arXiv subjects

Victor M. Preciado

Publications and source records attributed to Victor M. Preciado.

At least 19 recordsLinked to original sources

arXiv2026

Koopman Generator Decomposition for Port-Hamiltonian System

We study how the vector-field structure of nonlinear port-Hamiltonian systems is reflected in the infinitesimal Koopman generator. The generator admits a natural bracket decomposition into a conservative interconnection-bracket derivation, a dissipative metric-bracket derivation, and an input-port derivation. The conservative component is formally skew-adjoint on a test space whenever the conservative flow preserves the reference measure and the relevant boundary terms vanish. The dissipative component is not claimed to be a positive operator on arbitrary observables; rather, the positive semidefinite object is the metric bracket $[f,f]_R=\nabla f^\intercal\mathbf{R}\nabla f\ge 0$, which yields the exact port-Hamiltonian energy balance for the Hamiltonian observable: \[ \mathcal{K}_{\mathbf{u}}\mathcal{H} =-[\mathcal{H},\mathcal{H}]_R +\mathbf{y}^\intercal\mathbf{u} \le \mathbf{y}^\intercal\mathbf{u}. \] We use these bracket identities to motivate finite-dimensional weak Galerkin and data-driven lifted models: when the Galerkin measure is conservative for the Hamiltonian interconnection flow and boundary terms vanish, the conservative contribution is skew in the Galerkin mass metric, while the dissipative bracket induces a positive semidefinite Dirichlet matrix. These identities motivate structure-preserving lifted port-Hamiltonian surrogates that are passive and support damping injection in the lifted coordinates, while distinguishing exact bracket identities, projection residuals, finite-data estimation error, and the residual and injectivity assumptions needed to transfer lifted conclusions back to the original nonlinear state.

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arXiv2026

A Measure-Theoretic Formulation of Behavioral Systems

In Willems' behavioral systems theory, a dynamical system is identified with the set of all trajectories compatible with its laws of motion. In the linear time-invariant setting this trajectory set is a linear subspace, and its algebraic structure underpins the Fundamental Lemma: a single persistently exciting data trajectory generates the entire finite-horizon behavior. For nonlinear or stochastic systems, however, the admissible trajectory set is generally nonconvex, obstructing direct optimization over the behavior. In this paper, we lift the behavioral viewpoint from trajectories to probability measures on trajectories by representing a finite-horizon dynamical system with the set of all Borel probability measures supported on its admissible trajectories. For deterministic systems, this behavioral-measure set is convex and weakly closed even when the dynamics are nonlinear, because convex combinations of trajectory distributions remain dynamically admissible even when convex combinations of trajectories do not. Its extreme points are precisely the Dirac masses on individual admissible trajectories, so the classical deterministic theory is embedded as the extremal skeleton of the richer measure-valued object. On this foundation we establish two core deterministic results and outline a stochastic extension based on history-conditional kernel consistency.

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arXiv2023

Robust Model Predictive Control with Polytopic Model Uncertainty through System Level Synthesis

We propose a robust model predictive control (MPC) method for discrete-time linear systems with polytopic model uncertainty and additive disturbances. Optimizing over linear time-varying (LTV) state feedback controllers has been successfully used for robust MPC when only additive disturbances are present. However, it is challenging to design LTV state feedback controllers in the face of model uncertainty whose effects are difficult to bound. To address this issue, we propose a novel approach to over-approximate the effects of both model uncertainty and additive disturbances by a filtered additive disturbance signal. Using the System Level Synthesis framework, we jointly search for robust LTV state feedback controllers and the bounds on the effects of uncertainty online, which allows us to reduce the conservatism and minimize an upper bound on the worst-case cost in robust MPC. We provide a comprehensive numerical comparison of our method and representative robust MPC methods from the literature. Numerical examples demonstrate that our proposed method can significantly reduce the conservatism over a wide range of uncertainty parameters with comparable computational effort as the baseline methods.

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arXiv2023

Differentiable Safe Controller Design through Control Barrier Functions

Learning-based controllers, such as neural network (NN) controllers, can show high empirical performance but lack formal safety guarantees. To address this issue, control barrier functions (CBFs) have been applied as a safety filter to monitor and modify the outputs of learning-based controllers in order to guarantee the safety of the closed-loop system. However, such modification can be myopic with unpredictable long-term effects. In this work, we propose a safe-by-construction NN controller which employs differentiable CBF-based safety layers, and investigate the performance of safe-by-construction NN controllers in learning-based control. Specifically, two formulations of controllers are compared: one is projection-based and the other relies on our proposed set-theoretic parameterization. Both methods demonstrate improved closed-loop performance over using CBF as a separate safety filter in numerical experiments.

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arXiv2022

Stable and Transferable Hyper-Graph Neural Networks

We introduce an architecture for processing signals supported on hypergraphs via graph neural networks (GNNs), which we call a Hyper-graph Expansion Neural Network (HENN), and provide the first bounds on the stability and transferability error of a hypergraph signal processing model. To do so, we provide a framework for bounding the stability and transferability error of GNNs across arbitrary graphs via spectral similarity. By bounding the difference between two graph shift operators (GSOs) in the positive semi-definite sense via their eigenvalue spectrum, we show that this error depends only on the properties of the GNN and the magnitude of spectral similarity of the GSOs. Moreover, we show that existing transferability results that assume the graphs are small perturbations of one another, or that the graphs are random and drawn from the same distribution or sampled from the same graphon can be recovered using our approach. Thus, both GNNs and our HENNs (trained using normalized Laplacians as graph shift operators) will be increasingly stable and transferable as the graphs become larger. Experimental results illustrate the importance of considering multiple graph representations in HENN, and show its superior performance when transferability is desired.

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arXiv2022

Parameter-Covariance Maximum Likelihood Estimation

Linear time series modelling is dominated by the use of purely autoregressive models even though incorporating moving average components can greatly improve parsimony. We present a convex formulation for vector-ARMA system identification which respects this fundamental property, thus granting access to the nice properties afforded by convex programming. The identification procedure is done purely in the time domain which can accommodate non-stationarity through regime switching. As a proof of concept, we present experimental results demonstrating this convex program in action. Next, we show how to adapt the expectation-maximization algorithm to support regime switching behavior.

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arXiv2022

One-Shot Reachability Analysis of Neural Network Dynamical Systems

The arising application of neural networks (NN) in robotic systems has driven the development of safety verification methods for neural network dynamical systems (NNDS). Recursive techniques for reachability analysis of dynamical systems in closed-loop with a NN controller, planner, or perception can over-approximate the reachable sets of the NNDS by bounding the outputs of the NN and propagating these NN output bounds forward. However, this recursive reachability analysis may suffer from compounding errors, rapidly becoming overly conservative over a longer horizon. In this work, we prove that an alternative one-shot reachability analysis framework which directly verifies the unrolled NNDS can significantly mitigate the compounding errors for a general class of NN verification methods built on layerwise abstraction. Our analysis is motivated by the fact that certain NN verification methods give rise to looser bounds when applied in one shot than recursively. In our analysis, we characterize the performance gap between the recursive and one-shot frameworks for NNDS with general computational graphs. The applicability of one-shot analysis is demonstrated through numerical examples on a cart-pole system.

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arXiv2022

Robust Model Predictive Control of Time-Delay Systems through System Level Synthesis

We present a robust model predictive control method (MPC) for discrete-time linear time-delayed systems with state and control input constraints. The system is subject to both polytopic model uncertainty and additive disturbances. In the proposed method, a time-varying feedback control policy is optimized such that the robust satisfaction of all constraints for the closed-loop system is guaranteed. By encoding the effects of the delayed states and inputs into the feedback policy, we solve the robust optimal control problem in MPC using System Level Synthesis which results in a convex quadratic program that jointly conducts uncertainty over-approximation and robust controller synthesis. Notably, the number of variables in the quadratic program is independent of the delay horizon. The effectiveness and scalability of our proposed method are demonstrated numerically.

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arXiv2022

Learning Operators with Coupled Attention

Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the recent success of the attention mechanism. In our architecture, the input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function in the training set measurements is very small. Our formulation is accompanied by rigorous approximation theoretic guarantees on the universal expressiveness of the proposed model. Empirically, we evaluate the performance of LOCA on several operator learning scenarios involving systems governed by ordinary and partial differential equations, as well as a black-box climate prediction problem. Through these scenarios we demonstrate state of the art accuracy, robustness with respect to noisy input data, and a consistently small spread of errors over testing data sets, even for out-of-distribution prediction tasks.

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arXiv2021

System Level Synthesis-based Robust Model Predictive Control through Convex Inner Approximation

We propose a robust model predictive control (MPC) method for discrete-time linear time-invariant systems with norm-bounded additive disturbances and model uncertainty. In our method, at each time step we solve a finite time robust optimal control problem (OCP) which jointly searches over robust linear state feedback controllers and bounds the deviation of the system states from the nominal predicted trajectory. By leveraging the System Level Synthesis (SLS) framework, the proposed robust OCP is formulated as a convex quadratic program in the space of closed-loop system responses. When an adaptive horizon strategy is used, we prove the recursive feasibility of the proposed MPC controller and input-to-state stability of the origin for the closed-loop system. We demonstrate through numerical examples that the proposed method considerably reduces conservatism when compared with existing SLS-based and tube-based robust MPC methods, while also enjoying low computational complexity.

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arXiv2021

Stabilization of Complementarity Systems via Contact-Aware Controllers

We propose a control framework which can utilize tactile information by exploiting the complementarity structure of contact dynamics. Since many robotic tasks, like manipulation and locomotion, are fundamentally based in making and breaking contact with the environment, state-of-the-art control policies struggle to deal with the hybrid nature of multi-contact motion. Such controllers often rely heavily upon heuristics or, due to the combinatorial structure in the dynamics, are unsuitable for real-time control. Principled deployment of tactile sensors offers a promising mechanism for stable and robust control, but modern approaches often use this data in an ad hoc manner, for instance to guide guarded moves. This framework can close the loop on tactile sensors and it is non-combinatorial, enabling optimization algorithms to automatically synthesize provably stable control policies. We demonstrate this approach on multiple numerical examples, including quasi-static friction problems and a high dimensional problem with ten contacts. We also validate our results on an experimental setup and show the effectiveness of the proposed method on an underactuated multi-contact system.

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arXiv2021

Learning Region of Attraction for Nonlinear Systems

Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we propose a counterexample-guided method to estimate the ROA of general nonlinear dynamical systems provided that they can be approximated by piecewise linear neural networks and that the approximation error can be bounded. Specifically, our method searches for robust Lyapunov functions using counterexamples, i.e., the states at which the Lyapunov conditions fail. We generate the counterexamples using Mixed-Integer Quadratic Programming. Our method is guaranteed to find a robust Lyapunov function in the parameterized function class, if exists, after collecting a finite number of counterexamples. We illustrate our method through numerical examples.

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arXiv2021

AutoEKF: Scalable System Identification for COVID-19 Forecasting from Large-Scale GPS Data

We present an Extended Kalman Filter framework for system identification and control of a stochastic high-dimensional epidemic model. The scale and severity of the COVID-19 emergency have highlighted the need for accurate forecasts of the state of the pandemic at a high resolution. Mechanistic compartmental models are widely used to produce such forecasts and assist in the design of control and relief policies. Unfortunately, the scale and stochastic nature of many of these models often makes the estimation of their parameters difficult. With the goal of calibrating a high dimensional COVID-19 model using low-level mobility data, we introduce a method for tractable maximum likelihood estimation that combines tools from Bayesian inference with scalable optimization techniques from machine learning. The proposed approach uses automatic backward-differentiation to directly compute the gradient of the likelihood of COVID-19 incidence and death data. The likelihood of the observations is estimated recursively using an Extended Kalman Filter and can be easily optimized using gradient-based methods to compute maximum likelihood estimators. Our compartmental model is trained using GPS mobility data that measures the mobility patterns of millions of mobile phones across the United States. We show that, after calibrating against incidence and deaths data from the city of Philadelphia, our model is able to produce an accurate 30-day forecast of the evolution of the pandemic.

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arXiv2021

Data-Driven Methods for Present and Future Pandemics: Monitoring, Modelling and Managing

This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.

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arXiv2020

Learning Lyapunov Functions for Hybrid Systems

We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop dynamics of linear systems with model predictive controllers, piecewise affine/linear complementarity/mixed-logical dynamical system in feedback with a ReLU neural network controller, etc. The proposed method comprises an alternation between a learner and a verifier to find a valid Lyapunov function inside a convex set of Lyapunov function candidates. In each iteration, the learner uses a collection of state samples to select a Lyapunov function candidate through a convex program in the parameter space. The verifier then solves a mixed-integer quadratic program in the state space to either validate the proposed Lyapunov function candidate or reject it with a counterexample, i.e., a state where the Lyapunov condition fails. This counterexample is then added to the sample set of the learner to refine the set of Lyapunov function candidates. By designing the learner and the verifier according to the analytic center cutting-plane method from convex optimization, we show that when the set of Lyapunov functions is full-dimensional in the parameter space, our method finds a Lyapunov function in a finite number of steps. We demonstrate our stability analysis method on closed-loop MPC dynamical systems and a ReLU neural network controlled PWA system.

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arXiv2020

Learning Lyapunov Functions for Piecewise Affine Systems with Neural Network Controllers

We propose a learning-based method for Lyapunov stability analysis of piecewise affine dynamical systems in feedback with piecewise affine neural network controllers. The proposed method consists of an iterative interaction between a learner and a verifier, where in each iteration, the learner uses a collection of samples of the closed-loop system to propose a Lyapunov function candidate as the solution to a convex program. The learner then queries the verifier, which solves a mixed-integer program to either validate the proposed Lyapunov function candidate or reject it with a counterexample, i.e., a state where the stability condition fails. This counterexample is then added to the sample set of the learner to refine the set of Lyapunov function candidates. We design the learner and the verifier based on the analytic center cutting-plane method, in which the verifier acts as the cutting-plane oracle to refine the set of Lyapunov function candidates. We show that when the set of Lyapunov functions is full-dimensional in the parameter space, the overall procedure finds a Lyapunov function in a finite number of iterations. We demonstrate the utility of the proposed method in searching for quadratic and piecewise quadratic Lyapunov functions.

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arXiv2020

Adaptive Test Allocation for Outbreak Detection and Tracking in Social Contact Networks

We present a general framework for adaptive allocation of viral tests in social contact networks. We pose and solve several complementary problems. First, we consider the design of a social sensing system whose objective is the early detection of a novel epidemic outbreak. In particular, we propose an algorithm to select a subset of individuals to be tested in order to detect the onset of an epidemic outbreak as fast as possible. We pose this problem as a hitting time probability maximization problem and use submodularity optimization techniques to derive explicit quality guarantees for the proposed solution. Second, once an epidemic outbreak has been detected, we consider the problem of adaptively distributing viral tests over time in order to maximize the information gained about the current state of the epidemic. We formalize this problem in terms of information entropy and mutual information and propose an adaptive allocation strategy with quality guarantees. For these problems, we derive analytical solutions for any stochastic compartmental epidemic model with Markovian dynamics, as well as efficient Monte-Carlo-based algorithms for non-Markovian dynamics. Finally, we illustrate the performance of the proposed framework in numerical experiments involving a model of Covid-19 applied to a real human contact network.

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arXiv2020

Data-Driven Control of the COVID-19 Outbreak via Non-Pharmaceutical Interventions: A Geometric Programming Approach

In this paper we propose a data-driven model for the spread of SARS-CoV-2 and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of our data-driven model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on individuals' mobility patterns specific to each region. We propose an optimal control problem on this data-driven model with a tractable solution provided by geometric programming. The result of this framework is a mobility-based intervention strategy that curbs the spread of the epidemic while obeying a budget on the economic cost incurred. Furthermore, in the absence of a straightforward mapping from human mobility data to economic costs, we propose a practical method by which a budget on economic losses incurred may be chosen to eliminate excess deaths due to over-utilization of hospital resources. Our results are demonstrated with numerical simulations using real data from the Philadelphia metropolitan area.

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