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arXiv 2025年

作者： John, Yohan Shah, Vade Preiss, James A. Alizadeh, Mahnoosh Marden, Jason R. Center for Control Dynamical Systems and Computation The University of California Santa BarbaraCA United States

What is the performance cost of using simple, decoupled control policies in inherently coupled systems? Motivated by industrial refrigeration systems, where centralized compressors exhibit economies of scale yet traditional control employs decoupled room-by-room temperature regulation, we address this question through the lens of multi-location inventory control. Here, a planner manages multiple inventories to meet stochastic demand while minimizing costs that are coupled through nonlinear ordering functions reflecting economies of scale. Our main contributions are: (i) a surprising equivalence result showing that optimal stationary base-stock levels for individual locations remain unchanged despite the coupling when restricting attention to decoupled strategies;(ii) tight performance bounds for simple decoupled policies relative to optimal coupled policies, revealing that the worst-case ratio depends primarily on the degree of nonlinearity in the cost function and scales with the number of locations for systems with fixed costs;and (iii) analysis of practical online algorithms that achieve competitive performance without solving complex dynamic programs. Numerical simulations demonstrate that while decoupled policies significantly outperform their worst-case guarantees in typical scenarios, they still exhibit meaningful suboptimality compared to fully coordinated strategies. These results provide actionable guidance for system operators navigating the trade-off between control complexity and operational efficiency in coupled systems. © 2025, CC BY.

关键词： Stochastic systems

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Contractivity Analysis and control Design for Lur’e systems: Lipschitz, Incrementally Sector Bounded, and Monotone Nonlinearities

arXiv

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arXiv 2025年

作者： Shima, Ryotaro Davydov, Alexander Bullo, Francesco Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 United States

In this paper, we study the contractivity of Lur’e dynamical systems whose nonlinearity is either Lipschitz, incrementally sector bounded, or monotone. We consider both the discrete- and continuous-time settings. In each case, we provide state-independent linear matrix inequalities (LMIs) which are necessary and sufficient for contractivity. Additionally, we provide LMIs for the design of controller gains such that the closed-loop system is contracting. Finally, we provide a numerical example for control design. Copyright © 2025, The Authors. All rights reserved.

关键词： Continuous time systems

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Proximal Gradient Dynamics and Feedback control for Equality-Constrained Composite Optimization

arXiv

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arXiv 2025年

作者： Centorrino, Veronica Rossi, Francesca Bullo, Francesco Russo, Giovanni DIEM University of Salerno Italy Scuola Superiore Meridionale Italy Center for Control Dynamical Systems and Computation UC Santa Barbara CA United States

This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and convex inequality constraints, naturally arises in a wide range of engineering and machine learning applications. To tackle these minimization problems, we introduce the proportional–integral proximal gradient dynamics (PI–PGD): a closed-loop system where the Lagrange multipliers are control inputs and states are the problem decision variables. First, we establish the equivalence between the minima of the optimization problem and the equilibria of the PI–PGD. Then, leveraging tools from contraction theory, we give a comprehensive convergence analysis for the dynamics, showing linear–exponential convergence towards the equilibrium. That is, the distance between each solution and the equilibrium is upper bounded by a function that first decreases linearly and then exponentially. Our findings are illustrated numerically on a set of representative examples, which include an application to entropic-regularized optimal transport. Copyright © 2025, The Authors. All rights reserved.

关键词： Lagrange multipliers

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A Stochastic Surveillance Stackelberg Game: Co-Optimizing Defense Placement and Patrol Strategy

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IEEE Transactions on Automatic control 2025年

作者： John, Yohan Díaz-García, Gilberto Duan, Xiaoming Marden, Jason R. Bullo, Francesco UC Santa Barbara Center for Control Dynamical Systems and Computation Santa BarbaraCA93106-5070 United States Shanghai Jiao Tong University Department of Automation Shanghai200240 China

Stochastic patrol routing is known to be advantageous in adversarial settings;however, the optimal choice of stochastic routing strategy is dependent on a model of the adversary. We adopt a worst-case omniscient adversary model from the literature and extend the formulation to accommodate heterogeneous defenses at the various nodes of the graph. Introducing this heterogeneity leads to interesting new patrol strategies. We identify efficient methods for computing these strategies in certain classes of graphs. We assess the effectiveness of these strategies via comparison to an upper bound on the value of the game. Finally, we leverage the heterogeneous defense formulation to develop novel defense placement algorithms that complement the patrol strategies. © 1963-2012 IEEE.

关键词： Markov processes

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Supervisory control of nonlinear systems 9

Supervisory control of nonlinear systems

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2007 9th European control Conference, ECC 2007

作者： Hespanha, Joao P. Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

ISBN: (纸本)9783952417386

关键词： Nonlinear systems

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CONTRACTION AND CONCENTRATION OF MEASURES WITH APPLICATIONS TO THEORETICAL NEUROSCIENCE

arXiv

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arXiv 2025年

作者： Betteti, Simone Bullo, Francesco Department of Information Engineering Università degli Studi di Padova Padova35131 Italy Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 IT United States

We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or Br-contracting drift terms. While classical results often assume constant diffusion and gradient-based drifts, we extend the analysis to spatially inhomogeneous diffusion and non-integrable vector fields. We establish sufficient conditions for the existence and uniqueness of stationary measures under global contraction, showing that convergence is preserved when the contraction rate dominates diffusion inhomogeneity. For systems contracting only outside of a compact set and with constant diffusion, we demonstrate mass concentration near the minima of an associated non-convex potential, like in multistable regimes. The theoretical findings are illustrated through Hopfield networks, highlighting implications for memory retrieval dynamics in noisy *** Codes 35Q84, 60G10 © 2025, CC BY.

关键词： Random processes

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Distributed detection of cyber-physical attacks in power networks: A waveform relaxation approach

Distributed detection of cyber-physical attacks in power net...

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2011 49th Annual Allerton Conference on Communication, control, and Computing, Allerton 2011

作者： Dörfler, Florian Pasqualetti, Fabio Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara CA United States

ISBN: (纸本)9781457718168

Future power grids will be required to operate safely and reliably against cyber-physical attacks. The large dimensionality and the difficulty in calibrating dynamical network models precludes the use of centralized attack detection algorithms. This paper proposes a unified modeling framework and an advanced detection procedure whose implementation requires only local network knowledge. We model a power network as a linear time-invariant descriptor system and cyber-physical attacks as unknown inputs. This modeling framework captures, for instance, network components malfunction and measurements corruption. In our detection method the power network is partitioned among geographically deployed control centers, possibly located at transmission substations. Each control center has knowledge of only its respective subarea dynamics, is able to acquire information from neighboring areas, and is capable of performing basic computations. Under these minimal technological requirements and a reasonable observability assumption, we design an entirely distributed detection filter which requires only local network knowledge and yet achieves guaranteed global performance. Our detection filter is based on a sparse residual filter in descriptor form, which can be stabilized via decentralized output injection and implemented distributively via waveform relaxation. © 2011 IEEE.

关键词： Electric power transmission networks

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Bifurcation curves for electrical DC motors 2

Bifurcation curves for electrical DC motors

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2nd IEEE International Conference on Power Electronics, Intelligent control and Energy systems, ICPEICES 2018

作者： Valluru, Sudarshan K Singh, Madhusudan Verma, Aditya Gupta, Anshul Delhi Technological University Incubation Center for Control Dynamical Systems and Computation Delhi110042 India

ISBN: (纸本)9781538666258

This paper studies the numerical bifurcation analysis of three different types of DC Motor namely DC Series Motor, DC Shunt Motor, and permanent magnet DC (PMDC) motor. The bifurcation curves' role is to exemplify the bifurcation behavior in the motors while changing one of the parameters keeping other parameters constant for bifurcation curves. The variable parameter is along the abscissa, while the machine states are along the ordinate of the bifurcation curve. The mathematical models of DC Series Motor, DC Shunt Motor and PMDC Motor are first derived, which are suitable for bifurcation curves. Then, the effect of the input voltage and constant external torque on the motors are studied, and bifurcation curves are plotted with input voltage as a control parameter. © 2018 IEEE.

关键词： DC motors

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Design of multi-loop L-PID and NL-PID controllers: An experimental validation 2

Design of multi-loop L-PID and NL-PID controllers: An experi...

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2nd IEEE International Conference on Power Electronics, Intelligent control and Energy systems, ICPEICES 2018

作者： Valluru, Sudarshan K. Singh, Madhusudan Goel, Arnav Kaur, Manpreet Dobhal, Daksh Kartikeya, Kumar Verma, Aditya Gupta, Anshul Delhi Technological University Incubation Center for Control Dynamical Systems and Computation Delhi110042 India

ISBN: (纸本)9781538666258

The three-term PID controllers are significantly used in most of the benchmarked systems as controllers. However, the benchmarked Single Input Multiple Output (SIMO) systems may require more than one PID controllers in the control loops, the way to design PID controllers is not an easy task. Although, the linear PID (L-PID) controllers are not yielded a satisfactory control results for a benchmarked system due to the presence of inherent nonlinearities. In order to improve performance, the linear PID controllers are modified by nonlinear characteristics. In this paper, the linear and nonlinear PID (NL-PID) controllers are implemented for the stabilization and control of Gantry Crane System as a test problem. The experimental results prove that the multi-loop NL-PID controllers exhibit more robustness to outer large with fast external disturbances. The L-PID and NL-PID controllers are compared to find out the best controller, which gives optimum responses and can also handle external disturbances. © 2018 IEEE.

关键词： controllers

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Synchronization and power sharing for droop-controlled inverters in islanded microgrids

Synchronization and power sharing for droop-controlled inver...

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作者： Simpson-Porco, John W. Dörfler, Florian Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara CA 93106 United States

Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms, which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it preserves the power sharing properties of the primary droop controller. Our results hold for any acyclic network topology, and hold without assumptions on identical line admittances or voltage magnitudes. © 2013 Elsevier Ltd. All rights reserved.

关键词： Synchronization

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