arXiv subjects

Jorge Cortes

Publications and source records attributed to Jorge Cortes.

At least 55 records · Page 3Linked to original sources

arXiv2021

Online Stochastic Optimization for Unknown Linear Systems: Data-Driven Synthesis and Controller Analysis

This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available methods critically rely on a precise knowledge of the system dynamics (thus requiring off-line system identification and model refinement). To this aim, in this paper we first show that the steady-state transfer function of a linear system can be computed directly from control experiments, bypassing explicit model identification. Then, we leverage the estimated transfer function to design a controller -- which is inspired by stochastic gradient descent methods -- that regulates the system to the solution of the prescribed optimization problem. A distinguishing feature of our methods is that they do not require any knowledge of the system dynamics, disturbance terms, or their distributions. Our technical analysis combines concepts and tools from behavioral system theory, stochastic optimization with decision-dependent distributions, and stability analysis. We illustrate the applicability of the framework on a case study for mobility-on-demand ride service scheduling in Manhattan, NY.

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arXiv2021

Performance-Barrier-Based Event-Triggered Control with Applications to Network Systems

This paper proposes a novel framework for resource-aware control design termed performance-barrier-based triggering. Given a feedback policy, along with a Lyapunov function certificate that guarantees its correctness, we examine the problem of designing its digital implementation through event-triggered control while ensuring a prescribed performance is met and triggers occur as sparingly as possible. Our methodology takes into account the performance residual, i.e., how well the system is doing in regards to the prescribed performance. Inspired by the notion of control barrier function, the trigger design allows the certificate to deviate from monotonically decreasing, with leeway specified as an increasing function of the performance residual, resulting in greater flexibility in prescribing update times. We study different types of performance specifications, with particular attention to quantifying the benefits of the proposed approach in the exponential case. We build on this to design intrinsically Zeno-free distributed triggers for network systems. A comparison of event-triggered approaches in a vehicle platooning problem shows how the proposed design meets the prescribed performance with a significantly lower number of controller updates.

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arXiv2021

Structural Characterization of Oscillations in Brain Networks with Rate Dynamics

Among the versatile forms of dynamical patterns of activity exhibited by the brain, oscillations are one of the most salient and extensively studied, yet are still far from being well understood. In this paper, we provide various structural characterizations of the existence of oscillatory behavior in neural networks using a classical neural mass model of mesoscale brain activity called linear-threshold dynamics. Exploiting the switched-affine nature of this dynamics, we obtain various necessary and/or sufficient conditions on the network structure and its external input for the existence of oscillations in (i) two-dimensional excitatory-inhibitory networks (E-I pairs), (ii) networks with one inhibitory but arbitrary number of excitatory nodes, (iii) purely inhibitory networks with an arbitrary number of nodes, and (iv) networks of E-I pairs. Throughout our treatment, and given the arbitrary dimensionality of the considered dynamics, we rely on the lack of stable equilibria as a system-based proxy for the existence of oscillations, and provide extensive numerical results to support its tight relationship with the more standard, signal-based definition of oscillations in computational neuroscience.

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arXiv2021

Encoding Impact of Network Modification on Controllability via Edge Centrality Matrix

This paper develops tools to quantify the importance of agent interactions and its impact on global performance metrics for networks modeled as linear time-invariant systems. We consider Gramian-based performance metrics and propose a novel notion of edge centrality that encodes the first-order variation in the metric with respect to the modification of the corresponding edge weight, including for those edges not present in the network. The proposed edge centrality matrix (ECM) is additive over the set of inputs, i.e., it captures the specific contribution to each edge's centrality of the presence of any given actuator. We provide a full characterization of the ECM structure for the class of directed stem-bud networks, showing that non-zero entries are only possible at specific sub/super-diagonals determined by the network size and the length of its bud. We also provide bounds on the value of the trace, trace inverse, and log-det of the Gramian before and after single-edge modifications, and on the edge-modification weight to ensure the modified network retains stability. Simulations show the utility of the proposed edge centrality notion and validate our results.

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arXiv2021

Solving Linear Equations with Separable Problem Data over Directed Networks

This paper deals with linear algebraic equations where the global coefficient matrix and constant vector are given respectively, by the summation of the coefficient matrices and constant vectors of the individual agents. Our approach is based on reformulating the original problem as an unconstrained optimization. Based on this exact reformulation, we first provide a gradient-based, centralized algorithm which serves as a reference for the ensuing design of distributed algorithms. We propose two sets of exponentially stable continuous-time distributed algorithms that do not require the individual agent matrices to be invertible, and are based on estimating non-distributed terms in the centralized algorithm using dynamic average consensus. The first algorithm works for time-varying weight-balanced directed networks, and the second algorithm works for general directed networks for which the communication graphs might not be balanced. Numerical simulations illustrate our results.

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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.

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arXiv2021

Network Optimization via Smooth Exact Penalty Functions Enabled by Distributed Gradient Computation

This paper proposes a distributed algorithm for a network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained problem as the unconstrained optimization of a smooth (continuously differentiable) exact penalty function. Computing the gradient of this penalty function in a distributed way is challenging even under the separability assumptions on the original optimization problem. Our technical approach shows that the distributed computation problem for the gradient can be formulated as a system of linear algebraic equations defined by separable problem data. To solve it, we design an exponentially fast, input-to-state stable distributed algorithm that does not require the individual agent matrices to be invertible. We employ this strategy to compute the gradient of the penalty function at the current network state. Our distributed algorithmic solver for the original constrained optimization problem interconnects this estimation with the prescription of having the agents follow the resulting direction. Numerical simulations illustrate the convergence and robustness properties of the proposed algorithm.

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arXiv2021

Nesterov Acceleration for Equality-Constrained Convex Optimization via Continuously Differentiable Penalty Functions

We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously differentiable exact penalty function. This reformulation is based on replacing the Lagrange multipliers in the augmented Lagrangian of the original problem by Lagrange multiplier functions. The expressions of these Lagrange multiplier functions, which depend upon the gradients of the objective function and the constraints, can make the unconstrained penalty function non-convex in general even if the original problem is convex. We establish sufficient conditions on the objective function and the constraints of the original problem under which the unconstrained penalty function is convex. This enables us to use Nesterov's accelerated gradient method for unconstrained convex optimization and achieve a guaranteed rate of convergence which is better than the state-of-the-art first-order algorithms for constrained convex optimization. Simulations illustrate our results.

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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.

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arXiv2021

Enabling DER Participation in Frequency Regulation Markets

Distributed energy resources (DERs) are playing an increasing role in ancillary services for the bulk grid, particularly in frequency regulation. In this paper, we propose a framework for collections of DERs, combined to form microgrids and controlled by aggregators, to participate in frequency regulation markets. Our approach covers both the identification of bids for the market clearing stage and the mechanisms for the real-time allocation of the regulation signal. The proposed framework is hierarchical, consisting of a top layer and a bottom layer. The top layer consists of the aggregators communicating in a distributed fashion to optimally disaggregate the regulation signal requested by the system operator. The bottom layer consists of the DERs inside each microgrid whose power levels are adjusted so that the tie line power matches the output of the corresponding aggregator in the top layer. The coordination at the top layer requires the knowledge of cost functions, ramp rates and capacity bounds of the aggregators. We develop meaningful abstractions for these quantities respecting the power flow constraints and taking into account the load uncertainties, and propose a provably correct distributed algorithm for optimal disaggregation of regulation signal amongst the microgrids.

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arXiv2020

Exploiting timing information in event-triggered stabilization of linear systems with disturbances

In the same way that subsequent pauses in spoken language are used to convey information, it is also possible to transmit information in communication networks not only by message content, but also with its timing. This paper presents an event-triggering strategy that utilizes timing information by transmitting in a state-dependent fashion. We consider the stabilization of a continuous-time, time-invariant, linear plant over a digital communication channel with bounded delay and subject to bounded plant disturbances and establish two main results. On the one hand, we design an encoding-decoding scheme that guarantees a sufficient information transmission rate for stabilization. On the other hand, we determine a lower bound on the information transmission rate necessary for stabilization by any control policy.

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arXiv2020

Safety-Critical Event Triggered Control via Input-to-State Safe Barrier Functions

The efficient utilization of available resources while simultaneously achieving control objectives is a primary motivation in the event-triggered control paradigm. In many modern control applications, one such objective is enforcing the safety of a system. The goal of this paper is to carry out this vision by combining event-triggered and safety-critical control design. We discuss how a direct transcription, in the context of safety, of event-triggered methods for stabilization may result in designs that are not implementable on real hardware due to the lack of a minimum interevent time. We provide a counterexample showing this phenomena and, building on the insight gained, propose an event-triggered control approach via Input to State Safe Barrier Functions that achieves safety while ensuring that interevent times are uniformly lower bounded. We illustrate our results in simulation.

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arXiv2020

Distributed bilayered control for transient frequency safety and system stability in power grids

This paper considers power networks governed by swing nonlinear dynamics and subject to disturbances. We develop a bilayered control strategy for a subset of buses that simultaneously guarantees transient frequency safety of each individual bus and asymptotic stability of the entire network. The bottom layer is a model predictive controller that, based on periodically sampled system information, optimizes control resources to have transient frequency evolve close to a safe desired interval. The top layer is a real-time controller assisting the bottom-layer controller to guarantee transient frequency safety is actually achieved. We show that control signals at both layers are Lipschitz in the state and do not jeopardize stability of the network. Furthermore, we carefully characterize the information requirements at each bus necessary to implement the controller and employ saddle-point dynamics to introduce a distributed implementation that only requires information exchange with up to 2-hop neighbors in the power network. Simulations on the IEEE 39-bus power network illustrate our results.

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arXiv2019

Model predictive control for transient frequency regulation of power networks

This paper introduces a control strategy to simultaneously achieve asymptotic stabilization and transient frequency regulation of power networks. The control command is generated by iteratively solving an open-loop control cost minimization problem with stability and transient frequency constraints. To deal with the non-convexity of the stability constraint, we propose a convexification strategy that uses a reference trajectory based on the system's current state. We also detail how to employ network partitions to implement the proposed control strategy in a distributed way, where each region only requires system information from neighboring regions to execute its controller.

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arXiv2019

Tracking Control by the Newton-Raphson Method with Output Prediction and Controller Speedup

This paper presents a control technique for output tracking of reference signals in continuous-time dynamical systems. The technique is comprised of the following three elements: (i) output prediction which has to track the reference signal, (ii) a controller based on an integrator with variable gain, and (iii) a speedup of the control action for enhancing the tracker's accuracy and, in some cases, guaranteeing stability of the closed-loop system. The technique is suitable for linear and nonlinear systems, implementable by simple algorithms, can track reference points as well as time-dependent reference signals, and may have large, even global domains of attraction. The derived theoretical results include convergence of the tracking controller and error analysis, and are supported by illustrative simulation and laboratory experiments.

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arXiv2019

Event-Triggered Communication and Control of Networked Systems for Multi-Agent Consensus

This article provides an introduction to event-triggered coordination for multi-agent average consensus. We provide a comprehensive account of the motivations behind the use of event-triggered strategies for consensus, the methods for algorithm synthesis, the technical challenges involved in establishing desirable properties of the resulting implementations, and their applications in distributed control. We pay special attention to the assumptions on the capabilities of the network agents and the resulting features of the algorithm execution, including the interconnection topology, the evaluation of triggers, and the role of imperfect information. The issues raised in our discussion transcend the specific consensus problem and are indeed characteristic of cooperative algorithms for networked systems that solve other coordination tasks. As our discussion progresses, we make these connections clear, highlighting general challenges and tools to address them widespread in the event-triggered control of networked systems.

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arXiv2018

Heterogeneity of Central Nodes Explains the Benefits of Time-Varying Control in Complex Dynamical Networks

Despite extensive research and remarkable advancements in the control of complex dynamical networks, most studies and practical control methods limit their focus to time-invariant control schedules (TICS). This is both due to their simplicity and the fact that the benefits of time-varying control schedules (TVCS) have remained largely uncharacterized. In this paper we study networks with linear and discrete-time dynamics and analyze the role of network structure in TVCS. First, we show that TVCS can significantly enhance network controllability over TICS, especially when applied to large networks. Through the analysis of a scale-dependent notion of nodal centrality, we then show that optimal TVCS involves the actuation of the most central nodes at appropriate spatial scales at all times. Consequently, it is the scale-heterogeneity of the central-nodes in a network that determine whether, and to what extent, TVCS outperforms conventional policies based on TICS. Here, scale-heterogeneity of a network refers to how diverse the central nodes of the network are at different spatial (local vs. global) scales. Several analytical results and case studies support and illustrate this relationship.

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arXiv2018

Cooperative data-driven distributionally robust optimization

This paper studies a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown to the agents, so each one gathers samples of it. The agents aim to cooperatively find, using their data, a solution to the optimization problem with guaranteed out-of-sample performance. The approach is to formulate a data-driven distributionally robust optimization problem using Wasserstein ambiguity sets, which turns out to be equivalent to a convex program. We reformulate the latter as a distributed optimization problem and identify a convex-concave augmented Lagrangian function whose saddle points are in correspondence with the optimizers provided a min-max interchangeability criteria is met. Our distributed algorithm design then consists of the saddle-point dynamics associated to the augmented Lagrangian. We formally establish that the trajectories of the dynamics converge asymptotically to a saddle point and hence an optimizer of the problem. Finally, we provide a class of functions that meet the min-max interchangeability criteria. Simulations illustrate our results.

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