Concept
Hamiltonian (control theory)
Related concepts (5)
Shadow price
A shadow price is the monetary value assigned to an abstract or intangible commodity which is not traded in the marketplace. This often takes the form of an externality. Shadow prices are also known as the recalculation of known market prices in order to account for the presence of distortionary market instruments (e.g. quotas, tariffs, taxes or subsidies). Shadow prices are the real economic prices given to goods and services after they have been appropriately adjusted by removing distortionary market instruments and incorporating the societal impact of the respective good or service.
Pontryagin's maximum principle
Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It states that it is necessary for any optimal control along with the optimal state trajectory to solve the so-called Hamiltonian system, which is a two-point boundary value problem, plus a maximum condition of the control Hamiltonian.
Optimal control
Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Costate equation
The costate equation is related to the state equation used in optimal control. It is also referred to as auxiliary, adjoint, influence, or multiplier equation. It is stated as a vector of first order differential equations where the right-hand side is the vector of partial derivatives of the negative of the Hamiltonian with respect to the state variables. The costate variables can be interpreted as Lagrange multipliers associated with the state equations.
Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied.