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Function used in optimal control theory
Inspired by—but distinct from—the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part
Hamiltonian_(control_theory)
Topics referred to by the same term
Molecular Hamiltonian, the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule Hamiltonian (control theory), a function
Hamiltonian
Mathematical way of attaining a desired output from a dynamic system
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective
Optimal_control
Mathematical approach to quantum physics
perturbation theory, the perturbation Hamiltonian is static (i.e., possesses no time dependence). Time-independent perturbation theory was presented
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Formulation of classical mechanics using momenta
(generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close
Hamiltonian_mechanics
equation in control theory Hamilton–Jacobi–Einstein equation In both mathematics and physics (specifically mathematical physics): the term Hamiltonian refers
List of things named after William Rowan Hamilton
List_of_things_named_after_William_Rowan_Hamilton
Binary feedback controller
In control theory, a bang–bang controller (hysteresis, 2 step or on–off controller), is a feedback controller that switches abruptly between two states
Bang–bang_control
Probabilistic optimal control
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or
Stochastic_control
Change of state over time, especially in physics
of time Time translation symmetry Hamiltonian system Propagator Time evolution operator Hamiltonian (control theory) Lecture 1 | Quantum Entanglements
Time_evolution
Methods of mathematical approximation
Møller–Plesset perturbation theory uses the difference between the Hartree–Fock Hamiltonian and the exact non-relativistic Hamiltonian as the perturbation. The
Perturbation_theory
Principle in optimal control theory for best way to change state in a dynamical system
milestone in optimal control theory, the significance of the maximum principle lies in the fact that maximizing the Hamiltonian is much easier than the
Pontryagin's maximum principle
Pontryagin's_maximum_principle
Theory of quantum gravity merging quantum mechanics and general relativity
defined an anomaly-free Hamiltonian operator and showed the existence of a mathematically consistent background-independent theory. The covariant, or "spin
Loop_quantum_gravity
Key constraint in some theories admitting Hamiltonian formulations
The Hamiltonian constraint arises from any theory that admits a Hamiltonian formulation and is reparametrisation-invariant. The Hamiltonian constraint
Hamiltonian_constraint
Overview of mechanics based on the least action principle
and corresponding generalized velocities in configuration space) and Hamiltonian mechanics (using coordinates and corresponding momenta in phase space)
Analytical_mechanics
the "Lagrange multipliers" in Pontryagin's minimum principle Hamiltonian (control theory) — minimum principle says that this function should be minimized
List of numerical analysis topics
List_of_numerical_analysis_topics
Field of mathematics and science based on non-linear systems and initial conditions
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical
Chaos_theory
Field theory involving topological effects in physics
the Seiberg–Witten gauge theory which reduces SU(2) to U(1) in N = 2, d = 4 gauge theory. The Hamiltonian version of the theory has been developed by Andreas
Topological quantum field theory
Topological_quantum_field_theory
Proving validity without revealing other data
she knows a Hamiltonian cycle in H, then she translates her Hamiltonian cycle in G onto H and only uncovers the edges on the Hamiltonian cycle. That is
Zero-knowledge_proof
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Theory of subatomic structure
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called
String_theory
Physical theory with fields invariant under the action of local "gauge" Lie groups
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local
Gauge_theory
View of quantum mechanics
time-independent Hamiltonian HS, where H0,S is the free Hamiltonian, Duck, Ian; Sudarshan, E.C.G. (1998). "Chapter 6: Dirac's Invention of Quantum Field Theory". Pauli
Interaction_picture
systems and control theory at University of Groningen. He is most noted for his contributions to nonlinear control and port-Hamiltonian systems theory. Arjan
Arjan_van_der_Schaft
Form of quantum computing
eternal control is used to apply operations on a register of qubits, Hamiltonian quantum computers operate without external control. Hamiltonian quantum
Hamiltonian quantum computation
Hamiltonian_quantum_computation
Theory. 69 (1): 46–76. CiteSeerX 10.1.1.159.7029. doi:10.1002/jgt.20565. MR 2864622. S2CID 9120720.. Bailey, R. F.; Stevens, B. (2010). "Hamiltonian decompositions
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Principle of quantum mechanics
superposition of the eigenstates of an Hermitian operator, like the Hamiltonian, because the eigenstates form a complete basis: | α ⟩ = ∑ n c n | n ⟩
Quantum_superposition
Physical theory describing classical fields
field theory Classical unified field theories Variational methods in general relativity Higgs field (classical) Lagrangian (field theory) Hamiltonian field
Classical_field_theory
Description of large objects' physics
(generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close
Classical_mechanics
Optimality condition in optimal control theory
optimal control by taking the maximizer (or minimizer) of the Hamiltonian involved in the HJB equation. The equation is a result of the theory of dynamic
Hamilton–Jacobi–Bellman equation
Hamilton–Jacobi–Bellman_equation
Lowest possible energy of a quantum system or field
theory. The new Hamiltonian is said to be normally ordered (or Wick ordered) and is denoted by a double-dot symbol. The normally ordered Hamiltonian is
Zero-point_energy
Unitary transformation in quantum mechanics
perturbation theory. The Schrieffer–Wolff transformation is often used to project out the high energy excitations of a given quantum many-body Hamiltonian in order
Schrieffer–Wolff transformation
Schrieffer–Wolff_transformation
Matrix-valued random variable
the nuclear Hamiltonian could be modeled as a random matrix. For larger atoms, the distribution of the energy eigenvalues of the Hamiltonian could be computed
Random_matrix
Techniques to maintain quantum coherence
the controls if the control operators and the unperturbed Hamiltonian generate the Lie algebra of all Hermitian operators. Complete controllability implies
Coherent_control
Harmonic functions as solutions to Laplace's equation
mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" dates from 19th-century physics when it
Potential_theory
Quantum field theory enjoying conformal symmetry
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional
Conformal_field_theory
Mathematical model of the time dependence of a point in space
preserving dynamical systems (e.g. hamiltonian systems). It is also possible to draw an analogy between group representation theory (such as irreducible representations)
Dynamical_system
Category of theories
branches of theory sometimes included in classical physics are: Classical mechanics Newton's laws of motion Classical Lagrangian and Hamiltonian formalisms
Classical_physics
Type of approximation to an underlying physical theory
effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical
Effective_field_theory
Branch of applied mathematics
mechanics forms a separate field, which includes the theory of phase transitions. It relies upon the Hamiltonian mechanics (or its quantum version) and it is
Mathematical_physics
Notation for conserved quantities in physics and chemistry
of observables. When the corresponding observable commutes with the Hamiltonian of the system, the quantum number is said to be "good", and acts as a
Quantum_number
Formulation of quantum mechanics
form of the Hamiltonian. The new quantization rule was assumed to be universally true, even though the derivation from the old quantum theory required semiclassical
Matrix_mechanics
Study of abstract machines and automata
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical
Automata_theory
Study of the properties of codes and their fitness
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography
Coding_theory
Theory of getting acceptably close inexact mathematical calculations
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing
Approximation_theory
American mathematician
Michigan. He is known for his contributions to Hamiltonian and Lagrangian mechanics, geometric control theory, integrable systems, and nonholonomic mechanics
Anthony_M._Bloch
Concept in theoretical physics
\{J_{k}\}} . This function may be a partition function, an action, a Hamiltonian, so long as it contains the whole description of the physics of the system
Renormalization_group
Branch of ordinary differential equations
The topology of the driven system is analyzed by studying the Floquet Hamiltonian. Chicone 1999. Montagnier, Paige & Spiteri 2003, pp. 251–262. Magnus
Floquet_theory
Physical quantities taking values at each point in space and time
Conformal field theory Covariant Hamiltonian field theory Field strength Lagrangian and Eulerian specification of a field Scalar field theory Velocity field
Field_(physics)
Interpretation of quantum mechanics
ISBN 978-0-521-48543-2. Holland, P. (2001). "Hamiltonian theory of wave and particle in quantum mechanics II: Hamilton-Jacobi theory and particle back-reaction" (PDF)
De_Broglie–Bohm_theory
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
However, if we merely find quantum solutions of a Hamiltonian which is not approachable by perturbation theory, we may learn a great deal about quantum solutions
Quantum_chaos
Relativistic interaction in quantum physics
{\displaystyle \gamma } is the Lorentz factor of the moving particle. The Hamiltonian producing the spin precession Ω T {\displaystyle {\boldsymbol {\Omega
Spin–orbit_interaction
Model of interacting spinless bosons on a lattice
corresponding Hamiltonian is called the Bose–Fermi–Hubbard Hamiltonian. The physics of this model is given by the Bose–Hubbard Hamiltonian: H = − t ∑ ⟨
Bose–Hubbard_model
Converting classical mechanics to quantum mechanics
called | ν ⟩ {\displaystyle |\nu \rangle } and is an eigenvector of the Hamiltonian operator. One can obtain a state function representation of the state
First_quantization
Branch of applied probability theory
Decision theory or the theory of rational choice is a branch of probability, economics, and analytic philosophy that uses expected utility and probability
Decision_theory
Constraint in loop quantum gravity
such as time-evolutions of fields are controlled by the Hamiltonian constraint. The identity of the Hamiltonian constraint is a major open question in
Hamiltonian_constraint_of_LQG
Four-dimensional number system
robotics, nuclear magnetic resonance image sampling, control theory, signal processing, attitude control, physics, bioinformatics, molecular dynamics, computer
Quaternion
Method in ab initio Quantum Chemistry
The MP perturbation theory is a special case of RS perturbation theory. In RS theory one considers an unperturbed Hamiltonian operator H ^ 0 {\displaystyle
Møller–Plesset perturbation theory
Møller–Plesset_perturbation_theory
Force resulting from the quantisation of a field
In quantum field theory, the Casimir effect (or Casimir force) is a physical force acting on the macroscopic boundaries of a confined space which arises
Casimir_effect
Relativistic quantum mechanical wave equation
introduction of two terms for spin and relativity into the hydrogen Hamiltonian, allowing them to derive the first-order approximation of the Sommerfeld
Dirac_equation
Symmetry between bosons and fermions
can imagine a "bosonic Hamiltonian", whose eigenstates are the various bosons of our theory. The SUSY partner of this Hamiltonian would be "fermionic",
Supersymmetry
Control technique for improving qubit coherence in quantum computing
described using Average Hamiltonian Theory (AHT). The goal of AHT is to describe the net evolution of a system under a rapid, periodic control sequence with a
Dynamical_decoupling
Fundamental theorem in condensed matter physics
the effective potential but it shall commute with the Hamiltonian. Proof with character theory All translations are unitary and abelian. Translations
Bloch's_theorem
Simplified model in condensed matter physics
contribution of the second term, the Hamiltonian resolves to the tight binding formula from regular band theory. Including the second term yields a realistic
Hubbard_model
Inherent difficulty of computational problems
algorithm is known, such as the Boolean satisfiability problem, the Hamiltonian path problem and the vertex cover problem. Since deterministic Turing
Computational complexity theory
Computational_complexity_theory
Study of the relations between thermodynamics and quantum mechanics
where it is tempting to study Markovian dynamics with an arbitrary control Hamiltonian. Erroneous derivations of the quantum master equation can easily
Quantum_thermodynamics
Approximation method in quantum physics
terms to be replaced with quadratic terms, obtaining exactly solvable Hamiltonians. Especially in the older literature, the Hartree–Fock method is also
Hartree–Fock_method
Oscillating dynamical system with nonlinear damping
indeed is a Hopf bifurcation. One can also write a time-independent Hamiltonian formalism for the Van der Pol oscillator by augmenting it to a four-dimensional
Van_der_Pol_oscillator
American physicist
providing a controlled derivation of the superconducting instability. With his former student Ganpathy Murthy, Shankar developed a Hamiltonian theory of the
Ramamurti_Shankar
Interaction of a quantum system with a classical observer
freedom is the quantum harmonic oscillator. This system is defined by the Hamiltonian H = p 2 2 m + 1 2 m ω 2 x 2 , {\displaystyle {H}={\frac {{p}^{2}}{2m}}+{\frac
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Book by Leonard Susskind
physics concepts, such as principle of least action, Lagrangian mechanics, Hamiltonian mechanics, Poisson brackets, and electromagnetism. It is the first book
The_Theoretical_Minimum
Statistical mechanics model for phase transitions
In statistical mechanics, Lee–Yang theory, sometimes also known as Yang–Lee theory, is a scientific theory which seeks to describe phase transitions in
Lee–Yang_theory
Method for describing the electronic structure of molecules using quantum mechanics
(wave functions) of the self-consistent field Hamiltonian and it was at this point that molecular orbital theory became fully rigorous and consistent. This
Molecular_orbital_theory
Quantum mechanical system
is described by the Lieb–Liniger model. In the continuous limit the Hamiltonian is given in second quantization H ^ = ℏ 2 2 m ∫ d 3 r ∇ ϕ ^ † ( r ) ⋅
Weakly_interacting_Bose_gas
system analysis and control theory. The eminent researchers (born after 1920) include the winners of at least one award of the IEEE Control Systems Award,
List of people in systems and control
List_of_people_in_systems_and_control
Necessary condition for optimality associated with dynamic programming
to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory; though the basic
Bellman_equation
Theory in theoretical physics
In theoretical physics, topological string theory is a version of string theory. Topological string theory appeared in papers by theoretical physicists
Topological_string_theory
sequence – Fourier series – Frequency domain – Frequency spectrum – Hamiltonian (quantum mechanics) – Harmonic oscillator – Huygens–Fresnel principle
List_of_cycles
Loss of quantum coherence
{H}}_{B}} are the system and bath Hamiltonians respectively, H ^ I {\displaystyle {\hat {H}}_{I}} is the interaction Hamiltonian between the system and bath
Quantum_decoherence
Concept in quantum mechanics
enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. In simpler terms, a quantum mechanical system subjected to
Adiabatic_theorem
Trapped-ion quantum gate
in the Lamb-Dicke regime, and it produces an Ising-like interaction Hamiltonian using a bichromatic laser field. Following Mølmer and Sørensen's 1999
Mølmer–Sørensen_gate
French mathematician (born 1944)
lemma in optimization theory. He has contributed to the periodic solutions of Hamiltonian systems and particularly to the theory of Kreĭn indices for linear
Ivar_Ekeland
Collection of random variables
neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly
Stochastic_process
Type of quantum computer built out of Rydberg atoms
|01\rangle } ), then the Hamiltonian is given by H i {\displaystyle H_{i}} . This Hamiltonian is the standard two-level Rabi hamiltonian. It characterizes the
Neutral_atom_quantum_computer
Model in quantum optics
consists of the free field Hamiltonian, the atomic excitation Hamiltonian, and the Jaynes–Cummings interaction Hamiltonian: H ^ field = ℏ ω c a ^ † a
Jaynes–Cummings_model
Formulation of classical mechanics
A closely related formulation of classical mechanics is Hamiltonian mechanics. The Hamiltonian is defined by H = ∑ i = 1 n q ˙ i ∂ L ∂ q ˙ i − L {\displaystyle
Lagrangian_mechanics
difficulty in applying Pontryagin's principle arises when the Hamiltonian depends linearly on the control u {\displaystyle u} , i.e., is of the form: H ( u ) =
Singular_control
Field of economics and game theory
Mechanism design (sometimes implementation theory or institution design) is a branch of economics and game theory. It studies how to construct rules—called
Mechanism_design
NP-hard problem in combinatorial optimization
road), find a Hamiltonian cycle with the least weight. This is more general than the Hamiltonian path problem, which only asks if a Hamiltonian path (or cycle)
Travelling_salesman_problem
Quantum mechanical state change
to solve the time evolution of the wavefunction with an appropriate Hamiltonian. To solve for the transition amplitude, one needs to average over (integrate
Spontaneous_emission
Matrix representing the effect of scattering on a physical system
In the Hamiltonian approach to quantum field theory, the S-matrix may be calculated as a time-ordered exponential of the integrated Hamiltonian in the
S-matrix
Study of vector bundles, principal bundles, and fibre bundles
concept of a gauge theory in physics, which is a field theory that admits gauge symmetry. In mathematics theory means a mathematical theory, encapsulating
Gauge_theory_(mathematics)
Conjecture on zeros of the zeta function
Hamiltonian whose eigenvalues are the square of the imaginary part of the Riemann zeros, and also that the functional determinant of this Hamiltonian
Riemann_hypothesis
Class of theories in quantum mechanics
hypothetical superdeterministic theory "would be about as plausible, and appealing, as belief in ubiquitous alien mind-control". The first superdeterministic
Superdeterminism
Formulation of classical mechanics
formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is a formulation of mechanics
Hamilton–Jacobi_equation
Any analogy between electrical and mechanical systems, used for modelling
{p}}}}} Further, the time derivatives of the Hamiltonian variables are the power conjugate variables. The Hamiltonian variables in the electrical domain are
Mechanical–electrical analogies
Mechanical–electrical_analogies
Symmetry of spatially mirrored systems
operation i because of the effect of the nuclear hyperfine Hamiltonian. The nuclear hyperfine Hamiltonian can mix the rotational levels of g and u vibronic states
Parity_(physics)
Theory of stochastic partial differential equations
be removed by additional conditions. In quantum theory, the condition is Hermiticity of Hamiltonian, which is satisfied by the Weyl symmetrization rule
Supersymmetric theory of stochastic dynamics
Supersymmetric_theory_of_stochastic_dynamics
Branch of mathematics
and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied
Mathematical_analysis
1909 book by Herbert Croly
less of freedom than it did of social control." This idea was called "Hamiltonian means", which in the book is defined as "the establishment of federal
The_Promise_of_American_Life
Study of rational collective decision-making
Social choice theory is a branch of welfare economics that seeks to extend the theory of rational choice to collective decision-making. Social choice
Social_choice_theory
HAMILTONIAN CONTROL-THEORY
HAMILTONIAN CONTROL-THEORY
Boy/Male
Gaelic Irish Celtic
Wise.
Boy/Male
Gujarati, Hindu, Indian
Self Control
Boy/Male
Muslim/Islamic
Always in control
Boy/Male
Hindu
Check, Control
Boy/Male
Italian Spanish
Mountain. Abbreviation of Montague and Montgomery.
Boy/Male
Gujarati, Hindu, Indian, Punjabi, Sikh
Master; Authority; Power; Control
Boy/Male
Tamil
Check, Control
Boy/Male
Indian, Punjabi, Sikh
Light of Control
Boy/Male
Muslim
Prince, Always in control
Girl/Female
Tamil
Self control having complete control on all the senses
Boy/Male
Hindu, Indian
Control
Boy/Male
Indian, Sanskrit
Control of the Senses; Self-control
Boy/Male
Hindu, Indian, Sanskrit
Under Control
Male
English
Wise Man
Boy/Male
Indian
Control; Patient
Boy/Male
Hindu, Indian, Sanskrit
Agree; Control
Surname or Lastname
English (mainly central England)
English (mainly central England) : patronymic from a pet form of the personal name Thomas.
Boy/Male
Indian, Sikh
Who Control Love
Girl/Female
Hindu, Indian
Self Control; Having Complete Control on All the Senses
Girl/Female
Hindu, Indian
To have Control
HAMILTONIAN CONTROL-THEORY
HAMILTONIAN CONTROL-THEORY
Boy/Male
Muslim/Islamic
Joy Cheer
Boy/Male
Arabic, Muslim
Good Health
Boy/Male
Arabic, Muslim
Servant of the Awar
Boy/Male
Czechoslovakian
Manly.
Girl/Female
Arabic, Muslim
Abshamiyah's Daughter
Boy/Male
Tamil
Priyatar | பà¯à®°à¯€à®¯à®¾à®¤à®°
Dearer
Girl/Female
Indian
One endowed with speech
Surname or Lastname
English
English : habitational name from Varley or Varleys in Devon, or any of the other places in southwestern England named in Old English as ‘fern clearing’ (see Farley), the change from f to v arising from voicing of f which is characteristic of that area.English : (of Norman origin) habitational name from Verly in Aisne, Picardy, France, so named from the Gallo-Roman personal name Virilius + the locative suffix -acum, or from Vesly (La Manche); surnames of this origin are recorded in Suffolk from the 13th century. However, the overwhelming preponderence of the modern surname is in West Yorkshire.
Male
English
English variant spelling of French Dion, DEONNE means "god, Zeus."
Boy/Male
African Arabic
Teacher.
HAMILTONIAN CONTROL-THEORY
HAMILTONIAN CONTROL-THEORY
HAMILTONIAN CONTROL-THEORY
HAMILTONIAN CONTROL-THEORY
HAMILTONIAN CONTROL-THEORY
n.
Disposal; control; license.
n.
Control of one's self; restraint exercised over one's self; self-command.
n.
Rule; dominion; control.
superl.
Difficult to resist or control; powerful.
n.
Exercise of authority; control; government; arrangement.
n.
That which serves to check, restrain, or hinder; restraint.
adv.
In an independent manner; without control.
v. t.
To check by a counter register or duplicate account; to prove by counter statements; to confute.
n.
A counter account. See Control.
n.
One who, or that which, controls or restraines; one who has power or authority to regulate or control; one who governs.
v. t.
To exercise restraining or governing influence over; to check; to counteract; to restrain; to regulate; to govern; to overpower.
p. pr. & vb. n.
of Control
v. t.
To restrain; to control; to check.
n.
Control over one's own feelings, temper, etc.; self-control.
n.
A duplicate book, register, or account, kept to correct or check another account or register; a counter register.
a.
Miltonic.
n.
Power or authority to check or restrain; restraining or regulating influence; superintendence; government; as, children should be under parental control.
n. & v.
See Control.
n.
Authority; jurisdiction; control.
imp. & p. p.
of Control