Sentence examples for standard problem for from inspiring English sources

A lot of results concerning the standard problem for scalar second-order ordinary differential equations were generalized in various directions.

Then, tube-based MPC solves two optimal control problems, a standard problem for the nominal system to define a central guide path, and an ancillary problem to steer the state vector towards the central path with semi-optimal control effort.

The controller solves two optimal control problems, one which solves a standard problem for the nominal system to define a central guide path, and an ancillary problem to steer the states towards the central path despite the uncertainties and disturbances.

Several standard problems for structural optimization are solved to check the usefulness of the suggested method.

There are two standard problems for causal theories of this sort (whether they are elaborated in a mentalist or a non-mentalist way).

See Appendix D. Note that both subproblems, (26) and (27), are convex and represent standard problems for which many efficient (distributed) algorithms exist.

This heuristic results in comparable estimates for the evidence (see Figure S1 in the Additional file 1) and reduces the number of likelihood calls to 54 82% of the evaluations required for a fixed step size in tests on 5, 10, 20 and 30 dimensional Gaussian likelihood functions (standard problems for which the solutions are known), as can be seen in Additional file 1: Figure S2.

For accurate evaluation of the solution of the heat conduction equation with the help of the spline-method, the standard problem is created for a one-dimensional infinite flat plane which has the exact analytical solution.

To conduct an accuracy evaluation of the spline-method the standard problem has been created for one-dimensional infinite flat plane with temperature-dependent material properties, which has the exact analytical solution.

The specific form of this standard problem is also very interesting for gain scheduling.

The primary objective of this paper is to document the experiment and present a sample of the data set that has been established for this standard problem.