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Lyapunov Analysis of Sample-and-Hold Hybrid Feedbacks

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Lyapunov Analysis of Sample-and-Hold Hybrid Feedbacks

IEEE Conference on Decision and control

作者： Ricardo G. Sanfelice Andrew R. Teel Center for Control Dynamical Systems and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

ISBN: (纸本)1424401704;9781424401703

For hybrid closed-loop systems arising from hybrid control of nonlinear systems, we show that the sample-and-hold implementation of the hybrid controller preserves (semiglobally and practically) the stability properties of the closed-loop system. We provide a general model for the hybrid closed-loop system where the hybrid controller is implemented digitally and it is interfaced to the nonlinear system through sample and hold devices. We model the sample device and the digital controller/hold device as single asynchronous hybrid systems with independent timing constants and data. The main result is established by means of a Lyapunov function for the hybrid closed-loop system resulting from the interconnection of its hybrid and nonlinear subsystems

关键词： Feedback control systems Nonlinear control systems Nonlinear systems Digital control Stability analysis Emulation control system synthesis Military computing Asymptotic stability

RoSSO: A High-Performance Python Package for Robotic Surveillance Strategy Optimization Using JAX

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arXiv 2023年

作者： John, Yohan Hughes, Connor Díaz-García, Gilberto Marden, Jason R. Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106-5070 United States

To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning techniques such as reverse-mode automatic differentiation and constraint parametrization to achieve superior efficiency compared to general-purpose nonlinear programming solvers. Additionally, we supplement a game-theoretic stochastic surveillance formulation in the literature with a novel greedy algorithm and multi-robot extension. We close with numerical results for a police district in downtown San Francisco that demonstrate RoSSO’s capabilities on our new formulations and the prior work. Copyright © 2023, The Authors. All rights reserved.

关键词： Python

Algorithms for the Traveling Salesman Problem with Neighborhoods Involving a Dubins Vehicle

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Algorithms for the Traveling Salesman Problem with Neighborh...

2011 American control Conference (ACC)

作者： Jason T. Isaacs Daniel J. Klein Joao P. Hespanha Center for Control Dynamical Systems and Computation and the Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

We study the problem of finding the minimum-length curvature constrained closed path through a set of regions in the plane. This problem is referred to as the Dubins Traveling Salesperson Problem with Neighborhoods (DTSPN). Two algorithms are presented that transform this infinite dimensional combinatorial optimization problem into a finite dimensional asymmetric TSP by sampling and applying the appropriate transformations, thus allowing the use of existing approximation algorithms. We show for the case of disjoint regions, the first algorithm needs only to sample each region once to produce a tour within a factor of the length of the optimal tour that is independent of the number of regions. We present a second algorithm that performs no worse than the best existing algorithm and can perform significantly better when the regions overlap.

关键词： Approximation algorithms Approximation methods Traveling salesman problems Path planning Aircraft Vehicle dynamics Euclidean distance

Extending dynamic mode decomposition to data from multiple outputs

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arXiv 2021年

作者： Boddupalli, Nibodh Department of Mechanical Engineering Center for Control Dynamical Systems and Computation University of California Santa BarbaraCA United States

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the underlying system. Estimation of these spectral objects has become widely accessible with the numerous algorithms developed in recent years. We show how one such algorithm – extended dynamic mode decomposition – can be used on data from multiple outputs of a system. These outputs that are functions of state are called observables in the literature and could be known outputs like the state itself or unknown outputs like data from sensors used in systems of biological interest. To this end, we approximate the desired observables and their iterates in time using minimizers of regularized least-squares problems which have analytic solutions with heuristic provisions for expected estimates. © 2021, CC BY-SA.

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On hybrid controllers that induce input-to-state stability with respect to measurement noise

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On hybrid controllers that induce input-to-state stability w...

IEEE Conference on Decision and control

作者： R.G. Sanfelice A.R. Teel Center for Control Dynamical Systems and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

For a class of nonlinear systems affine in controls and with unknown high frequency gain, we develop a hybrid control strategy that guarantees (practical) global input-to-state stability (ISS) with respect to measurement noise. We provide a design procedure for the hybrid controller and apply it to Freeman’s counterexample and minimum-phase relative degree one systems.

关键词： Stability Noise measurement control systems Feedback Nonlinear control systems Nonlinear systems Noise robustness Frequency measurement Gain measurement Robust control

Distributionally robust formulation and model selection for the graphical lasso

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arXiv 2019年

作者： Cisneros-Velarde, Pedro Oh, Sang-Yun Petersen, Alexander Center for Control Dynamical Systems and Computation Department of Statistics and Applied Probability University of California Santa Barbara United States

Building on a recent framework for distributionally robust optimization in machine learning, we develop a similar framework for estimation of the inverse covariance matrix for multivariate data. We provide a novel notion of a Wasserstein ambiguity set specifically tailored to this estimation problem, from which we obtain a representation for a tractable class of regularized estimators. Special cases include penalized likelihood estimators for Gaussian data, specifically the graphical lasso estimator. As a consequence of this formulation, a natural relationship arises between the radius of the Wasserstein ambiguity set and the regularization parameter in the estimation problem. Using this relationship, one can directly control the level of robustness of the estimation procedure by specifying a desired level of confidence with which the ambiguity set contains a distribution with the true population covariance. Furthermore, a unique feature of our formulation is that the radius can be expressed in closed-form as a function of the ordinary sample covariance matrix. Taking advantage of this finding, we develop a simple algorithm to determine a regularization parameter for graphical lasso, using only the bootstrapped sample covariance matrices, meaning that computationally expensive repeated evaluation of the graphical lasso algorithm is not necessary. Alternatively, the distributionally robust formulation can also quantify the robustness of the corresponding estimator if one uses an off-the-shelf method such as cross-validation. Finally, we numerically study the obtained regularization criterion and analyze the robustness of other automated tuning procedures used in *** Codes 62F35, 62F40, 90C90 Copyright © 2019, The Authors. All rights reserved.

关键词： Parameterization

Markov chain-based stochastic strategies for robotic surveillance

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arXiv 2020年

作者： Duan, Xiaoming Bullo, Francesco Department of Mechanical Engineering Center of Control Dynamical Systems and Computation UC Santa BarbaraCA93106-5070 United States

This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where the efficiency is defined with respect to relevant underlying performance metrics. We first start by reviewing the basics of Markov chains, which is the primary motion model for stochastic robotic surveillance. Then two main criteria regarding the speed and unpredictability of surveillance strategies are discussed. The central objects that appear throughout the treatment is the hitting times of Markov chains, their distributions and expectations. We formulate various optimization problems based on the concerned metrics in different scenarios and establish their respective properties. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Inference of Infrastructure Network Flows via Physics-Inspired Implicit Neural Networks

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Inference of Infrastructure Network Flows via Physics-Inspir...

control Technology and Applications (CCTA),

作者： Francesco Seccamonte Ambuj K. Singh Francesco Bullo Center for Control Dynamical Systems and Computation University of California Santa Barbara Department of Computer Science University of California Santa Barbara

We study the problem of inferring edge flows and nodal injections in infrastructure networks. Leveraging the Thomson’s Principle from the electric circuits literature, we setup a framework to jointly learn network parameters and missing states. Despite being application agnostic, the proposed approach captures the fundamental physics of the infrastructure, and is able to handle partial observation, node and edge features as well as operational constraints. The physics inspired learning framework leads to a bilevel optimization problem, which is NP hard in general. By exploiting convexity properties, we reformulate the problem as a single level optimization, composed of a graph neural network and an additional implicit layer. The resulting architecture can be trained using standard gradient-based methods. We assess the validity of the proposed approach on two different infrastructure networks (power and traffic), and show it outperforms the current state of the art.

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Structural balance via gradient flows over signed graphs

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arXiv 2019年

作者： Cisneros-Velarde, Pedro Friedkin, Noah E. Proskurnikov, Anton V. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara United States Politecnico di Torino Turin Italy

Structural balance is a classic property of signed graphs satisfying Heider’s seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1940s. Recent research has focused on the development of dynamic models explaining the emergence of structural balance. In this paper, we introduce a novel class of parsimonious dynamic models for structural balance based on an interpersonal influence process. Our proposed models are gradient flows of an energy function, called the dissonance function, which captures the cognitive dissonance arising from the violations of Heider’s axioms. Thus, we build a new connection with the literature on energy landscape minimization. This gradient-flow characterization allows us to study the transient and asymptotic behaviors of our model. We provide mathematical and numerical results describing the critical points of the dissonance function. Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamic models