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

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arXiv 2023年

作者： John, Yohan Díaz-García, Gilberto Duan, Xiaoming Marden, Jason R. Bullo, Francesco the Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106-5070 United States the Department of Automation Shanghai Jiao Tong University 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. Copyright © 2023, The Authors. All rights reserved.

关键词： Game theory

IDKM: Memory Efficient Neural Network Quantization via Implicit, Differentiable k-Means

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arXiv 2023年

作者： Jaffe, Sean Singh, Ambuj K. Bullo, Francesco Department of Computer Science UC Santa Bar bara Santa Barbara United States Center for Control Dynamical Systems and Computation UC Santa Bar bara Santa Barbara United States

Compressing large neural networks with minimal performance loss is crucial to enabling their deployment on edge devices. (Cho et al., 2022) proposed a weight quantization method that uses an attention-based clustering algorithm called differentiable k-means (DKM). Despite achieving state-of-the-art results, DKM’s performance is constrained by its heavy memory dependency. We propose an implicit, differentiable k-means algorithm (IDKM), which eliminates the major memory restriction of DKM. Let t be the number of k-means iterations, m be the number of weight-vectors, and b be the number of bits per cluster address. IDKM reduces the overall memory complexity of a single k-means layer from O(t·m·2b) to O(m·2b). We also introduce a variant, IDKM with Jacobian-Free-Backpropagation (IDKM-JFB), for which the time complexity of the gradient calculation is independent of t as well. We provide a proof of concept of our methods by showing that, under the same settings, IDKM achieves comparable performance to DKM with less compute time and less memory. We also use IDKM and IDKM-JFB to quantize a large neural network, Resnet18, on hardware where DKM cannot train at all. Copyright © 2023, The Authors. All rights reserved.

关键词： Complex networks

Convergence of the Heterogeneous Deffuant-Weisbuch Model: A Complete Proof and Some Extensions

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arXiv 2024年

作者： Chen, Ge Su, Wei Mei, Wenjun Bullo, Francesco The Academy of Mathematics and Systems Science Chinese Academy of Sciences China The School of Mathematics and Statistics Beijing Jiaotong University China The Department of Mechanics and Engineering Science Peking University China The Center of Control Dynamical-Systems and Computation University of California Santa Barbara United States

The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over 20 years, its convergence proof is open. Our previous paper [1] solves the problem for the case of uniform weighting factors greater than or equal to 1/2, but the general case remains unresolved. This paper considers the DW model with heterogeneous confidence bounds and heterogeneous (unconstrained) weighting factors and shows that, with probability one, the opinion of each agent converges to a fixed vector. In other words, this paper resolves the convergence conjecture for the heterogeneous DW model. Our analysis also clarifies how the convergence speed may be arbitrarily slow under certain parameter conditions. © 2024, CC0.

关键词： Multi agent systems

Physics-informed implicit representations of equilibrium network flows 22

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Physics-informed implicit representations of equilibrium net...

Proceedings of the 36th International Conference on Neural Information Processing systems

作者： Kevin D. Smith Francesco Seccamonte Ananthram Swami Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara CA U.S. Army Research Laboratory Adelphi MD

ISBN: (纸本)9781713871088

Flow networks are ubiquitous in natural and engineered systems, and in order to understand and manage these networks, one must quantify the flow of commodities across their edges. This paper considers the estimation problem of predicting unlabeled edge flows from nodal supply and demand. We propose an implicit neural network layer that incorporates two fundamental physical laws: conservation of mass, and the existence of a constitutive relationship between edge flows and nodal states (e.g., Ohm's law). Computing the edge flows from these two laws is a nonlinear inverse problem, which our layer solves efficiently with a specialized contraction mapping. Using implicit differentiation to compute the solution's gradients, our model is able to learn the constitutive relationship within a semi-supervised framework. We demonstrate that our approach can accurately predict edge flows in AC power networks and water distribution systems.

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From Contraction Theory to Fixed Point Algorithms on Riemannian and Non-Euclidean Spaces

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From Contraction Theory to Fixed Point Algorithms on Riemann...

IEEE Conference on Decision and control

作者： Francesco Bullo Pedro Cisneros-Velarde Alexander Davydov Saber Jafarpour Center of Control Dynamical Systems and Computation University of California Santa Barbara USA

ISBN: (纸本)9781665436601

The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the relationship between Demidovich conditions, one-sided Lipschitz conditions, and contractivity theorems. We review the standard contraction theory on Euclidean spaces as well as little-known results for Riemannian manifolds. Special emphasis is placed on the setting of non-Euclidean norms and the recently introduced weak pairings for the ℓ 1 and ℓ ∞ norms. We highlight recent results on explicit and implicit fixed point schemes for non-Euclidean contracting systems.

关键词： Manifolds Heart Machine learning algorithms Conferences Tutorials Machine learning Aerospace electronics

Evaluation of Moth-Flame Optimization, Genetic and Simulated Annealing tuned PID controller for Steering control of Autonomous Underwater Vehicle

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Evaluation of Moth-Flame Optimization, Genetic and Simulated...

IOT, Electronics and Mechatronics Conference (IEMTRONICS), IEEE International

作者： Sudarshan K. Valluru Karan Sehgal Hitesh Thareja Center for Control of Dynamical Systems and Computation Delhi Technological University Delhi India

This paper describes an optimal bio-inspired PID controller for accurate steering management of the Autonomous Underwater Vehicle system (AUV). To achieve precise control performance, a PID controller is designed, and its gain parameters K_p, K_i, K_d are tuned by applying Simulated Annealing (SA), Genetic Algorithm (GA) and Moth-Flame Optimization Algorithm (MFO). The experimental response corresponding to the unit step and square input waveform for these proposed nature-inspired optimization algorithms were obtained. The response characteristics like overshoot, rise time, settling time and performances index ITAE were calculated and compared. The experimental results show that MFO-PID is highly efficient, followed by GA and SA, respectively.

关键词： Robust control Autonomous underwater vehicles Mechatronics Simulated annealing Genetics Performance analysis Indexes

Semicontraction and Synchronization of Kuramoto-Sakaguchi Oscillator Networks

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arXiv 2023年

作者： Delabays, Robin Bullo, Francesco The Institute of Sustainable Energy School of Engineering University of Applied Sciences and Arts of Western Switzerland The Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 United States

This paper studies the celebrated Kuramoto-Sakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets of the n-torus called winding cells. Second, we analyze the semicontractivity of the model, i.e., the property that the distance between trajectories decreases when measured according to a seminorm. This paper establishes the local semicontractivity of the Kuramoto-Sakaguchi model, which is equivalent to the local contractivity for the reduced model. The reduced model is defined modulo the rotational symmetry. The domains where the system is semicontracting are convex phase-cohesive subsets of winding cells. Our sufficient conditions and estimates of the semicontracting domains are less conservative and more explicit than in previous works. Based on semicontraction on phase-cohesive subsets, we establish the at most uniqueness of synchronous states within these domains, thereby characterizing the multistability of this model. © 2023, CC BY.

关键词： Winding

Positive Competitive Networks for Sparse Reconstruction

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arXiv 2023年

作者： Centorrino, Veronica Gokhale, Anand Davydov, Alexander Russo, Giovanni Bullo, Francesco Scuola Superiore Meridionale Italy The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States The Department of Information and Electric Engineering and Applied Mathematics University of Salerno Italy

We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (PFCN), to tackle sparse reconstruction problems with non-negativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including for example neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then, we prove that the PFCN is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence: (i) only depends on a property of the dictionary;(ii) is linear-exponential, in the sense that initially the convergence rate is at worst linear and then, after a transient, it becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without non-negativity constraints. Finally, we validate the effectiveness of our approach via a numerical example. Copyright © 2023, The Authors. All rights reserved.

关键词： Signal processing

HOW SOCIAL INFLUENCE AFFECTS THE WISDOM OF CROWDS IN INFLUENCE NETWORKS

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arXiv 2022年

作者： Tian, Ye Wang, Long Bullo, Francesco Center for Systems and Control College of Engineering Peking University Beijing100871 China Mechanical Engineering Department The Center of Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 United States

A long-standing debate is whether social influence improves the collective wisdom of a crowd or undermines it. This paper addresses the question based on a naïve learning setting in influence systems theory: in our models individuals evolve their estimates of an unknown truth according to the weighted-average opinion dynamics. A formal mathematization is provided with rigorous theoretical analysis. We obtain various conditions for improving, optimizing and undermining the crowd accuracy, respectively. We prove that if the wisdom of a finite-size group is improved, then the collective estimate converges to the truth as the group size increases. We show that whether social influence improves or undermines the wisdom is determined by the social power allocations in the influence system: if the influence system allocates relatively larger social power to relatively more accurate individuals, it improves the wisdom;on the contrary, if the influence system assigns less social power to more accurate individuals, it undermines the wisdom. At a population level, individuals' susceptibilities to interpersonal influence and network centralities are both crucial. To improve the wisdom, more accurate individuals should be less susceptible and have larger network centralities. Particularly, in democratic influence networks, if relatively more accurate individuals are relatively less susceptible, the wisdom is improved;if more accurate individuals are more susceptible, the wisdom is undermined, which is consistent with the reported empirical evidence. Our investigation provides a theoretical framework for understanding the role social influence plays in the emergence of collective wisdom. Copyright © 2022, The Authors. All rights reserved.

关键词： Economic and social effects