01 Introduction

• Historical Introduction
• Introduction Control Design

02 Finite-dimensional linear control

• Finite-dimensional linear control

03 Basic Tools

• Gradient descent Methods
• An Algorithm for Density
• Background on Fourier Analysis
• Ingham’s inequality
• Adjoint Methods

04 Waves

• Waves, history and applications
• Finite difference schemes and numerical dispersion
• 1d-Waves: Propagation, Control & Numerics
• Waves in non smooth media
• Wave propagation and discontinuous Garlerkin approximations
• Observability of time-discrete conservative systems
• Control of semilinear waves

05 Waves on Networks

• Waves on Networks

06 Heat Processes

• Heat Kernels
• Sharp observability estimates for heat equations
• Cost of parabolic control

07 Heat Waves

• Wave and heat processes : Some connections
• Control & numerics: Heat and Waves

08 Hybrid systems of PDE

• Hybrid systems of PDE’s arising in fluid-structure interaction and multi-structures

09 Parameter dependence

• Averaged and Greedy Control

10 Control of some diffusive models

• Reaction-diffusion models: dynamics, control and numerics

11 Turnpike and Constraints

• PDE control: Constraints, short and long time horizons
• Controllability under constraints

12 Time Inversion

• Inverse time design
• Inverse design of one-dimensional Burgers equation
• Flow control in the presence of shocks
• Inverse-time design for Hamilton-Jacobi equations

13 Viscous Hamilton-Jacobi

• Control of viscous Hamilton-Jacobi equations

14 NonLocal

• Control of PDEs involving non-local terms

15 Hardy

• Hardy inequalities, heat kernels and wave propagation

16 Age structured

• Control of a Population Dynamics Model with Age Structuring and Diffusion

17 Kolmogorov equation

• Control of Kolmogorov model
• Decay Kolmogorov

18 Guidance

• Dynamics and control for multi-agent networked systems
• Model Predictive Control with Random Batch Methods for a Guiding Problem

19 Optimal Location sensors

• Optimal placement of sensors and actuators for waves

20 Decay Partially Dissipative Hyperbolic

• Decay of Partially Dissipative Hyperbolic Systems

21 Dispersive Numerics

• Dispersive Numerics

22 Homogenization, numerics and design

• Homogenization, numerics and design

23 Data Sciences

• Control in Deep Learning and Neural Networks

24 Free boundaries

• Control and asymptotics for some free boundaries

25 DyCon Toolbox

• Gradient Descent Methods on Optimal Control Problems

26 Data-Driven COVID Modeling

• Data-Driven COVID Modeling

27 Open problems

• Open problems in PDE control