arXiv subjects

Santosh Mohan Rajkumar

Publications and source records attributed to Santosh Mohan Rajkumar.

5 recordsLinked to original sources

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.

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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.

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arXiv2023

Modeling and Analysis of Multiple Electrostatic Actuators on the Response of Vibrotactile Haptic Device

In this research, modeling and analysis of a beam-type touchscreen interface with multiple actuators is considered. As thin beams, a mechanical model of a touch screen system is developed with embedded electrostatic actuators at different spatial locations. This discrete finite element-based model is developed to compute the analytical and numerical vibrotactile response due to multiple actuators excited with varying frequency and amplitude. The model is tested with spring-damper boundary conditions incorporating sinusoidal excitations in the human haptic range. An analytical solution is proposed to obtain the vibrotactile response of the touch surface for different frequencies of excitations, the number of actuators, actuator stiffness, and actuator positions. The effect of the mechanical properties of the touch surface on vibrotactile feedback provided to the user feedback is explored. Investigation of optimal location and number of actuators for a desired localized response, such as the magnitude of acceleration and variation in acceleration response for a desired zone on the interface, is carried out. It has been shown that a wide variety of localizable vibrotactile feedback can be generated on the touch surface using different frequencies of excitations, different actuator stiffness, number of actuators, and actuator positions. Having a mechanical model will facilitate simulation studies capable of incorporating more testing scenarios that may not be feasible to physically test.

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arXiv2019

Development of Embedded Speed Control System for DC Servo Motor using Wireless Communication

In this experiment, a closed-loop discrete time system for speed control of a permanent magnet DC motor with discrete PI controller is implemented in embedded platform. The design & analysis of the system is based on the mathematical model of the DC motor obtained by system identification technique. After that the closed loop system is distributed through a wireless network created by means of Bluetooth without any change in the discrete controller. The network connects the controller on one side with the sensor, actuator & the plant on the other side. Then the performance of the closed loop system is observed with the wireless network in two configurations : with point-to-point connection between two nodes and a network structure with two intermediate nodes among the controller side node & the plant side node. It has been observed that the performance degrades with only the PI controller a little bit in point to point configuration and the performance severely degrades in intermediate node configuration. To tackle this issue time delay is measured in the WNCS and then a digital smith predictor structure is implemented to obtain better performance. It has been observed that in point to point configuration the time delay remains almost constant and in intermediate node configuration the time delay is varying. Hence the digital smith predictor fails to perform reasonably in intermediate node configuration. An online time delay measurement & estimation procedure has been implemented and proposed in this research. We have implemented an adaptive digital smith predictor using the online time delay measurement and identification. The implemented smith predictor provides good results for both intermediate node and point to point connection. An stability analysis of the DC motor system with variation of delay has been discussed.

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arXiv2019

Online Delay Estimation and Adaptive Compensation in Wireless Networked System: An Embedded Control Design

In the present work, an embedded PI controller is designed for speed regulation of DC servomotor over a wireless network. The embedded controller integrates PI controller with a proposed time-delay estimator and an adaptive digital Smith predictor for its real time operation, which is the novelty of the work. The real time or rather online operation of the developed embedded controller over wireless network is possible mainly due to the contributions in terms of proposing a new empirical formula for time-delay estimation, viable approximation of time-delay, discretization scheme in developing the proposed adaptive Smith predictor. The proposed embedded design validates that the deterioration of control performance due to random network-induced delay are mitigated in real time. The embedded controller is designed and tested for a short-range of 100 meters, and wireless technology chosen is suitable for biomedical applications.

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