Calculus of variations and optimal control; optimization Optimal control: formulation and existence Concept
Optimal control
Summary
Optimal control is the theory of choosing the input of a control system in the best way. The aim is to make a cost, which depends on the input and on the resulting trajectory, as small as possible. An optimal control is an admissible control whose cost is not larger than that of any other admissible control. The theory extends the calculus of variations to problems with constraints on the controls. Its main tools are Pontryagin's maximum principle, which gives necessary conditions, and dynamic programming with the Hamilton–Jacobi–Bellman equation. The definition states the problem in Bolza form.
Where this leads
17 pages build on this one.
- Mayer and Lagrange problems
- Bolza problem
- Value function
- Linear-quadratic-Gaussian control
- Optimal control of partial differential equations
- Hamiltonian of an optimal control problem
- Dynamic programming in continuous time
- Linear-quadratic regulator
- Zermelo's navigation problem
- Trajectory optimization
- Model predictive control
- Relaxed control
- Verification theorem
- Separation principle
- Sub-Riemannian geodesic problem
- Filippov's existence theorem
- Time-optimal control
Further reading
About this page
| Tag | T3V6ZNAMDN |
|---|---|
| URI | m2://T3V6ZNAMDN |
| Kind | concept |
| Writing | W0 stub |
| MSC | 49J15, 49K15, 93C15 |
| Same as |
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Results about this
- Mayer and Lagrange problems
- Bolza problem
- Goddard problem
- Linear-quadratic regulator
- Zermelo's navigation problem
- Filippov's existence theorem
- Time-optimal control
Used by
- Mayer and Lagrange problems
- Bolza problem
- Value function
- Optimal control of partial differential equations
- Hamiltonian of an optimal control problem
- Dynamic programming in continuous time
- Linear-quadratic regulator
- Trajectory optimization
- Model predictive control
- Sub-Riemannian geodesic problem
- Time-optimal control