Pontryagin maximum principle

E681627

mathematical theorem result in optimal control theory

The Pontryagin maximum principle is a fundamental result in optimal control theory that provides necessary conditions for an optimal control process by characterizing optimal trajectories via a Hamiltonian maximization condition.

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All labels observed (2)

Label	Occurrences
Pontryagin maximum principle canonical	2
Pontryagin maximum principle in optimal control	1

Statements (46)

Predicate	Object
instanceOf	mathematical theorem ⓘ result in optimal control theory ⓘ
alsoKnownAs	PMP NERFINISHED ⓘ Pontryagin’s maximum principle NERFINISHED ⓘ
appliesTo	dynamical systems with control inputs ⓘ finite-horizon optimal control problems ⓘ problems with state constraints (in extended forms) ⓘ
assumes	measurable controls ⓘ sufficient regularity of system dynamics ⓘ
characterizes	optimal control processes ⓘ optimal trajectories ⓘ
developedBy	Lev Pontryagin NERFINISHED ⓘ Pontryagin’s school of control theory ⓘ
field	applied mathematics ⓘ control theory ⓘ optimal control theory ⓘ
generalizes	classical variational principles to systems with controls ⓘ
hasFormulation	continuous-time version ⓘ discrete-time analogues ⓘ
hasLimitation	provides necessary but not sufficient conditions for optimality ⓘ
historicalDevelopment	developed in the mid-20th century ⓘ
implies	existence of an adjoint system ⓘ pointwise maximization of the Hamiltonian with respect to control ⓘ
influenced	modern optimal control theory ⓘ
involves	boundary conditions ⓘ control constraints ⓘ state equations ⓘ switching functions ⓘ transversality conditions ⓘ
isFoundationFor	many numerical optimal control methods ⓘ
namedAfter	Lev Pontryagin NERFINISHED ⓘ
provides	necessary conditions for optimality ⓘ
relatesTo	Euler–Lagrange equations NERFINISHED ⓘ Hamilton–Jacobi–Bellman equation NERFINISHED ⓘ calculus of variations ⓘ dynamic programming ⓘ
typeOf	first-order necessary condition ⓘ
usedIn	aerospace trajectory optimization ⓘ economics ⓘ engineering ⓘ resource management models ⓘ robotics ⓘ
usesConcept	Hamiltonian function ⓘ Hamiltonian maximization condition ⓘ adjoint variables ⓘ costate equations ⓘ

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Input

Subject: Pontryagin maximum principle
Description of subject: The Pontryagin maximum principle is a fundamental result in optimal control theory that provides necessary conditions for an optimal control process by characterizing optimal trajectories via a Hamiltonian maximization condition.

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Lev Pontryagin → notableWork → Pontryagin maximum principle ⓘ

Lev Pontryagin → notableIdea → Pontryagin maximum principle ⓘ

this entity surface form: Pontryagin maximum principle in optimal control

Dynamic Noncooperative Game Theory → subject → Pontryagin maximum principle ⓘ