The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period. Inspired by, but distinct from, the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part of his maximum principle. Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to optimize the Hamiltonian. (Wikipedia).
Everything You Need to Know About Control Theory
Control theory is a mathematical framework that gives us the tools to develop autonomous systems. Walk through all the different aspects of control theory that you need to know. Some of the concepts that are covered include: - The difference between open-loop and closed-loop control - How
From playlist Control Systems in Practice
Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.
From playlist Physics ONE
Ludovic Rifford : Geometric control and dynamics
Abstract: The geometric control theory is concerned with the study of control systems in finite dimension, that is dynamical systems on which one can act by a control. After a brief introduction to controllability properties of control systems, we will see how basic techniques from control
From playlist Dynamical Systems and Ordinary Differential Equations
Hamiltonian Mechanics in 10 Minutes
In this video I go over the basics of Hamiltonian mechanics. It is the first video of an upcoming series on a full semester university level Hamiltonian mechanics series. Corrections -4:33 the lagrangian should have a minus sign between the first two terms, not a plus.
From playlist Summer of Math Exposition 2 videos
Bernhard Maschke : Hamiltonian control systems for open Irreversible Thermodynamic systems
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 30, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Hamiltonian Simulation and Universal Quantum (...) - T. Cubitt - Main Conference - CEB T3 2017
Toby Cubitt (UCL) / 14.12.2017 Title: Hamiltonian Simulation and Universal Quantum Hamiltonians Abstract: Physical (or "analogue") Hamiltonian simulation involves engineering a Hamiltonian of interest in the laboratory, and studying its properties experimentally (somewhat analogous to b
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Graph Theory: Hamiltonian Graphs
This video is about Hamiltonian graphs and some of their basic properties.
From playlist Basics: Graph Theory
Derivation of Hamilton's Equations of Motion | Classical Mechanics
Hamilton’s equations of motion describe how a physical system will evolve over time if you know about the Hamiltonian of this system. 00:00 Introduction 00:12 Prerequisites 01:01 Derivation 01:47 Comparing Coefficients 02:27 Example If you want to read more about the Lagrangian form
From playlist Classical Mechanics
Hamiltonian Cycles, Graphs, and Paths | Hamilton Cycles, Graph Theory
What are Hamiltonian cycles, graphs, and paths? Also sometimes called Hamilton cycles, Hamilton graphs, and Hamilton paths, we’ll be going over all of these topics in today’s video graph theory lesson! A Hamilton cycle in a graph G is a cycle containing all vertices of G. A Hamilton path
From playlist Graph Theory
Juan Manuel Pérez Pardo: Controllability of infinite dimensional quantum systems based on Quantum...
Recorded during the meeting "Mathematical Aspects of Physics with Non-Self-Adjoint Operators: 10 Years After" the February 02, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldw
From playlist Mathematical Physics
Learning Optimal Control with Stochastic Models of Hamiltonian Dynamics for Shape & Function Optim.
Speaker: Chandrajit Bajaj (7/25/22) Abstract: Shape and Function Optimization can be achieved through Optimal Control over infinite-dimensional search space. All optimal control problems can be solved by first applying the Pontryagin maximum principle, and then computing a solution to the
From playlist Applied Geometry for Data Sciences 2022
Quantum thermodynamics of complex systems - A. del Campo - PRACQSYS 2018 - CEB T2 2018
Adolfo del Campo (Department of Physics, University of Massachusetts, Boston, USA) / 06.07.2018 Quantum thermodynamics of complex systems A universal relation is established between the quantum work probability distribution of an isolated driven quantum system and the Loschmidt echo dyna
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
Alpár Mészáros: "Global well-posedness of master equations for deterministic displacement convex..."
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "Global well-posedness of master equations for deterministic displacement convex potential mean field games" Alpár Mészáros - Durham University Abstract: In this talk we investigate the question of
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Quantum Metrology II by Girish Agarwal
Dates: Thursday 03 Jan, 2013 - Saturday 05 Jan, 2013 Venue: ICTS-TIFR, IISc Campus, Bangalore The school aims to provide students and researchers an introduction to the field of quantum information, computation and communication. Topics that will be covered include introduction to quantu
From playlist Mini Winter School on Quantum Information and Computation
Michael Jordan: "Optimization & Dynamical Systems: Variational, Hamiltonian, & Symplectic Perspe..."
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop II: PDE and Inverse Problem Methods in Machine Learning "Optimization and Dynamical Systems: Variational, Hamiltonian, and Symplectic Perspectives" Michael Jordan - University of California, Berkeley (UC Berkeley) Abstract: We analyze t
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Dong An - Improved complexity estimation for Hamiltonian simulation with Trotter formula
Recorded 25 January 2022. Dong An of the University of Maryland presents "Improved complexity estimation for Hamiltonian simulation with Trotter formula" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Trotter formula is one of the most widely used methods for time-dependent
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
Some questions around quasi-periodic dynamics – Bassam Fayad & Raphaël Krikorian – ICM2018
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From playlist Dynamical Systems and ODE
Vivien Kendon: How to compute using quantum walks
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since
From playlist Numerical Analysis and Scientific Computing
Efficient reservoir engineering of complex bosonic states - A. Clerk - PRACQSYS 2018 - CEB T2 2018
Aashish Clerk (Institute for Molecular Engineering, University of Chicago, Chicago, USA) / 05.07.2018 Efficient reservoir engineering of complex bosonic states The general strategy of engineering dissipation to stabilize non-trivial quantum states has been implemented with great success
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
Let's Learn Physics: Chaos in Phase Space
We have seen how Hamiltonian mechanics can be used to solve for the dynamics of physical systems. It turns out that there is quite a bit of hidden power in this formalism in that we can prove some fairly general statements about physics as a whole. We will see one of these results, known a
From playlist Let's Learn (Classical) Physics: ZAP Physics Livestreams