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Procedia Computer Science 2020年 171卷 1241-1250页

作者： Sudarshan K. Valluru Rajul Kumar Rahul Kumar Center for Control of Dynamical Systems and Computation Dept. of Electrical Engineering Delhi Technological University Delhi-110042 India

The insistence of this paper is to design Fractional order-proportional Integral Derivative (FO-PID) and Integral order –Proportional Integral Derivative (IO-PID) controllers for trajectory tracking control of Twin rotor Multiple Input Multiple Output (MIMO) system (TRMS). The aim of these designed controllers is to move the main and tail actuator at the desired angles accurately to fulfill the demanding attributes so that TRMS should stabilize while hovering. The controller parameters of both the controllers are optimized using fmincon function as well as Multiobjective genetic algorithm. Both the controller are tested in real time and their performance are compared for control of yaw and pitch angles of TRMS. Manual disturbances are given at after 40 seconds of first given disturbance, and the designed controllers are highly capable in diminishing quickly the effect of manual perturbations given to the main and tail rotor of TRMS. From experiment it is observed from comparative performance that FO-PID controller tuned using multiobjective genetic algorithm give best performance in term of time taken to stabilization after the given disturbance.

关键词： FO-PID IO-PID fmincon MOGA TRMS

A Tutorial on Multivariate k-Statistics and their computation

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arXiv 2020年

作者： Smith, Kevin D. Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

This document aims to provide an accessible tutorial on the unbiased estimation of multivariate cumulants, using k-statistics. We offer an explicit and general formula for multivariate k-statistics of arbitrary order. We also prove that the k-statistics are unbiased, using Möbius inversion and rudimentary combinatorics. Many detailed examples are considered throughout the paper. We conclude with a discussion of k-statistics computation, including the challenge of time complexity, and we examine a couple of possible avenues to improve the efficiency of this computation. The purpose of this document is threefold: to provide a clear introduction to k-statistics without relying on specialized tools like the umbral calculus;to construct an explicit formula for k-statistics that might facilitate future approximations and faster algorithms;and to serve as a companion paper to our Python library PyMoments [12], which implements this formula. Copyright © 2020, The Authors. All rights reserved.

关键词： Statistics

Multi-group SIS epidemics with simplicial and higher-order interactions

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arXiv 2020年

作者： Cisneros-Velarde, Pedro Bullo, Francesco The Center for Control Dynamical Systems and Computation University of California Santa Barbara United States

This paper analyzes a Susceptible-Infected-Susceptible (SIS) model of epidemic propagation over hypergraphs and, motivated by an important special case, we refer to the model as to the simplicial SIS model. Classically, the multi-group SIS model has assumed pairwise interactions of contagion across groups and thus has been vastly studied in the literature. It is only recently that a renewed special attention has been drawn to the study of contagion dynamics over higher-order interactions and over more general graph structures, like simplexes. Previous work on mean-field approximation scalar models of the simplicial SIS model has indicated that a new dynamical behavior domain, compared to the classical SIS model, appears due to the newly introduced higher order interaction terms: both a disease-free equilibrium and an endemic equilibrium coexist and are both locally asymptotically stable. This paper formally establishes that bistability (as a new epidemiological behavior) also appears in the multi-group simplicial SIS model. We give sufficient conditions over the model's parameters for the appearance of this and the other behavioral domains present in the classical multi-group SIS model. We additionally provide an algorithm to compute the value of the endemic equilibrium and report numerical analysis of the transition from the disease-free domain to the bistable *** Codes 92B05, 37N25, 37N99 Copyright © 2020, The Authors. All rights reserved.

关键词： Epidemiology

Data-driven Self-triggered control via Trajectory Prediction

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arXiv 2022年

作者： Liu, Wenjie Sun, Jian Wang, Gang Bullo, Francesco Chen, Jie The State Key Lab of Intelligent Control and Decision of Complex Systems The School of Automation Beijing Institute of Technology Beijing100081 China The Beijing Institute of Technology Chongqing Innovation Center Chongqing401120 China The Mechanical Engineering Department The Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States The Department of Control Science and Engineering Tongji University Shanghai201804 China The State Key Lab of Intelligent Control and Decision of Complex Systems Beijing Institute of Technology Beijing100081 China

Self-triggered control, a well-documented technique for reducing the communication overhead while ensuring desired system performance, is gaining increasing popularity. However, existing methods for self-triggered control require explicit system models that are assumed perfectly known a priori. An end-to-end control paradigm known as data-driven control learns control laws directly from data, and offers a competing alternative to the routine system identification-then-control method. In this context, the present paper puts forth data-driven self-triggered control schemes for unknown linear systems using data collected offline. Specifically, for output feedback control systems, a data-driven model predictive control (MPC) scheme is proposed, which computes a sequence of control inputs while generating a predicted system trajectory. A data-driven self-triggering law is designed using the predicted trajectory, to determine the next triggering time once a new measurement becomes available. For state feedback control systems, instead of capitalizing on MPC to predict the trajectory, a data-fitting problem using the pre-collected input-state data is solved, whose solution is employed to construct the self-triggering mechanism. Both feasibility and stability are established for the proposed self-triggered controllers, which are validated using numerical examples. © 2022, CC BY.

关键词： Model predictive control

PDMATLAB2D: A Peridynamics MATLAB Two-dimensional Code

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Journal of Peridynamics and Nonlocal Modeling 2024年第1期6卷 149-205页

作者： Seleson, Pablo Pasetto, Marco John, Yohan Trageser, Jeremy Reeve, Samuel Temple Computer Science and Mathematics Division Oak Ridge National Laboratory P.O. Box 2008 MS-6013 Oak Ridge 37831-6013 TN United States Department of Mechanical and Aerospace Engineering University of California San Diego 9500 Gilman Drive La Jolla 92093 CA United States George W. Woodruff School of Mechanical Engineering Georgia Institute of Technology 801 Ferst Dr Atlanta 30332 GA United States Center for Control Dynamical Systems and Computation University of California at Santa Barbara Harold Frank Hall Room 5119 Santa Barbara 93106 CA United States Engineering Sciences Center Sandia National Laboratories P.O. Box 5800 MS-1322 Albuquerque 87185-1322 NM United States Computational Sciences and Engineering Division Oak Ridge National Laboratory P.O. Box 2008 MS-6085 Oak Ridge 37831-6085 TN United States

PDMATLAB2D is a meshfree peridynamics implementation in MATLAB suitable for simulation of two-dimensional fracture problems. The purpose of this code is twofold. First, it provides an entry-level peridynamics computational tool for educational and training purposes. Second, it serves as an accessible and easily modifiable computational tool for peridynamics researchers who would like to adapt the code for a multitude of peridynamics simulation scenarios. The current version of the code implements a bond-based brittle elastic peridynamic model and a critical stretch criterion for bond breaking. However, the code is designed to be extendable for other peridynamic models and computational features. In this paper, we provide an overview of the code structure and functions with illustrative examples. Due to the integrated computation and postprocessing MATLAB capabilities, PDMATLAB2D can serve as an effective testbed for testing new constitutive models and advanced numerical features for peridynamics computations. © UT-Battelle, LLC, under exclusive licence to Springer Nature Switzerland AG 2024. corrected publication 2024.

关键词： Fracture Meshfree Peridynamics Two-dimensional

Adaptive learning in two-player Stackelberg games with application to network security

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arXiv 2021年

作者： Yang, Guosong Poovendran, Radha Hespanha, João P. the Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA93106 United States the Department of Electrical and Computer Engineering University of Washington SeattleWA98195 United States

We study a two-player Stackelberg game with incomplete information such that the follower’s strategy belongs to a known family of parameterized functions with an unknown parameter vector. We design an adaptive learning approach to simultaneously estimate the unknown parameter and minimize the leader’s cost, based on adaptive control techniques and hysteresis switching. Our approach guarantees that the leader’s cost predicted using the parameter estimate becomes indistinguishable from its actual cost in finite time, up to a preselected, arbitrarily small error threshold. Also, the first-order necessary condition for optimality holds asymptotically for the predicted cost. Additionally, if a persistent excitation condition holds, then the parameter estimation error becomes bounded by a preselected, arbitrarily small threshold in finite time as well. For the case where there is a mismatch between the follower’s strategy and the parameterized function that is known to the leader, our approach is able to guarantee the same convergence results for error thresholds larger than the size of the mismatch. The algorithms and the convergence results are illustrated via a simulation example in the domain of network *** Codes 91A26, 91A65 (Primary) 37N40, 93C40, 65L20 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： Network security

Game Theory for Autonomy: From Min-Max Optimization to Equilibrium and Bounded Rationality Learning

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Game Theory for Autonomy: From Min-Max Optimization to Equil...

American control Conference (ACC)

作者： Kyriakos G. Vamvoudakis Filippos Fotiadis João P. Hespanha Raphael Chinchilla Guosong Yang Mushuang Liu Jeff S. Shamma Lacra Pavel Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta GA USA Center for Control Dynamical Systems and Computation University of California Santa Barbara CA Department of Electrical and Computer Engineering Rutgers University Piscataway NJ USA Department of Mechanical and Aerospace Engineering University of Missouri Columbia MO USA Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana-Champaign IL USA Department of Electrical and Computer Engineering University of Toronto Canada

Finding Nash equilibria in non-cooperative games can be, in general, an exceptionally challenging task. This is owed to various factors, including but not limited to the cost functions of the game being nonconvex/nonconcave, the players of the game having limited information about one another, or even due to issues of computational complexity. The present tutorial draws motivation from this harsh reality and provides methods to approximate Nash or min-max equilibria in non-ideal settings using both optimization- and learning-based techniques. The tutorial acknowledges, however, that such techniques may not always converge, but instead lead to oscillations or even chaos. In that respect, tools from passivity and dissipativity theory are provided, which can offer explanations about these divergent behaviors. Finally, the tutorial highlights that, more frequently than often thought, the search for equilibrium policies is simply vain; instead, bounded rationality and non-equilibrium policies can be more realistic to employ owing to some players’ learning imperfectly or being relatively naive – "bounded rational." The efficacy of such plays is demonstrated in the context of autonomous driving systems, where it is explicitly shown that they can guarantee vehicle safety.

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Non-Euclidean Contraction Analysis of Continuous-Time Neural Networks

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arXiv 2021年

作者： Davydov, Alexander Proskurnikov, Anton V. Bullo, Francesco The Department of Mechanical Engineering The Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States The Department of Electronics and Telecommunications Politecnico di Torino Turin Italy

Critical questions in dynamical neuroscience and machine learning are related to the study of continuous-time neural networks and their stability, robustness, and computational efficiency. These properties can be simultaneously established via a contraction analysis. This paper develops a comprehensive non-Euclidean contraction theory for continuous-time neural networks. Specifically, we provide novel sufficient conditions for the contractivity of general classes of continuous-time neural networks including Hopfield, firing rate, Persidskii, Lur’e, and other neural networks with respect to the non-Euclidean 1/∞ norms. These sufficient conditions are based upon linear programming or, in some special cases, establishing the Hurwitzness of a particular Metzler matrix. To prove these sufficient conditions, we develop novel results on non-Euclidean logarithmic norms and a novel necessary and sufficient condition for contractivity of systems with locally Lipschitz dynamics. For each model, we apply our theoretical results to compute the optimal contraction rate and corresponding weighted non-Euclidean norm with respect to which the neural network is contracting. Copyright © 2021, The Authors. All rights reserved.

关键词： Hopfield neural networks

CONTRACTION AND CONCENTRATION OF MEASURES WITH APPLICATIONS TO THEORETICAL NEUROSCIENCE

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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

Minimum effort decentralized control design for contracting network systems

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arXiv 2022年

作者： Ofir, Ron Bullo, Francesco Margaliot, Michael The Andrew and Erna Viterbi Faculty of Electrical and Computers Eng. Technion-Israel Institute of Technology Haifa3200003 Israel The Dept. of Mechanical Eng. The Center for Control Dynamical Systems and Computation University of California Santa Barbara93106-5070 United States The School of Elc. Eng. - Systems Tel Aviv University 69978 Israel

We consider the problem of making a networked system contracting by designing "minimal effort" local controllers. Our method combines a hierarchical contraction characterization and a matrix-balancing approach to stabilizing a Metzler matrix via minimal diagonal perturbations. We demonstrate our approach by designing local controllers that render contractive a network of FitzHugh-Nagumo neurons with a general topology of interactions. © 2022, CC BY.

关键词： Large scale systems