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Learning Neural Contracting Dynamics: Extended Linearization and Global Guarantees 38

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Learning Neural Contracting Dynamics: Extended Linearization...

38th Conference on Neural Information Processing systems, NeurIPS 2024

作者： Jaffe, Sean Davydov, Alexander Lapsekili, Deniz Singh, Ambuj K. Bullo, Francesco Center for Control Dynamical Systems and Computation University of California Santa Barbara United States Department of Computer Science University of California Santa Barbara United States

Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), the first neural network-based dynamical system with global contractivity guarantees in arbitrary metrics. The key feature of ELCD is a parametrization of the extended linearization of the nonlinear vector field. In its most basic form, ELCD is guaranteed to be (i) globally exponentially stable, (ii) equilibrium contracting, and (iii) globally contracting with respect to some metric. To allow for contraction with respect to more general metrics in the data space, we train diffeomorphisms between the data space and a latent space and enforce contractivity in the latent space, which ensures global contractivity in the data space. We demonstrate the performance of ELCD on the high dimensional LASA, multi-link pendulum, and Rosenbrock datasets. © 2024 Neural information processing systems foundation. All rights reserved.

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

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

2023 IEEE Conference on control Technology and Applications, CCTA 2023

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

ISBN: (纸本)9798350335446

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. © 2023 IEEE.

关键词： Graph neural networks

The Price of Simplicity: Analyzing Decoupled Policies for Multi-Location Inventory control

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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

Maneuvering control of Autonomous Underwater Vehicle (AUV) by Simulated Annealing and Moth Flame Optimization Tuned controllers

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Maneuvering Control of Autonomous Underwater Vehicle (AUV) b...

2022 International Conference on Electronic systems and Intelligent Computing, ICESIC 2022

作者： Valluru, Sudarshan K. Thareia, Hitesh Center for Control of Dynamical Systems and Computation Dept. of Electrical Engineering Delhi Technological University Delhi110042 India

ISBN: (纸本)9781665483858

This paper emphasizes maneuvering control of Autonomous Underwater Vehicle (AUV) with the help of Linear-Proportional Integral Derivative (L-PID) and Fractional Order PID (FOPID) controllers. The values of the gain parameters of L-PID (Kp, Ki, Kd) and FOPID (Kp, Ki, Kd,λ, μ) are tuned by Simulated Annealing (SA) and Moth Flame optimization (MFO) techniques. The performance of both the controllers is compared and the better algorithm to tune the parameters of the controllers is determined. A step function is applied to the system's input to test the AUV, and the corresponding response to the input function is examined. The transient parameters of the AUV, such as rise time, settling time, overshoot, and performance index IT AE were calculated and compared. The investigatory results show that both the algorithms used to tune the FO PID controller accurately steer the AUV. Also, the MFO tuned FOPID controller is more efficient than the SA tuned FOPID controller. © 2022 IEEE.

关键词： Simulated annealing

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

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RoSSO: A High-Performance Python Package for Robotic Surveil...

IEEE International Conference on Robotics and Automation (ICRA)

作者： Yohan John Connor Hughes Gilberto Díaz-García Jason R. Marden Francesco Bullo Center for Control Dynamical Systems and Computation UC Santa Barbara Santa Barbara CA USA

ISBN: (数字)9798350384574

ISBN: (纸本)9798350384581

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.

关键词： Heating systems Greedy algorithms Measurement Surveillance Reinforcement learning Programming Resource management

Perspectives on Contractivity in control, Optimization, and Learning

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arXiv 2024年

作者： Davydov, Alexander Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States

Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction theory. These opinions are (i) contraction theory is a unifying framework emerging from classical and modern works, (ii) contractivity is computationally-friendly, robust, and modular stability, (iii) numerous dynamical systems are contracting, (iv) contraction theory is relevant to modern applications, and (v) contraction theory can be vastly extended in numerous directions. We survey recent theoretical and applied research in each of these five directions. Copyright © 2024, The Authors. All rights reserved.

关键词： System stability

Proximal Gradient Dynamics: Monotonicity, Exponential Convergence, and Applications

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arXiv 2024年

作者： Gokhale, Anand Davydov, Alexander Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States

In this letter we study the proximal gradient dynamics. This recently-proposed continuous-time dynamics solves optimization problems whose cost functions are separable into a nonsmooth convex and a smooth component. First, we show that the cost function decreases monotonically along the trajectories of the proximal gradient dynamics. We then introduce a new condition that guarantees exponential convergence of the cost function to its optimal value, and show that this condition implies the proximal Polyak-Lojasiewicz condition. We also show that the proximal Polyak-Lojasiewicz condition guarantees exponential convergence of the cost function. Moreover, we extend these results to time-varying optimization problems, providing bounds for equilibrium tracking. Finally, we discuss applications of these findings, including the LASSO problem, certain matrix based problems and a numerical experiment on a feed-forward neural network. Copyright © 2024, The Authors. All rights reserved.

关键词： Cost functions

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

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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

Exponential Stability of Parametric Optimization-Based controllers via Lur’e Contractivity

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arXiv 2024年

作者： Davydov, Alexander Bullo, Francesco The Center for Control Dynamical Systems and Computation UC Santa Barbara Santa BarbaraCA93106 United States

In this letter, we investigate sufficient conditions for the exponential stability of LTI systems driven by controllers derived from parametric optimization problems. Our primary focus is on parametric projection controllers, namely parametric programs whose objective function is the squared distance to a nominal controller. Leveraging the virtual system method of analysis and a novel contractivity result for Lur’e systems, we establish a sufficient LMI condition for the exponential stability of an LTI system with a parametric projection-based controller. Separately, we prove additional results for single-integrator systems. Finally, we apply our results to state-dependent saturated control systems and control barrier function-based control and provide numerical simulations. Copyright © 2024, The Authors. All rights reserved.

关键词： controllers