arXiv subjects

Raktim Bhattacharya

Publications and source records attributed to Raktim Bhattacharya.

At least 19 recordsLinked to original sources

arXiv2026

An Exact Instrument for State Usage in Selective State-Space Models, and the Input-Driven Migration It Reveals

Selective state-space models such as Mamba route information through a bank of first-order modes whose input coupling is set by a learned selection mechanism. We give an exact instrument for measuring how a trained model uses these modes. Because the state matrix is diagonal, each channel's output decomposes exactly into per-mode contributions, and a per-(layer, channel, window) Gram tensor yields the exact output error of dropping any subset of modes, offline, at any budget. Validated against the reference implementation to a relative error of $2.3\times10^{-7}$ on the Mamba-1 family where it is exact, the instrument predicts a layer's deployed pruning error to a median relative deviation of $5\times10^{-7}$ over $4{,}464$ configurations, its floor set by the reconstruction. Applying the instrument across the Mamba-1 family (130M--2.8B), the deployed 7B Falcon-Mamba, and Mamba-2, we find that trained models re-allocate their state space with the input: which modes carry the signal migrates across contexts, and at the most affected layers a per-input oracle roughly halves the output error of a fixed mode set. Frozen-signal counterfactuals attribute the migration primarily to the input-dependent write map $B_t$; the timestep usually identified with selectivity carries almost none of it. Input-scheduled mode pruning on this measurement outperforms static, Hankel-based, and layer-adaptive rankings at every scale from 130M to the deployed 7B Falcon-Mamba, and at half the state budget it matches the unpruned model. Because the scheduler reads each window's mode usage from a first pass, this demonstrates realizable headroom; we claim no deployed compute or memory saving.

cs.LG↗

arXiv2026

Spectral Koopman Approach for Reconstructing State-space Geometry of Cislunar Restricted 3-Body Problem

In this work, we propose a novel approach, based on the path integral formulation of Koopman spectrum, to discover the phase-space geometry of the planar Cislunar Restricted 3 Body Problem (CR3BP). In contrast to existing techniques, which use trajectory-based (usually) local analysis, we leverage the Koopman operator framework, which generates a global linear \emph{representation} of the system, to reconstruct the global phase space geometry of the CR3BP. In particular, we compute the principal eigenfunctions of the Koopman operator via the path integral approach and show how the zero level curves of these eigenfunctions encode the phase space characteristics of the planar CR3BP.

math.DS↗

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↗

arXiv2026

Improving D-Optimal Sensor Placement for Bearing-Only Localization via Maximum-Entropy Reweighting

In this paper, we present a two-layer architecture for bearing-only sensor placement that improves upon classical D-optimal design. The first layer reweights particles by minimizing Kullback-Leibler divergence from the current distribution subject to a distributional accuracy bound, concentrating mass on regions where the posterior is likely to settle, without reference to the sensor model. The second layer performs D-optimal sensor placement with respect to the reweighted Fisher information matrix, steering sensors toward geometrically informative configurations. Because the two layers are structurally decoupled, the reweighting generalizes across sensing modalities while the placement remains specific to bearing geometry. Systematic experiments on multi-source localization at two noise levels show that this reweighting reduces localization error on average, with the benefit growing as the sensor-to-source ratio increases and as measurements become more informative. The improvement is established in the first few iterations of the sequential procedure and persists as the posterior concentrates.

eess.SP↗

arXiv2026

Sensor Design for Accuracy-Bounded Estimation via Maximum-Entropy Likelihood Synthesis

Designing the sensing architecture for large-scale spatio-temporal systems is hard when accuracy requirements are specified but sensor models are uncertain or unavailable. Classical design treats sensor placement and estimation sequentially, requiring valid forward models for each sensing modality. This paper inverts the design flow: given an error budget, synthesize the measurement likelihood that enforces it while injecting minimal information beyond the dynamical prior. The likelihood is constructed by constrained optimization: among all posteriors satisfying a prescribed accuracy bound relative to a target, select the one minimizing Kullback-Leibler divergence from the prior. The solution is a maximum-entropy posterior in relative-entropy form, and the induced likelihood is the Radon-Nikodym derivative. The framework accommodates arbitrary discrepancies and is instantiated for Wasserstein distance, maximum mean discrepancy, $f$-divergences, moment constraints, and hybrid metrics. For each, we derive the discrete particle-level problem, analyze its convex or convex-relaxed structure, and present solvers with complexity scaling. A closed-form solution exists for the symmetric exponential-tilt case, and a distillation procedure converts nonparametric likelihood samples into parametric forms. A two-layer sensor design architecture embeds the synthesized likelihood in the recursive predict-update loop, connecting accuracy budgets to physical sensor placement, precision, and configuration. Numerical experiments comparing four metrics on unimodal and multimodal scenarios confirm the accuracy constraints are reliably enforced and reveal how metric choice determines the amount and spatial distribution of injected information.

cs.IT↗

arXiv2026

Robust $\mathcal{H}_\infty$ Observer Design via Finsler's Lemma and IQCs

This paper develops a Finsler-based LMI for robust $\mathcal{H}_\infty$ observer design with integral quadratic constraints (IQCs) and block-structured uncertainty. By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requirement $\mathrm{He}(PA) \prec 0$ (which fails for marginally stable dynamics), and a multiplier--Lyapunov trade-off that causes infeasibility for wide uncertainty ranges. For marginally stable dynamics, artificial damping in the design model balances certified versus actual performance. The framework is demonstrated on quaternion attitude estimation with angular velocity uncertainty and mass-spring-damper state estimation with uncertain physical parameters.

math.OC↗

arXiv2025

Robust Cislunar Navigation via LFT-Based $\mathcal{H}_\infty$ Filtering with Bearing-Only Measurements

This paper develops a robust estimation framework for cislunar navigation that embeds the Circular Restricted Three-Body Problem (CR3BP) dynamics and bearing-only optical measurements within a Linear Fractional Transformation (LFT) representation. A full-order $\mathcal{H}_\infty$ observer is synthesized with explicit $\mathcal{L}_2$ performance bounds. The formulation yields a nonlinear estimator that operates directly on the governing equations and avoids reliance on local linearizations. Dominant nonlinearities are expressed as structured real uncertainties, while measurement fidelity is represented through range-dependent weighting with Earth-Moon distances reconstructed from line-of-sight geometry. The sensing architecture assumes passive star-tracker-class optical instruments, eliminating the need for time-of-flight ranging or precision clocks. Simulations demonstrate bounded estimation errors and smooth position tracking over multiple orbital periods, with the largest deviations observed in the out-of-plane states, consistent with the stiffness of the vertical dynamics and the limitations of angle-only observability. Application to a Near Rectilinear Halo Orbit (NRHO) illustrates that the framework can achieve robust onboard navigation with bounded estimation errors with flight-representative sensors.

eess.SY↗

arXiv2025

Robust Attitude Control of Nonlinear UAV Dynamics with LFT Models and $\mathcal{H}_\infty$ Performance

Attitude stabilization of unmanned aerial vehicles (UAVs) in uncertain environments presents significant challenges due to nonlinear dynamics, parameter variations, and sensor limitations. This paper presents a comparative study of $\mathcal{H}_\infty$ and classical PID controllers for multi-rotor attitude regulation in the presence of wind disturbances and gyroscope noise. The flight dynamics are modeled using a linear parameter-varying (LPV) framework, where nonlinearities and parameter variations are systematically represented as structured uncertainties within a linear fractional transformation formulation. A robust controller based on $\mathcal{H}_\infty$ formulation is designed using only gyroscope measurements to ensure guaranteed performance bounds. Nonlinear simulation results demonstrate the effectiveness of the robust controllers compared to classical PID control, showing significant improvement in attitude regulation under severe wind disturbances.

eess.SY↗

arXiv2025

$\mathcal{H}_\infty$ Optimal Navigation in the Cislunar Space with LFT Models

Navigation in the cislunar domain presents significant challenges due to chaotic and unmodeled dynamics, as well as state-dependent sensor errors. This paper develops a robust estimation framework based on Linear Fractional Transformation (LFT) models, and state estimation in $\mathcal{H}_\infty$ and $\mu$ synthesis framework to address these challenges. The cislunar dynamics are embedded into an LFT form that captures nonlinearities in the gravitational model and state-dependent sensor errors as structured uncertainty. A nonlinear estimator is then synthesized in the $\mathcal{H}_\infty$ sense to ensure robust performance guarantees in the presence of the stated uncertainties. Simulation results demonstrate the effectiveness of the estimator for navigation in a surveillance constellation.

math.OC↗

arXiv2024

Optimal Sensing Precision for Celestial Navigation Systems in Cislunar Space using LPV Framework

This paper introduces two innovative convex optimization formulations to simultaneously optimize the H2/Hinf observer gain and sensing precision, and guarantee a specified estimation error bound for nonlinear systems in LPV form. Applied to the design of an onboard celestial navigation system for cislunar operations, these formulations demonstrate the ability to maintain accurate spacecraft positioning with minimal measurements and theoretical performance guarantees by design.

math.OC↗

arXiv2024

Sparse Actuation for LPV Systems with Full-State Feedback in $\mathcal{H}_2/\mathcal{H}_\infty$ Framework

This paper addresses the sparse actuation problem for nonlinear systems represented in the Linear Parameter-Varying (LPV) form. We propose a convex optimization framework that concurrently determines actuator magnitude limits and the state-feedback law that guarantees a user-specified closed-loop performance in the $\mathcal{H}_2/\mathcal{H}_\infty$ sense. We also demonstrate that sparse actuation is achieved when the actuator magnitude-limits are minimized in the $l_1$ sense. This is the first paper that addresses this problem for LPV systems. The formulation is demonstrated in a vibration control problem for a flexible wing.

eess.SY↗

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↗

arXiv2024

Optimal State Estimation in the Presence of Non-Gaussian Uncertainty via Wasserstein Distance Minimization

This paper presents a novel distribution-agnostic Wasserstein distance-based estimation framework. The goal is to determine an optimal map combining prior estimate with measurement likelihood such that posterior estimation error optimally reaches the Dirac delta distribution with minimal effort. The Wasserstein metric is used to quantify the effort of transporting from one distribution to another. We hypothesize that minimizing the Wasserstein distance between the posterior error and the Dirac delta distribution results in optimal information fusion and posterior state uncertainty. Framework validation is demonstrated by the successful recovery of the classical Kalman filter for linear systems with Gaussian uncertainties. Notably, the proposed Wasserstein filter does not rely on particle representation of uncertainty. Furthermore, the classical result for the Gaussian Sum Filter (GSF) is retrieved from the Wasserstein framework. This approach analytically exhibits the suboptimality of GSF and enables the use of nonlinear optimization techniques to enhance the accuracy of the Gaussian sum estimator.

eess.SY↗

arXiv2024

A Convex Optimization Framework for Computing Robustness Margins of Kalman Filters

This paper proposes a novel convex optimization framework for designing robust Kalman filters that guarantee a user-specified steady-state error while maximizing process and sensor noise. The proposed framework simultaneously determines the Kalman gain and the robustness margin in terms of the process and sensor noise. This is the first paper to present such a joint formulation for Kalman filtering. The proposed methodology is validated through two distinct examples: the Clohessy-Wiltshire-Hill equations for a chaser spacecraft in an elliptical orbit and the longitudinal motion model of an F-16 aircraft.

eess.SY↗

arXiv2024

Quantifying Maximum Actuator Degradation for a Given $H_2/H_{\infty}$ Performance with Full-State Feedback Control

In this paper, we address the issue of quantifying maximum actuator degradation in linear time-invariant dynamical systems. We present a new unified framework for computing the state-feedback controller gain that meets a user-defined closed-loop performance criterion while also maximizing actuator degradation. This degradation is modeled as a first-order filter with additive noise. Our approach involves two novel convex optimization formulations that concurrently determine the controller gain, maximize actuator degradation, and maintain the desired closed-loop performance in both the $H_2$ and $H_{\infty}$ system norms. The results are limited to open-loop stable systems. We demonstrate the application of our results through the design of a full-state feedback controller for a model representing the longitudinal motion of the F-16 aircraft.

eess.SY↗

arXiv2023

Privacy-aware Gaussian Process Regression

We propose a novel theoretical and methodological framework for Gaussian process regression subject to privacy constraints. The proposed method can be used when a data owner is unwilling to share a high-fidelity supervised learning model built from their data with the public due to privacy concerns. The key idea of the proposed method is to add synthetic noise to the data until the predictive variance of the Gaussian process model reaches a prespecified privacy level. The optimal covariance matrix of the synthetic noise is formulated in terms of semi-definite programming. We also introduce the formulation of privacy-aware solutions under continuous privacy constraints using kernel-based approaches, and study their theoretical properties. The proposed method is illustrated by considering a model that tracks the trajectories of satellites and a real application on a census dataset.

cs.LG↗

arXiv2021

Investigation of Flight Conditions where Box-Wing Outperforms Mono-Wing Configurations for Small UAVs

We investigate the aerodynamic efficiency and flight dynamics of mono-wing and box-wing configurations across various parameters, including aspect ratio, velocity, and lift requirements. We find that although mono-wing configurations exhibit superior aerodynamic efficiency in certain regimes, box-wing designs perform better in circumstances like high velocities and increased lift demands. Box-wing configurations also prove advantageous when induced drag is higher than friction drag due to their ability to suppress the tip vortices. Furthermore, while analyzing the flight dynamics, low aspect ratio box-wing configurations show improved gust tolerance and stability in longitudinal and lateral dynamics. However, no substantial difference in flight dynamics is observed between box-wing and mono-wing designs for high aspect ratio configurations. The findings underscore the importance of selecting the appropriate wing configuration based on specific performance requirements and operational conditions.

physics.flu-dyn↗

arXiv2021

Optimal Sensor Precision for Multi-Rate Sensing for Bounded Estimation Error

We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman filtering framework, where the sensor precisions are treated as variables. They are determined by solving a constrained convex optimization problem, which guarantees the specified upper bound on the posterior error variance. Optimal sensor precisions are determined by minimizing the l1 norm, which promotes sparseness in the solution and indirectly addresses the sensor selection problem. The theory is applied to realistic flight mechanics and astrodynamics problems to highlight its engineering value. These examples demonstrate the application of the presented theory to a) determine redundant sensing architectures for linear time invariant systems, b) accurately estimate states with low-cost sensors, and c) optimally schedule sensors for linear time-varying systems.

eess.SY↗