Partial Differential Equations

Estimation Problems for Partial and Fractional Differential Equations - Spring 2019

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B9 L2 H1

We will present some new methods for source and parameters estimation for partial and fractional differential equations and illustrate the results with some simulations and real applications.

Part 1: Boundary Control of Continuum Problems

Professor Mamadou L. Diagne, Rensselaer Polytechnic Institute

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B9 L3 R3131

Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. Generally, key aspects of these processes operating mode are driven by convection phenomena with a spatiotemporal dynamic that cannot be approximated straightforwardly using a finite-dimensional representation. This course will explore the boundary control of several class of PDEs via the well-known backstepping method.

Part 2: Boundary Control of Continuum Problems

Professor Mamadou L. Diagne, Rensselaer Polytechnic Institute

-

B9 L3 R3131

Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. Generally, key aspects of these processes operating mode are driven by convection phenomena with a spatiotemporal dynamic that cannot be approximated straightforwardly using a finite-dimensional representation. This course will explore the boundary control of several class of PDEs via the well-known backstepping method.

Part 3: Boundary Control of Continuum Problems

Professor Mamadou L. Diagne, Rensselaer Polytechnic Institute

-

B9 L3 R3131

Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. Generally, key aspects of these processes operating mode are driven by convection phenomena with a spatiotemporal dynamic that cannot be approximated straightforwardly using a finite-dimensional representation. This course will explore the boundary control of several class of PDEs via the well-known backstepping method.

Estimation Problems for Partial and Fractional Differential Equations - Autumn 2019

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B9 L2 H1 R2322

I will present an overview of our activities around estimation problems for partial and fractional differential equations. I will present the methods and the algorithms we develop for the state, source and parameters estimation and illustrate the results with some simulations and real applications.

Part 1B | PDE Backstepping Boundary Control of Parabolic PDEs

Prof. Mamadou Diagne, Rensselaer Polytechnic Institute

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KAUST

PDE Backstepping Boundary Control of Parabolic PDEs Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. This course will explore the boundary control of a class of parabolic PDE via the well-known backstepping method.

Part 1A | PDE Backstepping Boundary Control of Parabolic PDEs

Prof. Mamadou Diagne, Rensselaer Polytechnic Institute

-

KAUST

Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. This course will explore the boundary control of a class of parabolic PDE via the well-known backstepping method.

Part 2A | PDE Backstepping Boundary Control of Parabolic PDEs

Prof. Mamadou Diagne, Rensselaer Polytechnic Institute

-

KAUST

Abstract Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. Generally, key aspects of these processes operating mode are driven by convection phenomena with a spatiotemporal dynamic that cannot be approximated straightforwardly using a finite

Part 2B | PDE Backstepping Boundary Control of Parabolic PDEs

Prof. Mamadou Diagne, Rensselaer Polytechnic Institute

-

KAUST

Partial Differential Equations (PDEs) are often used to model various complex physical systems. Representative engineering applications such as heat exchangers, transmission lines, oil wells, road traffic, multiphase flow, melting phenomena, supply chains, collective dynamics, and even chemical processes governing the state of charge of Lithium-ion battery, extrusion, reactors to mention a few. This course will explore the boundary control of a class of parabolic PDE via the well-known backstepping method.