arXiv subjects

Vedang M. Deshpande

Publications and source records attributed to Vedang M. Deshpande.

13 recordsLinked to original sources

arXiv2026

On Improved Statistical Accuracy of Low-Order Polynomial Chaos Approximations

Polynomial chaos expansions provide surrogate models for stochastic systems, with coefficients typically derived using Galerkin projection, stochastic collocation, or least squares approximation. These traditional approaches often fail to accurately capture statistical moments without resorting to high-order approximations. We propose a constrained optimization framework that modifies standard techniques to determine polynomial chaos coefficients that precisely recover the first two statistical moments. The effectiveness of our approach is demonstrated on several candidate algebraic functions of random variables, showing significant improvements in statistical accuracy even with low-order approximations.

eess.SY↗

arXiv2025

Meta-Learning for Physically-Constrained Neural System Identification

We present a gradient-based meta-learning framework for rapid adaptation of neural state-space models (NSSMs) for black-box system identification. When applicable, we also incorporate domain-specific physical constraints to improve the accuracy of the NSSM. The major benefit of our approach is that instead of relying solely on data from a single target system, our framework utilizes data from a diverse set of source systems, enabling learning from limited target data, as well as with few online training iterations. Through benchmark examples, we demonstrate the potential of our approach, study the effect of fine-tuning subnetworks rather than full fine-tuning, and report real-world case studies to illustrate the practical application and generalizability of the approach to practical problems with physical-constraints. Specifically, we show that the meta-learned models result in improved downstream performance in model-based state estimation in indoor localization and energy systems.

cs.LG↗

arXiv2024

$\mathcal{H}_2/\mathcal{H}_\infty$ Optimal Control with Sparse Sensing and Actuation

In this paper, we present novel convex optimization formulations for designing full-state and output-feedback controllers with sparse actuation that achieve user-specified $\mathcal{H}_2$ and $\mathcal{H}_\infty$ performance criteria. For output-feedback control, we extend these formulations to simultaneously design control laws with sparse actuation and sensing. The sparsity is induced through the minimization of a weighted $\ell_1$ norm, promoting the efficient use of sensors and actuators while maintaining desired closed-loop performance. The proposed methods are applied to a nonlinear structural dynamics problem, demonstrating the advantages of simultaneous optimization of the control law, sensing, and actuation architecture in realizing an efficient closed-loop system.

eess.SY↗

arXiv2021

Sensor Placement with Optimal Precision for Temperature Estimation of Battery Systems

The temperature distribution in the battery significantly impacts the short-term and long-term performance of battery systems. Therefore, efficient, safe, and reliable battery system operation requires an accurate estimation of the temperature field. The current industry standard for sensors to battery cell ratio is quite frugal. Thus, the problem of sensor placement for accurate temperature estimation becomes non-trivial, especially for large-scale systems. In this paper, we explore a greedy approach for sensor placement suitable for large-scale battery systems. An observer to estimate the thermal field is designed in an $\mathcal{H}_{\infty}$ framework while simultaneously minimizing the sensor precisions, thus lowering the overall thermal management system's economic cost.

eess.SY↗

arXiv2021

Sensor Selection and Optimal Precision in $\mathcal{H}_2/\mathcal{H}_{\infty}$ Estimation Framework: Theory and Algorithms

We consider the problem of sensor selection for designing observer and filter for continuous linear time invariant systems such that the sensor precisions are minimized, and the estimation errors are bounded by the prescribed $\mathcal{H}_2/\mathcal{H}_{\infty}$ performance criteria. The proposed integrated framework formulates the precision minimization as a convex optimization problem subject to linear matrix inequalities, and it is solved using an algorithm based on the alternating direction method of multipliers (ADMM). We also present a greedy approach for sensor selection and demonstrate the performance of the proposed algorithms using numerical simulations.

eess.SY↗

arXiv2021

Sparse Sensing Architectures with Optimal Precision for Tracking Multi-agent Systems in Sensing-denied Environments

In this paper the tracking problem of multi-agent systems, in a particular scenario where a segment of agents entering a sensing-denied environment or behaving as non-cooperative targets, is considered. The focus is on determining the optimal sensor precisions while simultaneously promoting sparseness in the sensor measurements to guarantee a specified estimation performance. The problem is formulated in the discrete-time centralized Kalman filtering framework. A semi-definite program subject to linear matrix inequalities is solved to minimize the trace of precision matrix which is defined to be the inverse of sensor noise covariance matrix. Simulation results expose a trade-off between sensor precisions and sensing frequency.

eess.SY↗

arXiv2020

Sparse Sensing and Optimal Precision: Robust $\mathcal{H}_{\infty}$ Optimal Observer Design with Model Uncertainty

We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor configuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the $\mathcal{H}_{\infty}$ optimal observer design framework. We consider two types of uncertainties in the system, i.e. structured affine and unstructured uncertainties. The objective is to design an observer with a given $\mathcal{H}_{\infty}$ performance index with minimal number of sensors and minimal precision values, while guaranteeing the performance for all admissible uncertainties. The problem is posed as a convex optimization problem subject to linear matrix inequalities. Numerical simulations demonstrate the application of the theoretical results presented in this work.

eess.SY↗

arXiv2020

Kalman Filtering with Probabilistic Uncertainty in System Parameters

In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The uncertainty, characterized by mean and variance of the states, is propagated using conditional expectations and polynomial chaos expansion framework. The results obtained using the proposed filter are compared with existing robust filters in the literature. The proposed filter demonstrates better performance in terms of root mean squared error and rate of convergence.

eess.SY↗

arXiv2020

Sparse Sensing and Optimal Precision: An Integrated Framework for $\mathcal{H}_2/\mathcal{H}_{\infty}$ Optimal Observer Design

In this paper, we simultaneously determine the optimal sensor precision and the observer gain, which achieves the specified accuracy in the state estimates. Along with the unknown observer gain, the formulation parameterizes the scaling of the exogenous inputs that correspond to the sensor noise. Reciprocal of this scaling is defined as the sensor precision, and sparseness is achieved by minimizing the $l_1$ norm of the precision vector. The optimization is performed with constraints guaranteeing specified accuracy in state estimates, which are defined in terms of $\mathcal{H}_2$ or $\mathcal{H}_{\infty}$ norms of the error dynamics. The results presented in this paper are applied to the linearized longitudinal model of an F-16 aircraft.

eess.SY↗

arXiv2020

Data-driven Solution of Stochastic Differential Equations Using Maximum Entropy Basis Functions

In this paper we present a data-driven approach for uncertainty propagation. In particular, we consider stochastic differential equations with parametric uncertainty. Solution of the differential equation is approximated using maximum entropy (maxent) basis functions similar to polynomial chaos expansions. Maxent basis functions are derived from available data by maximization of information-theoretic entropy, therefore, there is no need to specify basis functions beforehand. We compare the proposed maxent based approach with existing methods.

math.NA↗

arXiv2019

A unified framework to generate optimized compact finite difference schemes

A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality constraints that ensure specified order of accuracy. A rigorous stability analysis for the optimized schemes is also presented. We analytically prove the relation between order of a derivative and symmetry or skew-symmetry of the optimal coefficients approximating it. We also show that other types of schemes e.g., spatially explicit, and biased finite differences, can be generated as special cases of the framework.

math.NA↗

arXiv2019

Surrogate Modeling of Dynamics From Sparse Data Using Maximum Entropy Basis Functions

In this paper we present a data driven approach for approximating dynamical systems. A dynamics is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly from the data provided. This approach has advantages over other methods, where a dictionary of basis functions have to be provided by the user, which is non trivial in some applications. We compare the accuracy of the proposed data-driven modeling approach to existing methods in the literature, and demonstrate that for some applications the maximum entropy basis functions provide significantly more accurate models.

math.DS↗

arXiv2019

On Improved Statistical Accuracy of Low-Order Polynomial Chaos Approximations

Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are applied to determine polynomial chaos coefficients, which define the surrogate model. Since the surrogate models are developed from a function approximation perspective, there is no reason to expect accuracy of statistics from these models. The statistical moments estimated from the surrogate model may significantly differ from the true moments, especially for lower order approximations. Often arbitrary high orders are required to recover, for example, the second moment. In this paper, we present modifications of standard techniques and determine polynomial chaos coefficients by solving a constrained optimization problem. We present this new approach for algebraic functions and differential equations with random parameters, and demonstrate that the surrogate models from the new approach are able to recover the first two moments exactly.

math.OC↗