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The optimal power allocation derived solves a convex optimization problem of minimizing network energy consumption under the constraint of the guaranteed quality of service for both PU and SUs.
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The discrete-time feedback controller gain is derived by solving a set of linear matrix inequalities with inversion constraints.
The filter gain matrix is derived through solving a recursive Riccati equation and a generalized Lyapunov equation.
In this particular situation, the results are derived by solving a nonhomogeneous Riemann-Hilbert problem.
The optimal control strategies are derived by solving a mixed-integer nonlinear programming problem.
The proposed fuzzy controller parameters are derived by solving a convex optimization problem via the semidefinite programming technique.
In addition, a simple and explicit formula for optimally determined macroscopic conductivity is derived by solving a nonlinear minimization problem.
The kinetic energy of the fluid is derived by solving a boundary-value problem related to the fluid motion.
With the aid of an operator optimization method, it is shown that a unified optimal solution can be derived by solving a coupled Riccati equation.
A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form.
New conditions on the existence of eight limit cycles for a class of cubic differential systems were derived by solving a system of large polynomial equations and inequalities.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com