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This paper presents a unified control framework that integrates a Feedback Linearization (FL) controller in the inner loop with an adaptive Data-Enabled Policy Optimization (DeePO) controller in the outer loop to balance an autonomous bicycle. While the FL controller stabilizes and partially linearizes the inherently unstable and nonlinear system, its performance is compromised by unmodeled dynamics and time-varying characteristics. To overcome these limitations, the DeePO controller is introduced to enhance adaptability and robustness. The initial control policy of DeePO is obtained from a finite set of offline, persistently exciting input and state data. To improve stability and compensate for system nonlinearities and disturbances, a robustness-promoting regularizer refines the initial policy, while the adaptive section of the DeePO framework is enhanced with a forgetting factor to improve adaptation to time-varying dynamics. The proposed DeePO+FL approach is evaluated through simulations and real-world experiments on an instrumented autonomous bicycle. Results demonstrate its superiority over the FL-only approach, achieving more precise tracking of the reference lean angle and lean rate.

Although social networks have expanded the range of ideas and information accessible to users, they are also criticized for amplifying the polarization of user opinions. Given the inherent complexity of these phenomena, existing approaches to counteract these effects typically rely on handcrafted algorithms and heuristics. We propose an elegant solution: we act on the network weights that model user interactions on social networks (e.g., frequency of communication), to optimize a performance metric (e.g., polarization reduction), while users' opinions follow the classical Friedkin-Johnsen model. Our formulation gives rise to a challenging large-scale optimization problem with non-convex constraints, for which we develop a gradient-based algorithm. Our scheme is simple, scalable, and versatile, as it can readily integrate different, potentially non-convex, objectives. We demonstrate its merit by: (i) rapidly solving complex social network intervention problems with 3 million variables based on the Reddit and DBLP datasets; (ii) significantly outperforming competing approaches in terms of both computation time and disagreement reduction.

Accurate differentiation of pseudoprogression (PsP) from True Progression (TP) following radiotherapy (RT) in glioblastoma (GBM) patients is crucial for optimal treatment planning. However, this task remains challenging due to the overlapping imaging characteristics of PsP and TP. This study therefore proposes a multimodal deep-learning approach utilizing complementary information from routine anatomical MR images, clinical parameters, and RT treatment planning information for improved predictive accuracy. The approach utilizes a self-supervised Vision Transformer (ViT) to encode multi-sequence MR brain volumes to effectively capture both global and local context from the high dimensional input. The encoder is trained in a self-supervised upstream task on unlabeled glioma MRI datasets from the open BraTS2021, UPenn-GBM, and UCSF-PDGM datasets to generate compact, clinically relevant representations from FLAIR and T1 post-contrast sequences. These encoded MR inputs are then integrated with clinical data and RT treatment planning information through guided cross-modal attention, improving progression classification accuracy. This work was developed using two datasets from different centers: the Burdenko Glioblastoma Progression Dataset (n = 59) for training and validation, and the GlioCMV progression dataset from the University Hospital Erlangen (UKER) (n = 20) for testing. The proposed method achieved an AUC of 75.3%, outperforming the current state-of-the-art data-driven approaches. Importantly, the proposed approach relies on readily available anatomical MRI sequences, clinical data, and RT treatment planning information, enhancing its clinical feasibility. The proposed approach addresses the challenge of limited data availability for PsP and TP differentiation and could allow for improved clinical decision-making and optimized treatment plans for GBM patients.

The large-scale allocation of public resources (e.g., transportation, energy) is among the core challenges of future Cyber-Physical-Human Systems (CPHS). In order to guarantee that these systems are efficient and fair, recent works have investigated non-monetary resource allocation schemes, including schemes that employ karma. Karma is a non-tradable token that flows from users gaining resources to users yielding resources. Thus far karma-based solutions considered the allocation of a single public resource, however, modern CPHS are complex as they involve the allocation of multiple coupled resources. For example, a user might want to trade-off fast travel on highways for convenient parking in the city center, and different users could have heterogeneous preferences for such coupled resources. In this paper, we explore how to optimally combine multiple karma economies for coupled resource allocations, using two mechanism-design instruments: (non-uniform) karma redistribution; and (non-unit) exchange rates. We first extend the existing Dynamic Population Game (DPG) model that predicts the Stationary Nash Equilibrium (SNE) of the multi-karma economies. Then, in a numerical case study, we demonstrate that the design of redistribution significantly affects the coupled resource allocations, while non-unit exchange rates play a minor role. To assess the allocation outcomes under user heterogeneity, we adopt Nash welfare as our social welfare function, since it makes no interpersonal comparisons and it is axiomatically rooted in social choice theory. Our findings suggest that the simplest mechanism design, that is, uniform redistribution with unit exchange rates, also attains maximum social welfare.

Online Feedback Optimization (OFO) is a control approach to drive a dynamical plant to an optimal steady state. By interconnecting optimization algorithms with real-time plant measurements, OFO provides all the benefits of feedback control, yet without requiring exact knowledge of plant dynamics for computing a setpoint. On the downside, existing stability guarantees for OFO require the controller to evolve on a sufficiently slower timescale than the plant, possibly affecting transient performance and responsiveness to disturbances. In this paper, we prove that, under suitable conditions, OFO ensures stability without any timescale separation. In particular, the condition we propose is independent of the time constant of the plant, hence it is scaling-invariant. Our analysis leverages a composite Lyapunov function, which is the $\max$ of plant-related and controller-related components. We corroborate our theoretical results with numerical examples.

This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems, leveraging optimization on the Grassmannian manifold leading to the Grassmannian Recursive Algorithm for Tracking (GREAT) method. The approach of representing linear systems by non-parametric subspace models has received significant interest in the field of data-driven control recently. We view subspaces as points on the Grassmannian manifold, and therefore, tracking is achieved by performing optimization on the manifold. At each time step, a single measurement from the current subspace corrupted by a bounded error is available. The subspace estimate is updated online using Grassmannian gradient descent on a cost function incorporating a window of the most recent data. Under suitable assumptions on the signal-to-noise ratio of the online data and the subspace's rate of change, we establish theoretical guarantees for the resulting algorithm. More specifically, we prove an exponential convergence rate and provide a consistent uncertainty quantification of the estimates in terms of an upper bound on their distance to the true subspace. The applicability of the proposed algorithm is demonstrated by means of numerical examples, and it is shown to compare favorably with competing parametric system identification methods., Comment: Submitted to IEEE Transactions on Automatic Control

We develop analysis results for optimization algorithms that are open, that is, with inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of control loop without timescale separation. To be precise, we consider an incremental small gain problem to analyze robustness. Moreover, we investigate the behaviors of the closed loop between incrementally dissipative nonlinear plants and optimization algorithms. The framework we develop is built upon the theories of incremental dissipativity and monotone operators, and yields tests in the form of linear matrix inequalities.

Static structured control refers to the task of designing a state-feedback controller such that the control gain satisfies a subspace constraint. Structured control has applications in control of communication-inhibited dynamical systems, such as systems in networked environments. This work performs $H_2$-suboptimal regulation under a common structured state-feedback controller for a class of data-consistent plants. The certification of $H_2$-performance is attained through a combination of standard $H_2$ LMIs, convex sufficient conditions for structured control, and a matrix S-lemma for set-membership. The resulting convex optimization problems are linear matrix inequalities whose size scales independently of the number of data samples collected. Data-driven structured $H_2$-regulation control is demonstrated on example systems., Comment: 7 pages

Power electronic converters are gradually becoming the main components of modern power systems due to the increasing integration of renewable energy sources. However, power converters may become unstable when interacting with the complex and time-varying power grid. To deal with this problem, an adaptive control design scheme for power converters is preferable, which can capture the closed-loop dynamical interaction between the converter and the grid via online data. In this paper, we propose an adaptive data-driven control method, called data-enabled policy optimization (DeePO), to stabilize power converters by using only online input-output data. Our contributions are threefold. First, we propose a covariance parameterization of partially observed linear systems with input-output data. Second, we develop a DeePO algorithm, which updates the parameterized policy with data-based gradient descent to achieve computationally efficient adaptive control. Third, we use high-fidelity simulations to verify that DeePO can effectively stabilize grid-connected power converters and quickly adapt to the changes in the power grid.

We prove that linear policies remain optimal for solving the Linear Quadratic Gaussian regulation problem in face of worst-case process and measurement noise distributions, when these are independent, stationary, and known to be within a radius (in the Wasserstein sense) to some reference Gaussian noise distributions. When the reference noise distributions are not Gaussian, we provide a closed-form solution for the worst-case distributions. Our main result suggests a computational complexity that scales only with the dimensionality of the system, and provides a less conservative alternative to recent work in distributionally robust control.

Data centers are significant contributors to carbon emissions and can strain power systems due to their high electricity consumption. To mitigate this impact and to participate in demand response programs, cloud computing companies strive to balance and optimize operations across their global fleets by making strategic decisions about when and where to place compute jobs for execution. In this paper, we introduce a load shaping scheme which reacts to time-varying grid signals by leveraging both temporal and spatial flexibility of compute jobs to provide risk-aware management guidelines and job placement with provable performance guarantees based on distributionally robust optimization. Our approach divides the problem into two key components: (i) day-ahead planning, which generates an optimal scheduling strategy based on historical load data, and (ii) real-time job placement and (time) scheduling, which dynamically tracks the optimal strategy generated in (i). We validate our method in simulation using normalized load profiles from randomly selected Google clusters, incorporating time-varying grid signals. We can demonstrate significant reductions in carbon cost and peak power with our approach compared to myopic greedy policies, while maintaining computational efficiency and abiding to system constraints.

This article explores a flexible and coordinated control design for an aggregation of heterogeneous distributed energy resources (DERs) in a dynamic virtual power plant (DVPP). The control design aims to provide a desired aggregate grid-forming (GFM) response based on the coordination of power contributions between different DERs. Compared to existing DVPP designs with an AC-coupled AC-output configuration, a more generic modular DVPP design is proposed in this article, which comprises four types of basic DVPP modules, involving AC- or DC-coupling and AC- or DC-output, adequately accommodating diverse DER integration setups, such as AC, DC, AC/DC hybrid microgrids and renewable power plants. The control design is first developed for the four basic modules by the aggregation of DERs and the disaggregation of the control objectives, and then extended to modular DVPPs through a systematic top-down approach. The control performance is comprehensively validated through simulation. The modular DVPP design offers scalable and standardizable advanced grid interfaces (AGIs) for building and operating AC/DC hybrid power grids.

We study the convex-concave bilinear saddle-point problem $\min_x \max_y f(x) + y^\top Ax - g(y)$, where both, only one, or none of the functions $f$ and $g$ are strongly convex, and suitable rank conditions on the matrix $A$ hold. The solution of this problem is at the core of many machine learning tasks. By employing tools from operator theory, we systematically prove the contractivity (in turn, the linear convergence) of several first-order primal-dual algorithms, including the Chambolle-Pock method. Our approach results in concise and elegant proofs, and it yields new convergence guarantees and tighter bounds compared to known results.

Understanding the mechanical interplay between silicon anodes and their surrounding solid-electrolyte interphase (SEI) is essential to improve the next generation of lithium-ion batteries. We model and simulate a 2D elliptical silicon nanowire with SEI via a thermodynamically consistent chemo-mechanical continuum ansatz using a higher order finite element method in combination with a variable-step, variable-order time integration scheme. Considering a soft viscoplastic SEI for three half cycles, we see at the minor half-axis the largest stress magnitude at the silicon nanowire surface, leading to a concentration anomaly. This anomaly is caused by the shape of the nanowire itself and not by the SEI. Also for the tangential stress of the SEI, the largest stress magnitudes are at this point, which can lead to SEI fracture. However, for a stiff SEI, the largest stress magnitude inside the nanowire occurs at the major half-axis, causing a reduced concentration distribution in this area. The largest tangential stress of the SEI is still at the minor half-axis. In total, we demonstrate the importance of considering the mechanics of the anode and SEI in silicon anode simulations and encourage further numerical and model improvements.

Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very difficult to establish convergence guarantees. This leads to a wide use of brute-force methods, such as grid searching and Monte-Carlo sampling and, when applicable, complex and problem-specific algorithms. In this paper, we consider inference problems where the variables are related by multiaffine expressions. We propose a novel Alternating and Iteratively-Reweighted Least Squares (AIRLS) algorithm, and prove its convergence for problems with Generalized Normal Distributions. We also provide an efficient method to compute the variance of the estimates obtained using AIRLS. Finally, we show how the method can be applied to graphical statistical models. We perform numerical experiments on several inference problems, showing significantly better performance than state-of-the-art approaches in terms of scalability, robustness to noise, and convergence speed due to an empirically observed super-linear convergence rate.

Personalized content on social platforms can exacerbate negative phenomena such as polarization, partly due to the feedback interactions between recommendations and the users. In this paper, we present a control-theoretic recommender system that explicitly accounts for this feedback loop to mitigate polarization. Our approach extends online feedback optimization - a control paradigm for steady-state optimization of dynamical systems - to develop a recommender system that trades off users engagement and polarization reduction, while relying solely on online click data. We establish theoretical guarantees for optimality and stability of the proposed design and validate its effectiveness via numerical experiments with a user population governed by Friedkin-Johnsen dynamics. Our results show these "network-aware" recommendations can significantly reduce polarization while maintaining high levels of user engagement.

Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of assumptions on the graphical structure of the model and observational data, represented as a non-causal covariance matrix. In this paper, we give a new sound and complete algorithm for generic identification which runs in polynomial space. By standard simulation results, this algorithm has exponential running time which vastly improves the state-of-the-art double exponential time method using a Gr\"obner basis approach. The paper also presents evidence that parameter identification is computationally hard in general. In particular, we prove, that the task asking whether, for a given feasible correlation matrix, there are exactly one or two or more parameter sets explaining the observed matrix, is hard for $\forall R$, the co-class of the existential theory of the reals. In particular, this problem is $coNP$-hard. To our best knowledge, this is the first hardness result for some notion of identifiability.

In this work, we analyze two large-scale surveys to examine how individuals think about sharing smartphone access with romantic partners as a function of trust in relationships. We find that the majority of couples have access to each others' devices, but may have explicit or implicit boundaries on how this access is to be used. Investigating these boundaries and related social norms, we find that there is little consensus about the level of smartphone access (i.e., transparency), or lack thereof (i.e., privacy) that is desirable in romantic contexts. However, there is broad agreement that the level of access should be mutual and consensual. Most individuals understand trust to be the basis of their decisions about transparency and privacy. Furthermore, we find individuals have crossed these boundaries, violating their partners' privacy and betraying their trust. We examine how, when, why, and by whom these betrayals occur. We consider the ramifications of these boundary violations in the case of intimate partner violence. Finally, we provide recommendations for design changes to enable technological enforcement of boundaries currently enforced by trust, bringing access control in line with users' sharing preferences.

Diffusion regulates numerous natural processes and the dynamics of many successful generative models. Existing models to learn the diffusion terms from observational data rely on complex bilevel optimization problems and model only the drift of the system. We propose a new simple model, JKOnet*, which bypasses the complexity of existing architectures while presenting significantly enhanced representational capabilities: JKOnet* recovers the potential, interaction, and internal energy components of the underlying diffusion process. JKOnet* minimizes a simple quadratic loss and outperforms other baselines in terms of sample efficiency, computational complexity, and accuracy. Additionally, JKOnet* provides a closed-form optimal solution for linearly parametrized functionals, and, when applied to predict the evolution of cellular processes from real-world data, it achieves state-of-the-art accuracy at a fraction of the computational cost of all existing methods. Our methodology is based on the interpretation of diffusion processes as energy-minimizing trajectories in the probability space via the so-called JKO scheme, which we study via its first-order optimality conditions., Comment: Accepted for presentation at, and publication in the proceedings of, the 38th Conference on Neural Information Processing Systems (NeurIPS 2024, oral)

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus, one typically resorts to the abstract machinery of infinite-dimensional analysis or other ad-hoc methodologies, not tailored to the probability space, which however involve projections or rely on convexity-type assumptions. We believe instead that these problems call for a comprehensive methodological framework for calculus in probability spaces. In this work, we combine ideas from optimal transport, variational analysis, and Wasserstein gradient flows to equip the Wasserstein space (i.e., the space of probability measures endowed with the Wasserstein distance) with a variational structure, both by combining and extending existing results and introducing novel tools. Our theoretical analysis culminates in very general necessary optimality conditions for optimality. Notably, our conditions (i) resemble the rationales of Euclidean spaces, such as the Karush-Kuhn-Tucker and Lagrange conditions, (ii) are intuitive, informative, and easy to study, and (iii) yield closed-form solutions or can be used to design computationally attractive algorithms. We believe this framework lays the foundation for new algorithmic and theoretical advancements in the study of optimization problems in probability spaces, which we exemplify with numerous case studies and applications to machine learning, drug discovery, and distributionally robust optimization.

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic Optimistic RL (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, we provide a first-of-its-kind regret bound of $O(\Gamma_T \sqrt{T})$ for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

Reinforcement learning (RL) excels in optimizing policies for discrete-time Markov decision processes (MDP). However, various systems are inherently continuous in time, making discrete-time MDPs an inexact modeling choice. In many applications, such as greenhouse control or medical treatments, each interaction (measurement or switching of action) involves manual intervention and thus is inherently costly. Therefore, we generally prefer a time-adaptive approach with fewer interactions with the system. In this work, we formalize an RL framework, Time-adaptive Control & Sensing (TaCoS), that tackles this challenge by optimizing over policies that besides control predict the duration of its application. Our formulation results in an extended MDP that any standard RL algorithm can solve. We demonstrate that state-of-the-art RL algorithms trained on TaCoS drastically reduce the interaction amount over their discrete-time counterpart while retaining the same or improved performance, and exhibiting robustness over discretization frequency. Finally, we propose OTaCoS, an efficient model-based algorithm for our setting. We show that OTaCoS enjoys sublinear regret for systems with sufficiently smooth dynamics and empirically results in further sample-efficiency gains.

Over the past decade, the continuous surge in cloud computing demand has intensified data center workloads, leading to significant carbon emissions and driving the need for improving their efficiency and sustainability. This paper focuses on the optimal allocation problem of batch compute loads with temporal and spatial flexibility across a global network of data centers. We propose a bilevel game-theoretic solution approach that captures the inherent hierarchical relationship between supervisory control objectives, such as carbon reduction and peak shaving, and operational objectives, such as priority-aware scheduling. Numerical simulations with real carbon intensity data demonstrate that the proposed approach successfully reduces carbon emissions while simultaneously ensuring operational reliability and priority-aware scheduling.

In this paper, we implement an advanced safety filter to smoothly limit the current of an inverter-based Battery Energy Storage System. The task involves finding suitable Control Barrier Function and Control Lyapunov Function via Sum-of-Squares optimization to certify the system's safety during grid transients. In contrast to the conventional safety filter, the advanced safety filter not only provides a safety certificate but also achieves finite-time convergence to a nominal region. Within this region, the action of the nominal control, i.e. the Enhanced Direct Power Control, remains unaltered by the safety filter. The advanced safety filter is implemented using a Quadratically Constrained Quadratic Program, providing the capability to also encode quadratic input constraints. Finally, we showcase the effectiveness of the implementation through simulations involving a load step at the Point of Common Coupling, and we compare the outcomes with those obtained using a standard vector current controller.

Background: This research aims to improve glioblastoma survival prediction by integrating MR images, clinical and molecular-pathologic data in a transformer-based deep learning model, addressing data heterogeneity and performance generalizability. Method: We propose and evaluate a transformer-based non-linear and non-proportional survival prediction model. The model employs self-supervised learning techniques to effectively encode the high-dimensional MRI input for integration with non-imaging data using cross-attention. To demonstrate model generalizability, the model is assessed with the time-dependent concordance index (Cdt) in two training setups using three independent public test sets: UPenn-GBM, UCSF-PDGM, and RHUH-GBM, each comprising 378, 366, and 36 cases, respectively. Results: The proposed transformer model achieved promising performance for imaging as well as non-imaging data, effectively integrating both modalities for enhanced performance (UPenn-GBM test-set, imaging Cdt 0.645, multimodal Cdt 0.707) while outperforming state-of-the-art late-fusion 3D-CNN-based models. Consistent performance was observed across the three independent multicenter test sets with Cdt values of 0.707 (UPenn-GBM, internal test set), 0.672 (UCSF-PDGM, first external test set) and 0.618 (RHUH-GBM, second external test set). The model achieved significant discrimination between patients with favorable and unfavorable survival for all three datasets (logrank p 1.9\times{10}^{-8}, 9.7\times{10}^{-3}, and 1.2\times{10}^{-2}). Conclusions: The proposed transformer-based survival prediction model integrates complementary information from diverse input modalities, contributing to improved glioblastoma survival prediction compared to state-of-the-art methods. Consistent performance was observed across institutions supporting model generalizability.

The framework of Pearl's Causal Hierarchy (PCH) formalizes three types of reasoning: probabilistic (i.e. purely observational), interventional, and counterfactual, that reflect the progressive sophistication of human thought regarding causation. We investigate the computational complexity aspects of reasoning in this framework focusing mainly on satisfiability problems expressed in probabilistic and causal languages across the PCH. That is, given a system of formulas in the standard probabilistic and causal languages, does there exist a model satisfying the formulas? Our main contribution is to prove the exact computational complexities showing that languages allowing addition and marginalization (via the summation operator) yield NP^PP, PSPACE-, and NEXP-complete satisfiability problems, depending on the level of the PCH. These are the first results to demonstrate a strictly increasing complexity across the PCH: from probabilistic to causal and counterfactual reasoning. On the other hand, in the case of full languages, i.e. allowing addition, marginalization, and multiplication, we show that the satisfiability for the counterfactual level remains the same as for the probabilistic and causal levels, solving an open problem in the field., Comment: accepted at ICLR 25

To characterize the computational complexity of satisfiability problems for probabilistic and causal reasoning within the Pearl's Causal Hierarchy, arXiv:2305.09508 [cs.AI] introduce a new natural class, named succ-$\exists$R. This class can be viewed as a succinct variant of the well-studied class $\exists$R based on the Existential Theory of the Reals (ETR). Analogously to $\exists$R, succ-$\exists$R is an intermediate class between NEXP and EXPSPACE, the exponential versions of NP and PSPACE. The main contributions of this work are threefold. Firstly, we characterize the class succ-$\exists$R in terms of nondeterministic real RAM machines and develop structural complexity theoretic results for real RAMs, including translation and hierarchy theorems. Notably, we demonstrate the separation of $\exists$R and succ-$\exists$R. Secondly, we examine the complexity of model checking and satisfiability of fragments of existential second-order logic and probabilistic independence logic. We show succ-$\exists$R- completeness of several of these problems, for which the best-known complexity lower and upper bounds were previously NEXP-hardness and EXPSPACE, respectively. Thirdly, while succ-$\exists$R is characterized in terms of ordinary (non-succinct) ETR instances enriched by exponential sums and a mechanism to index exponentially many variables, in this paper, we prove that when only exponential sums are added, the corresponding class $\exists$R^{\Sigma} is contained in PSPACE. We conjecture that this inclusion is strict, as this class is equivalent to adding a VNP-oracle to a polynomial time nondeterministic real RAM. Conversely, the addition of exponential products to ETR, yields PSPACE. Additionally, we study the satisfiability problem for probabilistic reasoning, with the additional requirement of a small model and prove that this problem is complete for $\exists$R^{\Sigma}., Comment: ISAAC 2024

This paper develops an adaptive traffic control policy inspired by Maximum Pressure (MP) while imposing coordination across intersections. The proposed Coordinated Maximum Pressure-plus-Penalty (CMPP) control policy features a local objective for each intersection that consists of the total pressure within the neighborhood and a penalty accounting for the queue capacities and continuous green time for certain movements. The corresponding control task is reformulated as a distributed optimization problem and solved via two customized algorithms: one based on the alternating direction method of multipliers (ADMM) and the other follows a greedy heuristic augmented with a majority vote. CMPP not only provides a theoretical guarantee of queuing network stability but also outperforms several benchmark controllers in simulations on a large-scale real traffic network with lower average travel and waiting time per vehicle, as well as less network congestion. Furthermore, CPMM with the greedy algorithm enjoys comparable computational efficiency as fully decentralized controllers without significantly compromising the control performance, which highlights its great potential for real-world deployment.

Opinion dynamics models are important in understanding and predicting opinion formation processes within social groups. Although the weighted-averaging opinion-update mechanism is widely adopted as the micro-foundation of opinion dynamics, it bears a non-negligibly unrealistic implication: opinion attractiveness increases with opinion distance. Recently, the weighted-median mechanism has been proposed as a new microscopic mechanism of opinion exchange. Numerous advancements have been achieved regarding this new micro-foundation, from theoretical analysis to empirical validation, in a discrete-time asynchronous setup. However, the original discrete-time weighted-median model does not allow for "compromise behavior" in opinion exchanges, i.e., no intermediate opinions are created between disagreeing agents. To resolve this problem, this paper propose a novel continuous-time weighted-median opinion dynamics model, in which agents' opinions move towards the weighted-medians of their out-neighbors' opinions. It turns out that the proof methods for the original discrete-time asynchronous model are no longer applicable to the analysis of the continuous-time model. In this paper, we first establish the existence and uniqueness of the solution to the continuous-time weighted-median opinion dynamics by showing that the weighted-median mapping is contractive on any graph. We also characterize the set of all the equilibria. Then, by leveraging a new LaSalle invariance principle argument, we prove the convergence of the continuous-time weighted-median model for any initial condition and derive a necessary and sufficient condition for the convergence to consensus., Comment: 13 pages, 1 figure

Motivated by the complex dynamics of cooperative and competitive interactions within networked agent systems, multi-cluster games provide a framework for modeling the interconnected goals of self-interested clusters of agents. For this setup, the existing literature lacks comprehensive gradient-based solutions that simultaneously consider constraint sets and directed communication networks, both of which are crucial for many practical applications. To address this gap, this paper proposes a distributed Nash equilibrium seeking algorithm that integrates consensus-based methods and gradient-tracking techniques, where inter-cluster and intra-cluster communications only use row- and column-stochastic weight matrices, respectively. To handle constraints, we introduce an averaging procedure, which can effectively address the complications associated with projections. In turn, we can show linear convergence of our algorithm, focusing on the contraction property of the optimality gap. We demonstrate the efficacy of the proposed algorithm through a microgrid energy management application.

We determine all functional closure properties of finite $\mathbb{N}$-weighted automata, even all multivariate ones, and in particular all multivariate polynomials. We also determine all univariate closure properties in the promise setting, and all multivariate closure properties under certain assumptions on the promise, in particular we determine all multivariate closure properties where the output vector lies on a monotone algebraic graph variety., Comment: Short version to be published at ICALP 2024

This article proposes a "cross-forming" control concept for grid-forming inverters operating against grid faults. Cross-forming refers to voltage angle forming and current magnitude forming. It differs from classical grid-forming and grid-following paradigms that feature voltage magnitude-and-angle forming and voltage magnitude-and-angle following (or current magnitude-and-angle forming), respectively. The cross-forming concept addresses the need for inverters to remain grid-forming (particularly voltage angle forming, as required by grid codes) while managing fault current limitation. Simple and feasible cross-forming control implementations are proposed, enabling inverters to quickly limit fault currents to a prescribed level while preserving voltage angle forming for grid-forming synchronization and providing dynamic ancillary services, during symmetrical or asymmetrical fault ride-through. Moreover, the cross-forming control yields an equivalent system featuring a constant virtual impedance and a "normal form" representation, allowing for the extension of previously established transient stability results to include scenarios involving current saturation. Simulations and experiments validate the efficacy of the proposed cross-forming control implementations.

Game-theoretic MPC (or Receding Horizon Games) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion. This control paradigm has recently received an increasing attention in various application fields, including robotics, autonomous driving, traffic networks, and energy grids, due to its ability to model the competitive nature of self-interested agents with shared resources while incorporating future predictions, dynamic models, and constraints into the decision-making process. In this work, we present the first formal stability analysis based on dissipativity and monotone operator theory that is valid also for non-potential games. Specifically, we derive LMI-based certificates that ensure asymptotic stability and are numerically verifiable. Moreover, we show that, if the agents have decoupled dynamics, the numerical verification can be performed in a scalable manner. Finally, we present tuning guidelines for the agents' cost function weights to fulfill the certificates and, thus, ensure stability.

This work addresses the scattering problem of an incident wave at a junction connecting two semi-infinite waveguides, which we intend to solve using Physics-Informed Neural Networks (PINNs). As with other deep learning-based approaches, PINNs are known to suffer from a spectral bias and from the hyperbolic nature of the Helmholtz equation. This makes the training process challenging, especially for higher wave numbers. We show an example where these limitations are present. In order to improve the learning capability of our model, we suggest an equivalent formulation of the Helmholtz Boundary Value Problem (BVP) that is based on splitting the total wave into a tapered continuation of the incoming wave and a remaining scattered wave. This allows the introduction of an inhomogeneity in the BVP, leveraging the information transmitted during back-propagation, thus, enhancing and accelerating the training process of our PINN model. The presented numerical illustrations are in accordance with the expected behavior, paving the way to a possible alternative approach to predicting scattering problems using PINNs.

Complex droop control, alternatively known as dispatchable virtual oscillator control (dVOC), stands out for its unique capabilities in synchronization and voltage stabilization among existing control strategies for grid-forming converters. Complex droop control leverages the novel concept of ``complex frequency'', thereby establishing a coupled connection between active and reactive power inputs and frequency and rate-of-change-of voltage outputs. However, its reliance on static droop gains limits its ability to exhibit crucial dynamic response behaviors required in future power systems. To address this limitation, this paper introduces dynamic complex-frequency control, upgrading static droop gains with dynamic transfer functions to enhance the richness and flexibility in dynamic responses for frequency and voltage control. Unlike existing approaches, the complex-frequency control framework treats frequency and voltage dynamics collectively, ensuring small-signal stability for frequency synchronization and voltage stabilization simultaneously. The control framework is validated through detailed numerical case studies on the IEEE nine-bus system, also showcasing its applicability in multi-converter setups., Comment: 6 Pages, 7 Figures

In this paper, we investigate the transient stability of a state-of-the-art grid-forming complex-droop control (i.e., dispatchable virtual oscillator control, dVOC) under current saturation. We quantify the saturation level of a converter by introducing the concept of degree of saturation (DoS), and we propose a provably stable current-limiting control with saturation-informed feedback, which feeds the degree of saturation back to the inner voltage-control loop and the outer grid-forming loop. As a result, although the output current is saturated, the voltage phase angle can still be generated from an internal virtual voltage-source node that is governed by an equivalent complex-droop control. We prove that the proposed control achieves transient stability during current saturation under grid faults. We also provide parametric stability conditions for multi-converter systems under grid-connected and islanded scenarios. The stability performance of the current-limiting control is validated with various case studies.

Feedback optimization enables autonomous optimality seeking of a dynamical system through its closed-loop interconnection with iterative optimization algorithms. Among various iteration structures, model-based approaches require the input-output sensitivity of the system to construct gradients, whereas model-free approaches bypass this need by estimating gradients from real-time evaluations of the objective. These approaches own complementary benefits in sample efficiency and accuracy against model mismatch, i.e., errors of sensitivities. To achieve the best of both worlds, we propose gray-box feedback optimization controllers, featuring systematic incorporation of approximate sensitivities into model-free updates via adaptive convex combination. We quantify conditions on the accuracy of the sensitivities that render the gray-box approach preferable. We elucidate how the closed-loop performance is determined by the number of iterations, the problem dimension, and the cumulative effect of inaccurate sensitivities. The proposed controller contributes to a balanced closed-loop behavior, which retains provable sample efficiency and optimality guarantees for nonconvex problems. We further develop a running gray-box controller to handle constrained time-varying problems with changing objectives and steady-state maps.

A system of non-tradable credits that flow between individuals like karma, hence proposed under that name, is a mechanism for repeated resource allocation that comes with attractive efficiency and fairness properties, in theory. In this study, we test karma in an online experiment in which human subjects repeatedly compete for a resource with time-varying and stochastic individual preferences or urgency to acquire the resource. We confirm that karma has significant and sustained welfare benefits even in a population with no prior training. We identify mechanism usage in contexts with sporadic high urgency, more so than with frequent moderate urgency, and implemented as a simple (binary) karma bidding scheme as particularly effective for welfare improvements: relatively larger aggregate efficiency gains are realized that are (almost) Pareto superior. These findings provide guidance for further testing and for future implementation plans of such mechanisms in the real world.

Amorphous silicon is a highly promising anode material for next-generation lithium-ion batteries. Large volume changes of the silicon particle have a critical effect on the surrounding solid-electrolyte interphase (SEI) due to repeated fracture and healing during cycling. Based on a thermodynamically consistent chemo-elasto-plastic continuum model we investigate the stress development inside the particle and the SEI. Using the example of a particle with SEI, we apply a higher order finite element method together with a variable-step, variable-order time integration scheme on a nonlinear system of partial differential equations. Starting from a single silicon particle setting, the surrounding SEI is added in a first step with the typically used elastic Green--St-Venant (GSV) strain definition for a purely elastic deformation. For this type of deformation, the definition of the elastic strain is crucial to get reasonable simulation results. In case of the elastic GSV strain, the simulation aborts. We overcome the simulation failure by using the definition of the logarithmic Hencky strain. However, the particle remains unaffected by the elastic strain definitions in the particle domain. Compared to GSV, plastic deformation with the Hencky strain is straightforward to take into account. For the plastic SEI deformation, a rate-independent and a rate-dependent plastic deformation are newly introduced and numerically compared for three half cycles for the example of a radial symmetric particle.

Motivated by how forecast errors exacerbate order fluctuations in supply chains, we leverage robust feedback controller synthesis to characterize, compute, and minimize the worst-case order fluctuation experienced by an individual supply chain vendor. Assuming bounded forecast errors and demand fluctuations, we model forecast error and demand fluctuations as inputs to linear inventory dynamics, and use the $\ell_\infty$ gain to define a transient Bullwhip measure. In contrast to the existing Bullwhip measure, the transient Bullwhip measure explicitly depends on the forecast error. This enables us to separately quantify the transient Bullwhip measure's sensitivity to forecast error and demand fluctuations. To compute the controller that minimizes the worst-case peak gain, we formulate an optimization problem with bilinear matrix inequalities and show that it is equivalent to minimizing a quasi-convex function on a bounded domain. We simulate our model for vendors with non-zero perishable rates and order backlogging rates, and prove that the transient Bullwhip measure can be bounded by a monotonic quasi-convex function whose dependency on the product backlog rate and perishing rate is verified in simulation., Comment: 7 pages, 4 figures

Online feedback optimization (OFO) enables optimal steady-state operations of a physical system by employing an iterative optimization algorithm as a dynamic feedback controller. When the plant consists of several interconnected sub-systems, centralized implementations become impractical due to the heavy computational burden and the need to pre-compute system-wide sensitivities, which may not be easily accessible in practice. Motivated by these challenges, we develop a fully distributed model-free OFO controller, featuring consensus-based tracking of the global objective value and local iterative (projected) updates that use stochastic gradient estimates. We characterize how the closed-loop performance depends on the size of the network, the number of iterations, and the level of accuracy of consensus. Numerical simulations on a voltage control problem in a direct current power grid corroborate the theoretical findings.

We present SIM-FSVGD for learning robot dynamics from data. As opposed to traditional methods, SIM-FSVGD leverages low-fidelity physical priors, e.g., in the form of simulators, to regularize the training of neural network models. While learning accurate dynamics already in the low data regime, SIM-FSVGD scales and excels also when more data is available. We empirically show that learning with implicit physical priors results in accurate mean model estimation as well as precise uncertainty quantification. We demonstrate the effectiveness of SIM-FSVGD in bridging the sim-to-real gap on a high-performance RC racecar system. Using model-based RL, we demonstrate a highly dynamic parking maneuver with drifting, using less than half the data compared to the state of the art.

A promising step from linear towards nonlinear data-driven control is via the design of controllers for linear parameter-varying (LPV) systems, which are linear systems whose parameters are varying along a measurable scheduling signal. However, the interplay between uncertainty arising from corrupted data and the parameter-varying nature of these systems impacts the stability analysis and limits the generalization of well-understood data-driven methods available for linear time-invariant systems. In this work, we decouple this interplay using a recently developed variant of the Fundamental Lemma for LPV systems and the concept of data-informativity, in combination with biquadratic Lyapunov forms. Together, these allow us to develop novel linear matrix inequality conditions for the existence of scheduling-dependent Lyapunov functions, incorporating the intrinsic nonlinearity. Appealingly, these results are stated purely in terms of the collected data and bounds on the noise, and they are computationally favorable to check., Comment: Accepted for the 63rd IEEE Conference on Decision and Control

In competitive multi-player interactions, simultaneous optimality is a key requirement for establishing strategic equilibria. This property is explicit when the game-theoretic equilibrium is the simultaneously optimal solution of coupled optimization problems. However, no such optimization problems exist for the correlated equilibrium, a strategic equilibrium where the players can correlate their actions. We address the lack of a coupled optimization framework for the correlated equilibrium by introducing an {unnormalized game} -- an extension of normal-form games in which the player strategies are lifted to unnormalized measures over the joint actions. We show that the set of fully mixed generalized Nash equilibria of this unnormalized game is a subset of the correlated equilibrium of the normal-form game. Furthermore, we introduce an entropy regularization to the unnormalized game and prove that the entropy-regularized generalized Nash equilibrium is a sub-optimal correlated equilibrium of the normal form game where the degree of sub-optimality depends on the magnitude of regularization. We prove that the entropy-regularized unnormalized game has a closed-form solution, and empirically verify its computational efficacy at approximating the correlated equilibrium of normal-form games., Comment: 8 pages, 2 figures

A closed-loop control model to analyze the impact of recommendation systems on opinion dynamics within social networks is introduced. The core contribution is the development and formalization of model-free and model-based approaches to recommendation system design, integrating the dynamics of social interactions within networks via an extension of the Friedkin-Johnsen (FJ) model. Comparative analysis and numerical simulations demonstrate the effectiveness of the proposed control strategies in maximizing user engagement and their potential for influencing opinion formation processes.

Recent years have seen a surge of artificial currency-based mechanisms in contexts where monetary instruments are deemed unfair or inappropriate, e.g., in allocating food donations to food banks, course seats to students, and, more recently, even for traffic congestion management. Yet the applicability of these mechanisms remains limited in repeated auction settings, as it is challenging for users to learn how to bid an artificial currency that has no value outside the auctions. Indeed, users must jointly learn the value of the currency in addition to how to spend it optimally. Moreover, in the prominent class of karma mechanisms, in which artificial karma payments are redistributed to users at each time step, users do not only spend karma to obtain public resources but also gain karma for yielding them. For this novel class of karma auctions, we propose an adaptive karma pacing strategy that learns to bid optimally, and show that this strategy a) is asymptotically optimal for a single user bidding against competing bids drawn from a stationary distribution; b) leads to convergent learning dynamics when all users adopt it; and c) constitutes an approximate Nash equilibrium as the number of users grows. Our results require a novel analysis in comparison to adaptive pacing strategies in monetary auctions, since we depart from the classical assumption that the currency has known value outside the auctions, and consider that the currency is both spent and gained through the redistribution of payments., Comment: Manuscript accepted at the 24th International Conference on Autonomous Agents and Multi-agent Systems(AAMAS 2025)

Due to more volatile generation, flexibility will become more important in transmission grids. One potential source of this flexibility can be distribution grids. A flexibility request from the transmission grid to a distribution grid then needs to be split up onto the different flexibility providing units (FPU) in the distribution grid. One potential way to do this is Online Feedback Optimization (OFO). OFO is a new control method that steers power systems to the optimal solution of an optimization problem using minimal model information and computation power. This paper will show how to choose the optimization problem and how to tune the OFO controller. Afterward, we test the resulting controller on a real distribution grid laboratory and show its performance, its interaction with other controllers in the grid, and how it copes with disturbances. Overall, the paper makes a clear recommendation on how to phrase the optimization problem and tune the OFO controller. Furthermore, it experimentally verifies that an OFO controller is a powerful tool to disaggregate flexibility requests onto FPUs while satisfying operational constraints inside the flexibility providing distribution grid.

The problem PosSLP is the problem of determining whether a given straight-line program (SLP) computes a positive integer. PosSLP was introduced by Allender et al. to study the complexity of numerical analysis (Allender et al., 2009). PosSLP can also be reformulated as the problem of deciding whether the integer computed by a given SLP can be expressed as the sum of squares of four integers, based on the well-known result by Lagrange in 1770, which demonstrated that every natural number can be represented as the sum of four non-negative integer squares. In this paper, we explore several natural extensions of this problem by investigating whether the positive integer computed by a given SLP can be written as the sum of squares of two or three integers. We delve into the complexity of these variations and demonstrate relations between the complexity of the original PosSLP problem and the complexity of these related problems. Additionally, we introduce a new intriguing problem called Div2SLP and illustrate how Div2SLP is connected to DegSLP and the problem of whether an SLP computes an integer expressible as the sum of three squares. By comprehending the connections between these problems, our results offer a deeper understanding of decision problems associated with SLPs and open avenues for further exciting research

In this paper, we propose a systematic closed-loop approach to provide optimal dynamic ancillary services with converter-interfaced generation systems based on local power grid perception. In particular, we structurally encode dynamic ancillary services such as fast frequency and voltage regulation in the form of a parametric transfer function matrix, which includes several parameters to define a set of different feasible response behaviors, among which we aim to find the optimal one to be realized by the converter system. Our approach is based on a so-called "perceive-and-optimize" (P&O) strategy: First, we identify a grid dynamic equivalent at the interconnection terminals of the converter system. Second, we consider the closed-loop interconnection of the identified grid equivalent and the parametric transfer function matrix, which we optimize for the set of transfer function parameters, resulting in a stable and optimal closed-loop performance for ancillary services provision. In the process, we ensure that grid-code and device-level requirements are satisfied. Finally, we demonstrate the effectiveness of our approach in different numerical case studies based on a modified Kundur two-area test system., Comment: 15 pages, 20 Figures