Jorge Cortes

Bahman Gharesifard, Jorge Cortes

This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios, we show that the consensus-based dynamics that solves the continuous-time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting. This study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge, on any strongly connected weight-balanced digraph, to the set of minimizers of a sum of convex differentiable functions with globally Lipschitz gradients. Our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results.

Solmaz S. Kia, Bryan Van Scoy, Jorge Cortes et al.

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.

Bahman Gharesifard, Jorge Cortes

This paper considers a class of strategic scenarios in which two networks of agents have opposing objectives with regards to the optimization of a common objective function. In the resulting zero-sum game, individual agents collaborate with neighbors in their respective network and have only partial knowledge of the state of the agents in the other network. For the case when the interaction topology of each network is undirected, we synthesize a distributed saddle-point strategy and establish its convergence to the Nash equilibrium for the class of strictly concave-convex and locally Lipschitz objective functions. We also show that this dynamics does not converge in general if the topologies are directed. This justifies the introduction, in the directed case, of a generalization of this distributed dynamics which we show converges to the Nash equilibrium for the class of strictly concave-convex differentiable functions with locally Lipschitz gradients. The technical approach combines tools from algebraic graph theory, nonsmooth analysis, set-valued dynamical systems, and game theory.

Mohammad Javad Khojasteh, Pavankumar Tallapragada, Jorge Cortes et al.

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.

Ashish Cherukuri, Jorge Cortes

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.

Mohammad Javad Khojasteh, Mojtaba Hedayatpour, Jorge Cortes et al.

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.

Erfan Nozari, Fabio Pasqualetti, Jorge Cortes

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.

Mohammad Javad Khojasteh, Mojtaba Hedayatpour, Jorge Cortes et al.

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.

William Retnaraj, Simone Betteti, Alexander Davydov et al.

Linear-threshold networks (LTNs) capture the mesoscale behavior of interacting populations of neurons and are of particular interest to control theorists due to their dynamical richness and relative ease of analysis. The aim of this paper is to advance the study of global asymptotic stability in LTNs with asymmetric neural interactions and heterogeneous dissipation under the structural Lyapunov diagonal stability (LDS) condition. To this end, we introduce a one-parameter family of LTNs that preserves the LDS condition and has a parameter-independent equilibrium set. In the fast limit, this family converges to a projected dynamical system (PDS), while in the slow limit, it converges to a discontinuous hard-selector system (HSS). Under LDS, we prove that the fast PDS limit is globally exponentially stable and that the HSS limit is globally asymptotically stable. This alignment suggests that the limiting systems capture essential mechanisms governing stability across the entire LTN family. Together with numerical evidence, these findings indicate that resolving stability at the fast and slow endpoints provides a promising and structurally grounded path toward establishing global stability for LTNs with biologically plausible recurrence and diagonal dissipation.

Dhruv Shah, Jorge Cortes

Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image under the operator. To systematically minimize this error, we propose an algebraic framework for subspace pruning utilizing principal vectors. We establish the equivalence of this approach to existing consistency-based methods while providing a foundation for broader generalizations. To ensure scalability, we introduce an efficient numerical update scheme based on rank-one modifications, reducing the computational complexity of tracking principal angles by an order of magnitude. Finally, we demonstrate the effectiveness of our framework through numerical simulations.

Dhruv Shah, Jorge Cortes

Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, which formally corresponds to the largest principal angle between the subspace and its image under the operator. Yet, existing techniques are largely restricted to Euclidean settings. To bridge this gap, this paper presents an approach for computing principal angles and vectors to enable Koopman subspace pruning within a Reproducing Kernel Hilbert Space (RKHS) geometry. We first outline an exact computational routine, which is subsequently scaled for large datasets using randomized Nystrom approximations. Based on these foundations, we introduce the Kernel-SPV and Approximate Kernel-SPV algorithms for targeted subspace refinement via principal vectors. Simulation results validate our approach.

Kehan Long, Jorge Cortes, Nikolay Atanasov

This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for uncertain systems is the accurate determination of and adaptation to shifts in model parametric uncertainty during online deployment. We tackle this with a novel distributionally robust formulation of the Lyapunov derivative chance constraint ensuring a monotonic decrease of the Lyapunov certificate. To avoid the computational complexity involved in dealing with the space of probability measures, we identify a sufficient condition in the form of deterministic convex constraints that ensures the Lyapunov derivative constraint is satisfied. We integrate this condition into a loss function for training a neural network-based controller and show that, for the resulting closed-loop system, the global asymptotic stability of its equilibrium can be certified with high confidence, even with Out-of-Distribution (OoD) model uncertainties. To demonstrate the efficacy and efficiency of the proposed methodology, we compare it with an uncertainty-agnostic baseline approach and several reinforcement learning approaches in two control problems in simulation.

Yifu Zhang, Jorge Cortes

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.

Yifu Zhang, Jorge Cortes

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.

Yifu Zhang, Jorge Cortes

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.

Yifu Zhang, Jorge Cortes

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.

Pavankumar Tallapragada, Massimo Franceschetti, Jorge Cortes

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.

Pavankumar Tallapragada, Jorge Cortes

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.

Bahman Gharesifard, Jorge Cortes

Weight-balanced and doubly stochastic digraphs are two classes of digraphs that play an essential role in a variety of cooperative control problems, including formation control, distributed averaging, and optimization. We refer to a digraph as doubly stochasticable (weight-balanceable) if it admits a doubly stochastic (weight-balanced) adjacency matrix. This paper studies the characterization of both classes of digraphs, and introduces distributed algorithms to compute the appropriate set of weights in each case.