agents are deployed. We do this in a hierarchical fashion by

searching subspaces of the environment, called sub-environments, and

creating plans to optimally take actions in those sub-environments.

Next, we utilize game-theoretic techniques paired with simulated

annealing as an approach for agent cooperation when planning in a

finite time horizon. One problem with this approach is that agents

are capable of breaking promises with other agents right before

execution. To address this, we propose several variations that

discourage agents from changing plans in the near future and

encourages joint planning in the long term. Lastly, we propose a

tree-search algorithm that is aided by a convolutional neural

network. The convolutional neural network takes advantage of

spatial features that are natural in UxV deployment and offers

recommendations for action selection during tree search. In

addition, we propose some design features for the tree search that

target multi-agent deployment applications.

This thesis contributes to the body of research in the design and analysis of distributed algorithms for the optimization of a sum of convex functions, that finds applications in networked and multi-agent systems. In this framework, a group of agents cooperate with each other to optimize the sum of their local objectives in a decentralized way by means of local interactions. We consider four aspects. In the first scenario, the agents need to agree on a global decision vector that minimizes the unconstrained sum. In this case, we study a family of distributed,

continuous-time algorithms that have each agent update its estimate of the global optimizer doing gradient descent on its local cost function while, at the same time, seeking to agree with its neighbors’ estimates via proportional-integral feedback on their disagreement. Our aim is to characterize the algorithm robustness properties against the additive persistent noise resulting from errors in communication and computation. We model this algorithm as a stochastic differential equation and develop a novel Lyapunov technique to establish the noise-to-state stability property in 2nd moment.

In the second scenario, we consider the online case, whereby each agent in the network commits to a decision and incurs a local cost given by functions that are revealed over time and whose unknown evolution might be adversarially adaptive to the agent’s behavior. The goal of each agent is to incur a cumulative cost over time with respect to the sum of local functions across the network that is competitive with the best centralized decision in hindsight. The proposed algorithms evolve in discrete time using first-order information of the objectives in the form of subgradients, and the communication topology is modeled as a sequence of time-varying weight-balanced digraphs such that the consecutive unions over time periods of some length are strongly connected. We illustrate our results in an application to medical diagnosis, where networked hospitals use patient data to improve their decision models cooperatively in an online fashion.

In the third scenario, we depart from the cooperative search of a global decision vector. Instead, the agents now wish to estimate local decision vectors that minimize the sum of their objectives and are coupled through a constraint that is a sum of convex functions. Motivated by dual-decompositions of constrained optimization problems through the Lagrangian formulation, we consider subgradient algorithms to find a saddle-point of general convex-concave functions under

agreement constraints. This framework also encodes minimization problems with semidefinite constraints, which results in novel distributed strategies that are scalable if the order of the matrix inequalities is independent of the size of the network or under decompositions using chordal sparsity.

In the fourth scenario, we show a distributed treatment of nuclear-norm regularization, a widely used convex surrogate of the rank function on the spectral ball. To this end, we exploit our previous strategies for saddle-point problems using two variational characterizations of the nuclear norm that are separable under an agreement condition on auxiliary matrices that are independent of the size of the network. As a result, we derive two novel distributed algorithms to address standard optimization models for multi-task learning and low-rank matrix completion.

The share of renewable energy generation in meeting our electricity needs is growing by the day. A majority of these renewables have small generation capacity and they are geographically distributed. It is for this reason that they are often termed as distributed energy resources (DERs). In addition to the capacity constraint, DERs' generation is highly variable and uncertain. The current electricity grid, on the other hand, was designed for centralized bulk generation. Therefore, regulating authorities like the Independent System Operator (ISO) or the Regional Transmission Organization (RTO) find it quite challenging to seamlessly integrate these DERs into the current grid, without affecting the quality of service to consumers. As one of the measures of tackling this issue, regulating authorities envision a hierarchical architecture where, at the lower layer, different sets of distributed energy resources (DERs) coordinate their response under an aggregator and, at the upper layer, the ISO interacts (through a market) with the aggregators to solve the optimal dispatch problem. In this scenario, aggregators function as virtual, large-capacity generators. While the DERs under one aggregator can cooperate among themselves, the aggregators compete with each other in the market. Given this context, this thesis designs and analyzes coordination among DERs and competition among aggregators.

Specifically, the thesis can be divided into three parts. The first part focusses on the static and the dynamic optimal dispatch problems, where the aim for a set of DERs is to plan their generation so as to meet a particular load, minimize the total cost of generation, and respect individual constraints. For these optimization problems we design a suit of Laplacian-gradient based distributed algorithmic solutions and study their performance. The second part studies the asymptotic convergence and robustness properties of the saddle-point dynamics. This dynamics serves as the backbone of numerous distributed algorithms for network constrained optimization problems, including the dispatch problem. Finally, the third part investigates an electricity market designed for optimal dispatch among the aggregators. We design and analyze an iterative bid update scheme for the aggregators, discussing the advantages of this scheme using rationality and robustness arguments.

Due to recent technological advances, robotic swarms are currently a large

interest for surveillance, disaster response, and exploration. In order to solve this

problem, we develop distributed deployment strategies for 1.5D and 2.5D polyhedral

terrains that are inuenced by research in computational geometry, graph theory,

and distributed controls. Similarly to the guarding of art gallery problems, we guard

an environment through the collective visibility of a team of robots. We consider

scenarios where the robots are constrained to moving on the ground in 1.5D and 2.5D

polyhedral terrains. Our objective is to determine strategies for deploying robots in polyhedral terrains that guarantees complete visibility of the terrain.

In the 1.5D polyhedral terrain, we determine a set of locations, that guarantees

that the terrain is completely visible when occupied. We then develop a set

of instructions that each robot distributively executes in order to occupy the set of

locations. Finally, we nd a closed-form expression for the time required for the 1.5D

deployment strategy to complete that scales with the size of the terrain.

In the 2.5D polyhedral terrain, we develop a set of instructions for the robots to

follow that collectively explores, colors, and guards the polyhedral terrain. We dene

rules for the agents to label certain locations that must be occupied in order to achieve

complete visibility, inspired by coloring of planar graphs. Finally, we characterize the

best and worse time complexity for the algorithm

This paper analyzes a number of basic coordination algorithms running on synchronous robotic networks. We provide upper and lower bounds on the time complexity of the move-toward-average and circumcenter laws, both achieving rendezvous, and of the centroid law, achieving deployment over a region of interest. The results are derived via novel analysis methods, including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal Toeplitz and circulant matrices.

This paper proposes a formal model for a network of robotic agents that move and communicate. Building on concepts from distributed computation, robotics, and control theory, we define notions of robotic network, control and communication law, coordination task, and time and communication complexity. We illustrate our model and compute the proposed complexity measures in the example of a network of locally connected agents on a circle that agree upon a direction of motion and pursue their immediate neighbors.