13 papers
Policy iteration for Hamilton-Jacobi-Isaacs equations with control constraints and comparison with Hamilton-Jacobi-Bellman equations
Sudeep Kundu, Karl Kunisch
Convergence of the bilevel policy iteration algorithm for the value function, satisfying the Hamilton-Jacobi-Isaacs (HJI) equation, is analyzed in the presence of control constrain…
Global stabilization and finite element analysis of the viscous Burgers' equation with memory subject to Neumann boundary feedback control
Shishu Pal Singh, Sudeep Kundu
This paper presents a global stabilization result of the viscous Burgers' equation with the memory term by applying Neumann boundary feedback control laws. We construct suitable fe…
Finite element theta schemes for the viscous Burgers' equation with nonlinear Neumann boundary feedback control
Shishu Pal Singh, Sudeep Kundu
In this article, we develop a fully discrete numerical scheme for the one-dimensional (1D) and two-dimensional (2D) viscous Burgers equations with nonlinear Neumann boundary feedba…
Finite Element Analysis for the Chafee-Infante Equation Using Distributed Feedback Control
Shishu Pal Singh, Sudeep Kundu
In this paper, we propose a \( C^0 \)-conforming finite element method for the Chafee-Infante equation with a finite-parameter feedback control. We establish error analysis for bot…
Finite Difference Method for Global Stabilization of the Viscous Burgers' Equation with Nonlinear Neumann Boundary Feedback Control
Shishu Pal Singh, Sudeep Kundu
This article focuses on a nonlinear Neumann boundary feedback control formulation for the viscous Burgers' equation and develops a class of finite difference schemes to achieve glo…
Penalty-Based Feedback Control and Finite Element Analysis for the Stabilization of Nonlinear Reaction-Diffusion Equations
Sudeep Kundu, Shishu pal Singh
In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabiliz…
Policy iteration for Hamilton-Jacobi-Bellman equations with control constraints
Sudeep Kundu, Karl Kunisch
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analys…
Global Stabilization of 2D Forced Viscous Burgers' Equation Around Nonconstant Steady State Solution by Nonlinear Neumann Boundary Feedback Control:Theory and Finite Element Analysis
Sudeep Kundu, Amiya Kumar Pani
Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global sta…
Robust feedback control of nonlinear PDEs by numerical approximation of high-dimensional Hamilton-Jacobi-Isaacs equations
Dante Kalise, Sudeep Kundu, Karl Kunisch
We propose an approach for the synthesis of robust and optimal feedback controllers for nonlinear PDEs. Our approach considers the approximation of infinite-dimensional control sys…
Global Stabilization of BBM-Burgers' Type Equations by Nonlinear Boundary Feedback Control Laws: Theory and Finite Element Error Analysis
Sudeep Kundu, Amiya Kumar Pani
In this article, global stabilization results for the Benjamin-Bona-Mahony-Burgers' (BBM-B) type equations are obtained using nonlinear Neumann boundary feedback control laws. Base…
Global Stabilization of Two Dimensional Viscous Burgers' Equation by Nonlinear Neumann Boundary Feedback Control and its Finite Element Analysis
Sudeep Kundu, Amiya Kumar Pani
In this article, global stabilization results for the two dimensional (2D) viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solutio…
Stabilization of Kelvin-Voigt viscoelastic Fuid Fow model
Sudeep Kundu, Amiya K. Pani
In this article, stabilization result for the viscoelastic fluid flow problem governed by Kelvin-Voigt model, that is, convergence of the unsteady solution to a steady state soluti…
On Kirchhoff's Model of Parabolic Type
Sudeep Kundu, Amiya K. Pani, Morrakot Khebchareon
In this paper, existence of a strong global solution for all finite time is derived for the Kirchhoff's model of parabolic type. Based on exponential weight function, some new regu…