Faculty Publications

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Author: search.filters.author.Madankar, S.R.Subject: search.filters.subject.Haar-wavelets

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    Error analysis of Haar wavelet-based Galerkin numerical method with application to various nonlinear optimal control problems
    (Taylor and Francis Ltd., 2024) Madankar, S.R.; Setia, A.; M, M.; Vatsala, A.S.
    First, this paper defines a general nonlinear optimal control problem with state/control constraints and its approximation problem as the Haar wavelet Galerkin optimal control problem (HWGOCP). Then, a Haar wavelet-based Galerkin numerical method has been developed, which converts it to a nonlinear optimization problem. We theoretically prove that a Haar wavelet feasible solution of HWGOCP will exist. We also show that the approximate solutions of HWGOCP are consistent and converge to the optimal solution of the problem. A variety of application problems have been considered, which include optimal control of tumour growth using Chemotherapy drugs, optimal control of infection via the SIS model using treatment, the Brachistochrone problem in mechanics, optimal control of mold using a fungicide, optimal control of pH value of a chemical reaction to determine the quality of a product, etc. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
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    Haar wavelet-based Galerkin method with its feasibility, consistency, and application to unmanned vehicle navigation around moving obstacles
    (Elsevier Ltd, 2025) Madankar, S.R.; Setia, A.; M, M.; Agarwal, R.P.
    In this study, we propose a novel Haar wavelet-based Galerkin method to solve nonlinear optimal control problems with applications to unmanned vehicle navigation. The method addresses the critical challenge of optimizing energy consumption while ensuring safe navigation in dynamic environments with multiple moving obstacles. By leveraging the computational efficiency and scalability of Haar wavelets, combined with the robustness of the Galerkin approach, we demonstrate convergence to the optimal solution under feasibility and consistency conditions. Comprehensive numerical simulations, including diverse and complex obstacle scenarios, validate the method's practicality. Through detailed trajectory, speed, and direction analyses, we highlight the approach's ability to adapt to real-world navigation challenges, making it a promising tool for autonomous system optimization. © 2025 European Control Association