arXiv subjects

S. Janardhanan

Publications and source records attributed to S. Janardhanan.

8 recordsLinked to original sources

arXiv2026

Comparing Point and Interval Methods for Equilibrium Computation under Parametric Uncertainty

Equilibrium points define operating conditions for nonlinear dynamical and control systems. Their existence, multiplicity, and stability under parametric uncertainty determine feasible operating regimes and the validity of robustness claims. With parameters constrained to a bounded set, one can (i) compute equilibria at sampled parameter values, (ii) trace equilibria along a prescribed path in parameter space, or (iii) identify states in a given operating domain that are equilibria for at least one admissible parameter realization. We compare standard pointwise workflows-direct simulation, numerical continuation, residual minimization, and a multistart Newton-Raphson method-with validated interval-analysis-based workflows. The latter (a) provide formal certificates of exclusion, existence, and uniqueness of equilibria for fixed parameters and, under parametric inclusion conditions, uniformly over entire parameter boxes, and (b) construct rigorous outer enclosures in state space that provably contain all equilibria associated with the full admissible parameter set. Biomolecular circuit models governed by nonlinear ODEs serve as a representative application domain. We benchmark three canonical architectures across four levels of parameter uncertainty, including a genetic toggle switch near a symmetry-breaking bifurcation. Sampling- and slice-based approaches can miss or underrepresent multistability, whereas interval-based outer enclosures yield mathematically rigorous bounds on the equilibrium set induced by parametric uncertainty.

eess.SY↗

arXiv2026

Certified Detection of Bifurcation Candidates in Uncertain Nonlinear Systems using Interval Analysis

Qualitative transitions in nonlinear dynamical systems (e.g., loss of stability, onset of oscillations, emergence of multistability) delimit operating regimes and can arise as implicit constraints in robust analysis and design under parametric uncertainty. When parameters are inferred from data, admissible values are naturally represented as uncertainty sets, motivating certified tests for the presence or absence of regime-transition candidates. We propose a validated interval workflow that encodes saddle-node and Hopf candidate conditions as square augmented algebraic systems and applies the Krawczyk operator to certify, over a prescribed state-parameter box, either (i) existence and local uniqueness of a candidate solution or (ii) certified absence. Numerical experiments on uncertain synthetic gene-network ODE models yield locally certified saddle-node candidate enclosures on a two-parameter slice for a bistable circuit and certified Hopf candidate enclosures for a three-state oscillator using a Routh-Hurwitz specialization. The resulting certificates are intended to support regime-aware analysis and design under bounded uncertainty by complementing non-validated, pointwise baselines (e.g., Newton method solves at discrete parameter values) and sampling-based workflows with rigorous presence/absence guarantees on user-specified parameter slices.

eess.SY↗

arXiv2026

Observer-Based Fixed-Time Nested Sliding-Mode Control for Tip-Position Regulation of a Single-Link Flexible Manipulator

This paper presents a novel position control strategy for a single-link flexible manipulator, tailored for applications where precise position must be achieved within strict time constraints. To accomplish this objective, firstly, a nested non-singular terminal sliding mode controller is designed for the system, enabling precise and robust control. Furthermore, a fixed-time sliding mode observer is designed to estimate unmeasured system states accurately in a fixed time, thereby enabling closed-loop control implementation. A stability analysis is presented to guarantee the robustness and efficacy of the proposed composite control algorithm. The effectiveness of the proposed fixed-time controller is demonstrated through numerical simulation on accuracy, stability, and convergence speed. The proposed controller's performance is also compared with that of other state-of-the-art control schemes. The proposed controller is further validated through experiments conducted on a real hardware setup.

eess.SY↗

arXiv2026

Computational Complexity Analysis of Interval Methods in Solving Uncertain Nonlinear Systems

This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its adoption is often limited by computational cost in high dimensions. We develop an algorithm-level worst-case framework that makes explicit the dependence on the problem dimension $n$, the initial search region size $\mathrm{Vol}(X_0)$, the target tolerance $\varepsilon$, and the costs of validated primitives (inclusion-function evaluation, Jacobian evaluation, and interval linear algebra). Within this framework, we derive worst-case time and space bounds for interval bisection, subdivision$+$filter, interval constraint propagation, interval Newton, and interval Krawczyk, and identify dominant cost drivers. We also show that the computation of the determinant and inverse of interval matrices via naive Laplace expansion exhibits factorial growth with increasing matrix dimension, motivating specialized interval linear algebra. We complement the worst-case bounds with computational results on two application-motivated biochemical steady-state models (a Hill-type regulatory network and an enzyme-saturation-based winner-take-all circuit) in dimensions $n\in\{2,5,10\}$, including instances that process millions of boxes. The resulting analysis and experiments support the practical design of validated solvers for uncertainty-aware steady-state screening tasks such as robust operating-point certification and multistability assessment.

cs.DS↗

arXiv2025

Elastic anisotropy and Surface Acoustic Wave propagation in CoFeB/Au multilayers: influence of thickness and light penetration depth

Surface acoustic waves in multilayered nanostructures represent a critical frontier in understanding material behavior at the nanoscale, with profound implications for emerging acoustic and spintronic technologies. In this study, we investigate the influence of the magnetic layer thickness on the propagation of surface acoustic waves in CoFeB based multilayers. Two approaches to effective medium modelling are considered: one treating the entire multilayer as a homogeneous medium and another focusing on the region affected by light penetration. The elastic properties of the system are analyzed using Brillouin light scattering and numerical modelling, with a particular emphasis on the anisotropy of Young s modulus and its dependence on CoFeB thickness. The results reveal a significant variation in surface acoustic wave velocity and elastic anisotropy as a function of the multilayer configuration, highlighting the role of the penetration depth in effective medium approximations. These findings provide valuable insights into the tunability of acoustic and spin-wave frequencies through structural modifications, which is crucial for the development of high-performance resonators, surface acoustic wave filters, and spin-wave-based information processing devices.

cond-mat.mtrl-sci↗

arXiv2023

Approximate Dynamic Programming based Model Predictive Control of Nonlinear systems

This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the proposed approach, the value function is approximated as a quadratic function for which the parametric matrix is computed using a switched system approximate of the nonlinear system. The approach is modified further using a multi-stage scheme to improve the control accuracy and an extension to incorporate state constraints. The MPC scheme is validated experimentally on a multi-tank system which is modeled as a third-order nonlinear system. The experimental results show the proposed MPC scheme results in significantly lesser online computation compared to the Nonlinear MPC scheme.

eess.SY↗

arXiv2023

Position Control of Single Link Flexible Manipulator: A Functional Observer Based Sliding Mode Approach

This paper proposes a functional observer-based sliding mode control technique for position control of a single-link flexible manipulator. The proposed method considers the unmodelled system dynamics as uncertainty and aims to achieve accurate position control. The functional observer is used to directly estimate the sliding mode control design components and a sliding mode controller to generate the control signal, which guarantees the system's robustness and stability. The proposed control scheme is validated using numerical simulations.

eess.SY↗

arXiv2022

Comparative Analysis and Calibration of Low Cost Resistive and Capacitive Soil Moisture Sensor

Soil moisture is an essential parameter in agriculture. It determines several environmental and agricultural activities such as climate change, drought prediction, irrigation, etc. Smart irrigation management requires continuous soil moisture monitoring to reduce unnecessary water usage. In recent times, the use of low-cost sensors is becoming popular among farmers for soil moisture monitoring. In this paper, a comparison of low-cost resistive and capacitive soil moisture sensors is demonstrated in two ways. One way is the calibration of the sensors in gravimetric and volumetric water content, and the other is the sensors' response analysis when different quantities of water are added to the same amount of soil. The analysis shown in this work is essential before choosing cost-effective sensors for any soil moisture monitoring platform.

cs.NI↗