Sentence examples for maximum principles are from inspiring English sources

In contrast with the previous results of the fractional diffusion equations, the obtained maximum principles are analogous to the ones with the Caputo fractional derivative; however, extra necessary conditions for the existence of a solution of the linear and nonlinear fractional diffusion models are imposed.

The celebrated Pontryagin's maximum principles is employed to conduct the physical solutions of the state vector and the control force vector of stochastic optimal controls of closed-loop systems by synthesizing deterministic optimal control solutions of a collection of representative excitation driven systems using the generalized density evolution equation.

Modified versions of the maximum principle are briefly described.

The second-order variational equation for the BSDE (3) and the maximum principle are obtained.

The variational equations for BSDEs and the maximum principle are deduced in Variational equation for BSDEs and maximum principle.

Necessary conditions in the form of Pontryagin's maximum principle are derived for impulsive control problems with mixed constraints.

Different types of local extremals obtained in solving trajectory optimization problems related to space vehicle injection and reentry by applying the Pontryagin's maximum principle are demonstrated.

On this reduced space, both nonoptimal and optimal controllers, the latter using Pontryagin's maximum principle, are investigated with the control objective of changing the vortex orbit from a bound to a scattering type and vice versa.

Ways to systematically optimize the reciprocal upper and lower bounds obtained using the Maximum Principle are developed, with special attention paid to ease of application, efficacy in establishing rigorous error bounds and accuracy of results.

The maximum principle is obtained.

Then the proof of the maximum principle is completed.