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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. [ 1 ]
Widely regarded as a milestone in optimal control theory, the significance of the maximum principle lies in the fact that maximizing the Hamiltonian is much easier than the original infinite-dimensional control problem; rather than maximizing over a function space, the problem is converted to a pointwise optimization. [8]
Its solution is the value function of the optimal control problem which, once known, can be used to obtain the optimal control by taking the maximizer (or minimizer) of the Hamiltonian involved in the HJB equation. [2] [3] The equation is a result of the theory of dynamic programming which was pioneered in the 1950s by Richard Bellman and ...
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of ... Form the Hamiltonian and ...
The costate equation is related to the state equation used in optimal control. [1] [2] It is also referred to as auxiliary, adjoint, influence, or multiplier equation.It is stated as a vector of first order differential equations
For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function (profit) due to the relaxation of a given constraint (e.g. through a change in income); in such a context is the marginal cost of the ...
The latest issue of Hello! magazine describes Melania Trump as someone who has "grown in confidence" and now has "newfound authority" during her second stint in the White House as first lady.
Hamiltonian (control theory), a function used to solve a problem of optimal control for a dynamical system; Hamiltonian path, a path in a graph that visits each vertex exactly once; Hamiltonian matrix, a matrix with certain special properties commonly used in linear algebra; Hamiltonian group, a non-abelian group the subgroups of which are all ...