arXiv subjects

Debdipta Goswami

Publications and source records attributed to Debdipta Goswami.

18 recordsLinked to original sources

arXiv2026

Robust Peak-cost Constrained Reinforcement Learning

We study robust peak-cost constrained reinforcement learning (RP-CRL), where the objective is to maximize expected reward while controlling the maximum cost encountered along a trajectory. This setting is motivated by safety-critical applications in which a single large violation can be catastrophic and therefore cannot be adequately captured by the standard CMDP framework based on expected cumulative cost. Existing reachability-constrained RL methods adopt Lagrangian-based approaches, yet the underlying duality properties of peak-cost constrained MDPs remain unclear. We show that, unlike standard CMDPs, peak-cost constrained MDPs may not admit zero duality gap. We further consider a robust formulation to address simulator-to-real-world mismatch in the transition dynamics. To solve this problem, we develop a surrogate optimization framework and a robust value estimation method based on integral probability metrics. We prove that, with appropriate hyperparameter choices, the surrogate solution attains the same robust reward value as the original problem while violating the constraint by at most epsilon. Experiments show that the proposed method effectively enforces safety under dynamics perturbations while retaining strong reward performance.

cs.LG↗

arXiv2026

Parametric Interpolation of Dynamic Mode Decomposition for Predicting Nonlinear Systems

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods which interpolate modes, eigenvalues, or reduced operators and can be fragile with sparse training data or multi-dimensional parameter spaces, piDMD learns a single parameter-affine Koopman surrogate reduced order model (ROM) across multiple training parameter samples and predicts at unseen parameter values without retraining. We validate piDMD on fluid flow past a cylinder, electron beam oscillations in transverse magnetic fields, and virtual cathode oscillations -- the latter two being simulated using an electromagnetic particle-in-cell (EMPIC) method. Across all benchmarks, piDMD achieves accurate long-horizon predictions and improved robustness over state-of-the-art interpolation-based parametric DMD baselines, with less training samples and with multi-dimensional parameter spaces.

eess.SY↗

arXiv2026

On Data-Driven Koopman Representations of Nonlinear Delay Differential Equations

This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary differential equations (ODEs) and partially for partial differential equations (PDEs), its extension to delay differential equations (DDEs) remains limited due to the infinite-dimensional phase space of DDEs. We propose a finite-dimensional Koopman approximation framework based on history discretization and a suitable reconstruction operator, enabling a tractable representation of the Koopman operator via kernel-based extended dynamic mode decomposition (kEDMD). Deterministic error bounds are derived for the learned predictor, decomposing the total error into contributions from history discretization, kernel interpolation, and data-driven regression. Additionally, we develop a kernel-based reconstruction method to recover discretized states from lifted Koopman coordinates, with provable guarantees. Numerical results demonstrate reliable prediction of nonlinear delay systems, with potential relevance to future control applications.

eess.SY↗

arXiv2025

Data to Certificate: Guaranteed Cost Control with Quantization-Aware System Identification

Cloud-assisted system identification and control have emerged as practical solutions for low-power, resource-constrained control systems such as micro-UAVs. In a typical cloud-assisted setting, state and input data are transmitted from local agents to a central computer over low-bandwidth wireless links, leading to quantization. This paper investigates the impact of state and input data quantization on a linear time invariant (LTI) system identification, derives a worst-case bound on the identification error, and develops a robust controller for guaranteed cost control. We establish a fundamental bound on the model error that depends only on the quantized data and quantization resolution, and develop a linear matrix inequality (LMI) based guaranteed cost robust controller under this error bound.

eess.SY↗

arXiv2025

Temporally-Consistent Bilinearly Recurrent Autoencoders for Control Systems

This paper introduces the temporally-consistent bilinearly recurrent autoencoder (tcBLRAN), a Koopman operator based neural network architecture for modeling a control-affine nonlinear control system. The proposed method extends traditional Koopman autoencoders (KAE) by incorporating bilinear recurrent dynamics that are consistent across predictions, enabling accurate long-term forecasting for control-affine systems. This overcomes the roadblock that KAEs face when encountered with limited and noisy training datasets, resulting in a lack of generalizability due to inconsistency in training data. Through a blend of deep learning and dynamical systems theory, tcBLRAN demonstrates superior performance in capturing complex behaviors and control systems dynamics, providing a superior data-driven modeling technique for control systems and outperforming the state-of-the-art Koopman bilinear form (KBF) learned by autoencoder networks.

eess.SY↗

arXiv2025

QSID-MPC: Model Predictive Control with System Identification from Quantized Data

Least-square system identification is widely used for data-driven model-predictive control (MPC) of unknown or partially known systems. This letter investigates how the system identification and subsequent MPC is affected when the state and input data is quantized. Specifically, we examine the fundamental connection between model error and quantization resolution and how that affects the stability and boundedness of the MPC tracking error. Furthermore, we demonstrate that, with a sufficiently rich dataset, the model error is bounded by a function of quantization resolution and the MPC tracking error is also ultimately bounded similarly. The theory is validated through numerical experiments conducted on two different linear dynamical systems.

eess.SY↗

arXiv2025

Koopman Meets Limited Bandwidth: Effect of Quantization on Data-Driven Linear Prediction and Control of Nonlinear Systems

Koopman-based lifted linear identification have been widely used for data-driven prediction and model predictive control (MPC) of nonlinear systems. It has found applications in flow-control, soft robotics, and unmanned aerial vehicles (UAV). For autonomous systems, this system identification method works by embedding the nonlinear system in a higher-dimensional linear space and computing a finite-dimensional approximation of the corresponding Koopman operator with the Extended Dynamic Mode Decomposition (EDMD) algorithm. EDMD is a data-driven algorithm that estimates an approximate linear system by lifting the state data-snapshots via nonlinear dictionary functions. For control systems, EDMD is further modified to utilize both state and control data-snapshots to estimate a lifted linear predictor with control input. This article investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental connection between estimates of the linear predictor matrices obtained from unquantized data and those from quantized data via modified EDMD. Furthermore, using the law of large numbers, we demonstrate that, under a large data regime, the quantized estimate can be considered a regularized version of the unquantized estimate. We also explore the relationship between the two estimates in the finite data regime. We further analyze the effect of nonlinear lifting functions on this regularization due to quantization. The theory is validated through repeated numerical experiments conducted on several control systems. The effect of quantization on the MPC performance is also demonstrated.

eess.SY↗

arXiv2024

Real-Time Linear MPC for Quadrotors on SE(3): An Analytical Koopman-based Realization

This letter presents an analytical linear parameter-varying (LPV) representation of quadrotor dynamics utilizing Koopman theory, facilitating computationally efficient linear model predictive control (LMPC) for real-time trajectory tracking. By leveraging carefully designed Koopman observables, the proposed approach enables a compact lifted-space evolution that mitigates the curse of dimensionality while preserving the nonlinear characteristics of the system. Although model predictive control (MPC) is a powerful strategy for quadrotor control, it faces a trade-off between the high computational cost of nonlinear MPC (NMPC) and the reduced accuracy of LMPC. To address this gap, we introduce KQ-LMPC (Koopman Quasilinear LPV MPC), which leverages the Koopman-lifted LPV formulation to enforce constraints, ensure lower computational burden and real-time feasibility, and deliver tracking performance comparable to NMPC. Experimental validation confirms the effectiveness of the framework in reasonably agile flight. To the best of our knowledge, this is the first experimentally validated LMPC for quadrotors that employs analytically derived Koopman observables without requiring training data.

eess.SY↗

arXiv2024

On the Effect of Quantization on Extended Dynamic Mode Decomposition

Extended Dynamic Mode Decomposition (EDMD) is a widely used data-driven algorithm for estimating the Koopman Operator. EDMD extends Dynamic Mode Decomposition (DMD) by lifting the snapshot data using nonlinear dictionary functions before performing the estimation. This letter investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental connection between estimates of the operator obtained from unquantized data and those from quantized data via EDMD. Furthermore, using the law of large numbers, we demonstrate that, under a large data regime, the quantized estimate can be considered a regularized version of the unquantized estimate. We also explore the relationship between the two estimates in the finite data regime. We further analyze the effect of nonlinear lifting functions on this regularization due to quantization. The theory is validated through repeated numerical experiments conducted on two different dynamical systems.

eess.SY↗

arXiv2024

On the Effect of Quantization on Dynamic Mode Decomposition

Dynamic Mode Decomposition (DMD) is a widely used data-driven algorithm for estimating the Koopman Operator.This paper investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental connection between estimates of the operator obtained from unquantized data and those from quantized data. Furthermore, using the law of large numbers, we demonstrate that, under a large data regime, the quantized estimate can be considered a regularized version of the unquantized estimate. This key theoretical finding paves the way to accurately recover the unquantized estimate from quantized data. We also explore the relationship between the two estimates in the finite data regime. The theory is validated through repeated numerical experiments conducted on three different dynamical systems.

eess.SY↗

arXiv2024

Feature-Based Echo-State Networks: A Step Towards Interpretability and Minimalism in Reservoir Computer

This paper proposes a novel and interpretable recurrent neural-network structure using the echo-state network (ESN) paradigm for time-series prediction. While the traditional ESNs perform well for dynamical systems prediction, it needs a large dynamic reservoir with increased computational complexity. It also lacks interpretability to discern contributions from different input combinations to the output. Here, a systematic reservoir architecture is developed using smaller parallel reservoirs driven by different input combinations, known as features, and then they are nonlinearly combined to produce the output. The resultant feature-based ESN (Feat-ESN) outperforms the traditional single-reservoir ESN with less reservoir nodes. The predictive capability of the proposed architecture is demonstrated on three systems: two synthetic datasets from chaotic dynamical systems and a set of real-time traffic data.

cs.LG↗

arXiv2024

Temporally Consistent Koopman Autoencoders for Forecasting Dynamical Systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the temporally consistent Koopman autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE's superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

cs.LG↗

arXiv2023

Sequential Learning from Noisy Data: Data-Assimilation Meets Echo-State Network

This paper explores the problem of training a recurrent neural network from noisy data. While neural network based dynamic predictors perform well with noise-free training data, prediction with noisy inputs during training phase poses a significant challenge. Here a sequential training algorithm is developed for an echo-state network (ESN) by incorporating noisy observations using an ensemble Kalman filter. The resultant Kalman-trained echo-state network (KalT-ESN) outperforms the traditionally trained ESN with least square algorithm while still being computationally cheap. The proposed method is demonstrated on noisy observations from three systems: two synthetic datasets from chaotic dynamical systems and a set of real-time traffic data.

eess.SY↗

arXiv2022

Delay Embedded Echo-State Network: A Predictor for Partially Observed Systems

This paper considers the problem of data-driven prediction of partially observed systems using a recurrent neural network. While neural network based dynamic predictors perform well with full-state training data, prediction with partial observation during training phase poses a significant challenge. Here a predictor for partial observations is developed using an echo-state network (ESN) and time delay embedding of the partially observed state. The proposed method is theoretically justified with Taken's embedding theorem and strong observability of a nonlinear system. The efficacy of the proposed method is demonstrated on three systems: two synthetic datasets from chaotic dynamical systems and a set of real-time traffic data.

eess.SY↗

arXiv2022

Optimal Control with Learning on the Fly: System with Unknown Drift

This paper derives an optimal control strategy for a simple stochastic dynamical system with constant drift and an additive control input. Motivated by the example of a physical system with an unexpected change in its dynamics, we take the drift parameter to be unknown, so that it must be learned while controlling the system. The state of the system is observed through a linear observation model with Gaussian noise. In contrast to most previous work, which focuses on a controller's asymptotic performance over an infinite time horizon, we minimize a quadratic cost function over a finite time horizon. The performance of our control strategy is quantified by comparing its cost with the cost incurred by an optimal controller that has full knowledge of the parameters. This approach gives rise to several notions of "regret." We derive a set of control strategies that provably minimize the worst-case regret; these arise from Bayesian strategies that assume a specific fixed prior on the drift parameter. This work suggests that examining Bayesian strategies may lead to optimal or near-optimal control strategies for a much larger class of realistic dynamical models with unknown parameters.

math.OC↗

arXiv2017

Feature-rich bifurcations in a simple electronic circuit

A simple electronic circuit with a voltage controlled current source is investigated. The circuit exhibits rich dynamics upon varying the circuit elements such as L,C and R, and the control factor of the current source. Among several other interesting features, the circuit demonstrates two local bifurcations, namely, node to spiral and Hopf bifurcation, and a global homoclinic bifurcation. Phase-portraits corresponding to these bifurcations are presented and the implications of these bifurcations on system stability are discussed. In particular, the circuit parameters corresponding to the onset of Hopf bifurcation may be exploited to design an oscillator with stable frequency and amplitude. The circuit may be easily implemented with nonlinear resistive elements such as diodes or transistors in saturation and a gyrator block as the voltage controlled current source.

nlin.AO↗

arXiv2014

Investigation of A Collective Decision Making System of Different Neighbourhood-Size Based on Hyper-Geometric Distribution

The study of collective decision making system has become the central part of the Swarm- Intelligence Related research in recent years. The most challenging task of modelling a collec- tive decision making system is to develop the macroscopic stochastic equation from its microscopic model. In this report we have investigated the behaviour of a collective decision making system with specified microscopic rules that resemble the chemical reaction and used different group size. Then we ventured to derive a generalized analytical model of a collective-decision system using hyper-geometric distribution. Index Terms-swarm; collective decision making; noise; group size; hyper-geometric distribution

cs.AI↗

arXiv2014

Multi-Agent Shape Formation and Tracking Inspired from a Social Foraging Dynamics

Principle of Swarm Intelligence has recently found widespread application in formation control and automated tracking by the automated multi-agent system. This article proposes an elegant and effective method inspired by foraging dynamics to produce geometric-patterns by the search agents. Starting from a random initial orientation, it is investigated how the foraging dynamics can be modified to achieve convergence of the agents on the desired pattern with almost uniform density. Guided through the proposed dynamics, the agents can also track a moving point by continuously circulating around the point. An analytical treatment supported with computer simulation results is provided to better understand the convergence behaviour of the system.

cs.NE↗