arXiv subjects

Sonia Martinez

Publications and source records attributed to Sonia Martinez.

At least 37 records · Page 2Linked to original sources

arXiv2021

Risk-perception-aware control design under dynamic spatial risks

This work proposes a novel risk-perception-aware (RPA) control design using non-rational perception of risks associated with uncertain dynamic spatial costs. We use Cumulative Prospect Theory (CPT) to model the risk perception of a decision maker (DM) and use it to construct perceived risk functions that transform the uncertain dynamic spatial cost to deterministic perceived risks of a DM. These risks are then used to build safety sets which can represent risk-averse to risk-insensitive perception. We define a notions of "inclusiveness" and "versatility" based on safety sets and use it to compare with other models such as Conditional value at Risk (CVaR) and Expected risk (ER). We theoretically prove that CPT is the most "inclusive" and "versatile" model of the lot in the context of risk-perception-aware controls. We further use the perceived risk function along with ideas from control barrier functions (CBF) to construct a class of perceived risk CBFs. For a class of truncated-Gaussian costs, we find sufficient geometric conditions for the validity of this class of CBFs, thus guaranteeing safety. Then, we generate perceived-safety-critical controls using a Quadratic program (QP) to guide an agent safely according to a given perceived risk model. We present simulations in a 2D environment to illustrate the performance of the proposed controller.

eess.SY↗

arXiv2021

Distributed Stochastic Nested Optimization via Cubic Regularization

This paper considers a nested stochastic distributed optimization problem. In it, approximate solutions to realizations of the inner-problem are leveraged to obtain a Distributed Stochastic Cubic Regularized Newton (DiSCRN) update to the decision variable of the outer problem. We provide an example involving electric vehicle users with various preferences which demonstrates that this model is appropriate and sufficiently complex for a variety of data-driven multi-agent settings, in contrast to non-nested models. The main two contributions of the paper are: (i) development of local stopping criterion for solving the inner optimization problem which guarantees sufficient accuracy for the outer-problem update, and (ii) development of the novel DiSCRN algorithm for solving the outer-problem and a theoretical justification of its efficacy. Simulations demonstrate that this approach is more stable and converges faster than standard gradient and Newton outer-problem updates in a highly nonconvex scenario, and we also demonstrate that the method extends to an EV charging scenario in which resistive battery losses and a time-of-use pricing model are considered over a time horizon.

math.OC↗

arXiv2021

Iterative Algorithms for Assessing Network Resilience Against Structured Perturbations

This paper studies network resilience against structured additive perturbations to its topology. We consider dynamic networks modeled as linear time-invariant systems subject to perturbations of bounded energy satisfying specific sparsity and entry-wise constraints. Given an energy level, the structured pseudospectral abscissa captures the worst-possible perturbation an adversary could employ to de-stabilize the network, and the structured stability radius is the maximum energy in the structured perturbation that the network can withstand without becoming unstable. Building on a novel characterization of the worst-case structured perturbation, we propose iterative algorithms that efficiently compute the structured pseudospectral abscissa and structured stability radius. We provide theoretical guarantees of the local convergence of the algorithms and illustrate their efficacy and accuracy on several network examples.

eess.SY↗

arXiv2021

Data-driven Predictive Control for a Class of Uncertain Control-Affine Systems

This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are feasible and provide superior performance guarantees with high probability. This results into the formulation of a stochastic optimization problem (P), which is intractable due to the unknown distribution of the uncertainty variables. By developing a distributionally robust optimization framework, we present an equivalent and yet tractable reformulation of (P). Further, we propose an efficient algorithm that provides online suboptimal data-driven solutions and guarantees performance with high probability. To illustrate the effectiveness of the proposed approach, we consider a highway speed-limit control problem. We then develop a set of data-driven speed controls that allow us to prevent traffic congestion with high probability. Finally, we employ the resulting control method on a traffic simulator to illustrate the effectiveness of this approach numerically.

math.OC↗

arXiv2021

Frequency Regulation with Heterogeneous Energy Resources: A Realization using Distributed Control

This paper presents one of the first real-life demonstrations of coordinated and distributed resource control for secondary frequency response in a power distribution grid. We conduct a series of tests with up to 69 heterogeneous active devices consisting of air handling units, unidirectional and bidirectional electric vehicle charging stations, a battery energy storage system, and 107 passive devices consisting of building loads and photovoltaic generators. Actuation commands for the test devices are obtained by solving an economic dispatch problem at every regulation instant using distributed ratio-consensus, primal-dual, and Newton-like algorithms. The distributed control setup consists of a set of Raspberry Pi end-points exchanging messages via an ethernet switch. The problem formulation minimizes the sum of device costs while tracking the setpoints provided by the system operator. We demonstrate accurate and fast real-time distributed computation of the optimization solution and effective tracking of the regulation signal by measuring physical device outputs over 40-minute time horizons. We also perform an economic benefit analysis which confirms eligibility to participate in an ancillary services market and demonstrates up to $53K of potential annual revenue for the selected population of devices.

eess.SY↗

arXiv2020

Planning under non-rational perception of uncertain spatial costs

This work investigates the design of risk-perception-aware motion-planning strategies that incorporate non-rational perception of risks associated with uncertain spatial costs. Our proposed method employs the Cumulative Prospect Theory (CPT) to generate a perceived risk map over a given environment. CPT-like perceived risks and path-length metrics are then combined to define a cost function that is compliant with the requirements of asymptotic optimality of sampling-based motion planners (RRT*). The modeling power of CPT is illustrated in theory and in simulation, along with a comparison to other risk perception models like Conditional Value at Risk (CVaR). Theoretically, we define a notion of expressiveness for a risk perception model and show that CPT's is higher than that of CVaR and expected risk. We then show that this expressiveness translates to our path planning setting, where we observe that a planner equipped with CPT together with a simultaneous perturbation stochastic approximation (SPSA) method can better approximate arbitrary paths in an environment. Additionally, we show in simulation that our planner captures a rich set of meaningful paths, representative of different risk perceptions in a custom environment. We then compare the performance of our planner with T-RRT* (a planner for continuous cost spaces) and Risk-RRT* (a risk-aware planner for dynamic human obstacles) through simulations in cluttered and dynamic environments respectively, showing the advantage of our proposed planner.

cs.RO↗

arXiv2020

Online Learning of Parameterized Uncertain Dynamical Environments with Finite-sample Guarantees

We present a novel online learning algorithm for a class of unknown and uncertain dynamical environments that are fully observable. First, we obtain a novel probabilistic characterization of systems whose mean behavior is known but which are subject to additive, unknown subGaussian disturbances. This characterization relies on recent concentration of measure results and is given in terms of ambiguity sets. Second, we extend the results to environments whose mean behavior is also unknown but described by a parameterized class of possible mean behaviors. Our algorithm adapts the ambiguity set dynamically by learning the parametric dependence online, and retaining similar probabilistic guarantees with respect to the additive, unknown disturbance. We illustrate the results on a differential-drive robot subject to environmental uncertainty.

eess.SY↗

arXiv2020

Distributed Resource Allocation with Binary Decisions via Newton-like Neural Network Dynamics

This paper aims to solve a distributed resource allocation problem with binary local constraints. The problem is formulated as a binary program with a cost function defined by the summation of agent costs plus a global mismatch/penalty term. We propose a modification of the Hopfield Neural Network (HNN) dynamics in order to solve this problem while incorporating a novel Newton-like weighting factor. This addition lends itself to fast avoidance of saddle points, which the gradient-like HNN is susceptible to. Turning to a multi-agent setting, we reformulate the problem and develop a distributed implementation of the Newton-like dynamics. We show that if a local solution to the distributed reformulation is obtained, it is also a local solution to the centralized problem. A main contribution of this work is to show that the probability of converging to a saddle point of an appropriately defined energy function in both the centralized and distributed settings is zero under light assumptions. Finally, we enlarge our algorithm with an annealing technique which gradually learns a feasible binary solution. Simulation results demonstrate that the proposed methods are competitive with centralized greedy and SDP relaxation approaches in terms of solution quality, while the main advantage of our approach is a significant improvement in runtime over the SDP relaxation method and the distributed quality of implementation.

math.OC↗

arXiv2020

Data assimilation and online optimization with performance guarantees

This paper considers a class of real-time stochastic optimization problems dependent on an unknown probability distribution. In the considered scenario, data is streaming frequently while trying to reach a decision. Thus, we aim to devise a procedure that incorporates samples (data) of the distribution sequentially and adjusts decisions accordingly. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm (ONDA Algorithm) for this purpose. This algorithm guarantees out-of-sample performance of decisions with high probability, and gradually improves the quality of the decisions by incorporating the streaming data. We show that the ONDA Algorithm converges under a sufficiently slow data streaming rate, and provide a criteria for its termination after certain number of data have been collected. Simulations illustrate the results.

math.OC↗

arXiv2020

Online data assimilation in distributionally robust optimization

This paper considers a class of real-time decision making problems to minimize the expected value of a function that depends on a random variable $ξ$ under an unknown distribution $\mathbb{P}$. In this process, samples of $ξ$ are collected sequentially in real time, and the decisions are made, using the real-time data, to guarantee out-of-sample performance. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm for this purpose. This algorithm guarantees the out-of-sample performance in high probability, and gradually improves the quality of the data-driven decisions by incorporating the streaming data. We show that the Online Data Assimilation Algorithm guarantees convergence under the streaming data, and a criteria for termination of the algorithm after certain number of data has been collected.

math.OC↗

arXiv2019

Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization

Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel Distributed-Approx Newton algorithms that approximate the standard Newton optimization method. We first develop the notion of an optimal edge weighting for the communication graph over which agents implement the second-order algorithm, and propose a convex approximation for the nonconvex weight design problem. We next build on the optimal weight design to develop a discrete Distributed Approx-Newton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full box-constrained problem, we develop a continuous Distributed Approx-Newton algorithm which is inspired by first-order saddle-point methods and rigorously prove its convergence to the primal and dual optimizers. A main property of each of these distributed algorithms is that they only require agents to exchange constant-size communication messages, which lends itself to scalable implementations. Simulations demonstrate that the Distributed Approx-Newton algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods.

math.OC↗

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.

eess.SY↗

arXiv2018

Data-driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method.

math.OC↗

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

Gesture based Human-Swarm Interactions for Formation Control using interpreters

We propose a novel Human-Swarm Interaction (HSI) framework which enables the user to control a swarm shape and formation. The user commands the swarm utilizing just arm gestures and motions which are recorded by an off-the-shelf wearable armband. We propose a novel interpreter system, which acts as an intermediary between the user and the swarm to simplify the user's role in the interaction. The interpreter takes in a high level input drawn using gestures by the user, and translates it into low level swarm control commands. This interpreter employs machine learning, Kalman filtering and optimal control techniques to translate the user input into swarm control parameters. A notion of Human Interpretable dynamics is introduced, which is used by the interpreter for planning as well as to provide feedback to the user. The dynamics of the swarm are controlled using a novel decentralized formation controller based on distributed linear iterations and dynamic average consensus. The framework is demonstrated theoretically as well as experimentally in a 2D environment, with a human controlling a swarm of simulated robots in real time.

cs.RO↗

arXiv2018

Cooperative Robot Localization Using Event-triggered Estimation

This paper describes a novel communication-spare cooperative localization algorithm for a team of mobile unmanned robotic vehicles. Exploiting an event-based estimation paradigm, robots only send measurements to neighbors when the expected innovation for state estimation is high. Since agents know the event-triggering condition for measurements to be sent, the lack of a measurement is thus also informative and fused into state estimates. The robots use a Covariance Intersection (CI) mechanism to occasionally synchronize their local estimates of the full network state. In addition, heuristic balancing dynamics on the robots' CI-triggering thresholds ensure that, in large diameter networks, the local error covariances remains below desired bounds across the network. Simulations on both linear and nonlinear dynamics/measurement models show that the event-triggering approach achieves nearly optimal state estimation performance in a wide range of operating conditions, even when using only a fraction of the communication cost required by conventional full data sharing. The robustness of the proposed approach to lossy communications, as well as the relationship between network topology and CI-based synchronization requirements, are also examined.

cs.RO↗

arXiv2017

Server assisted distributed cooperative localization over unreliable communication links

This paper considers the problem of cooperative localization (CL) using inter-robot measurements for a group of networked robots with limited on-board resources. We propose a novel recursive algorithm in which each robot localizes itself in a global coordinate frame by local dead reckoning, and opportunistically corrects its pose estimate whenever it receives a relative measurement update message from a server. The computation and storage cost per robot in terms of the size of the team is of order O(1), and the robots are only required to transmit information when they are involved in a relative measurement. The server also only needs to compute and transmit update messages when it receives an inter-robot measurement. We show that under perfect communication, our algorithm is an alternative but exact implementation of a joint CL for the entire team via Extended Kalman Filter (EKF). The perfect communication however is not a hard requirement. In fact, we show that our algorithm is intrinsically robust with respect to communication failures, with formal guarantees that the updated estimates of the robots receiving the update message are of minimum variance in a first-order approximate sense at that given timestep. We demonstrate the performance of the algorithm in simulation and experiments.

cs.RO↗

arXiv2017

Maximizing Algebraic Connectivity of Constrained Graphs in Adversarial Environments

This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design problem of adding edges to an initial graph, which introduces a nonconvex binary decision variable, in addition to subjugation to general convex constraints on the feasible edge set. Unlike previous methods, our method is justifiably not greedy and capable of accommodating these additional constraints. We also study a scenario in which a coordinator must selectively protect edges of the network from a chance of failure due to a physical disturbance or adversarial attack. The coordinator needs to strategically respond to the adversary's action without presupposed knowledge of the adversary's feasible attack actions. We propose three heuristic algorithms for the coordinator to accomplish the objective and identify worst-case preventive solutions. Each algorithm is shown to be effective in simulation and we provide some discussion on their compared performance.

math.OC↗