Methods for Optimal Control and Control Theory

Article # 1_2016

11 p.

PDF

Gurman V.I., Rasina I.V.
Turnpike Solutions in the Problem of Excitation Transfer Along a Spin Chain

It is considered the problem of excitation transfer along a spin chain related to the applied problem of quantum computations. The model of a quantum system of interacting spins based on the Shr¨odinger equation with unbounded linear control is transformed to an equivalent derived system (known from the degenerate problems theory), and then approximately to derived systems of higher stages with reducing order. Their investigation performed analytically or via simple computations leads at least to approximate solutions
and lower estimates of the transfer time, which can be used in subsequent improving procedures.

Key words: quantum system, spin chain, Shr¨odinger equation, optimal control, derived system, degenerate problem, impulse control, turnpike solution, global improvement method.

article citation

DOI

https://doi.org/10.25209/2079-3316-2016-7-1-3-13

Article # 10_2016

16 p.

PDF

Gurman V.I., Rasina I.V.
Global Control Improvement Method for Non-homogeneous Discrete Systems

The class of non-homogeneous discrete systems is considered. These systems are prevalent in practice and can be obtained from discretization of continuous systems when optimization problems are solving using iterative methods. For this class of systems Krotov type sufficient optimality conditions are formulated in two different forms. The prototype of Krotov global improvement method is constructed. An illustrative example is presented. (In Russian).

Key words: non-homogeneous discrete systems, global improvement method, optimal control.

article citation

DOI

https://doi.org/10.25209/2079-3316-2016-7-1-171-186