The survey examines the current state of the speed gradient method, developed in the
1970–80s for synthesizing control and adaptation algorithms in nonlinear systems, as well as
numerous applications of the method to solving scientific and engineering problems. Brief
information about speed gradient algorithms and conditions of their applicability, optimality, and
passivity are given. Applications of the method to problems of adaptive control and identification,
nonlinear control, energy and nonlinear oscillation control, and control in network, multiagent,
and distributed systems are discussed. Applications of the method to control of technical systems
and to problems in physics, biology, and ecology are presented. Modern modifications and
generalizations of the method are provided, including non-Euclidean speed gradient algorithms
based on Lyapunov–Bregman functions.

Speed Gradient Method and Its Applications

A new approach to synthesize algorithms for selective control of the observables in quantum mechanical systems in the presence of additional constraints during the whole period of control is proposed Analytic results of achieving the goal of control under some additional assumptions were obtained It was demonstrated that the error in achieving the goal of control is proportionate to the error in prescribing the initial state of system and the error in realizing the control action Numerical results for the problem of selective control for energy of hydrogen molecules (H2) with different isotopes are represented The proposed algorithms are easy to design

Selective control of the observables in the ensemble of quantum mechanical molecular systems

An exact analytic solution was obtained for the correlation function of the motion of a phase-modulated Gauss wave packet in an anharmonic potential. The solution is expressed through the theta-function with the parameters depending on both the potential and phase modulation of the initial wave packet. Changes in both linear and quadratic chirps result in an invariant correlation function time shift in a weakly anharmonic potential with the conservation of all the total and fractional revivals. At a strong potential anharmonicity, translational invariance with respect to a quadratic chirp is preserved in certain instances, whereas the dynamics of packets experiences qualitative changes depending on linear phase modulation. This approach can be used to qualitatively analyze intramolecular dynamics if the potential energy surface is not known exactly, which is especially useful for quantum control of large molecules, in particular, photochromes.

Invariants of the dynamics of molecular vibrational wave packets in phase modulation

We introduce two approaches to the synthesis of the optimized schemes of dissociation control of diatomic molecules. The first one bases on the early introduced speed-gradient algorithms of the quantum control. We use the semi classical model of molecular dynamics onto the ground state. The introduced algorithm is a robust and it has only one tuning parameter. The numerical results of the control of the predissociation of iodine molecule illustrate the high possibility of the dissociation for 100 fs laser pulse. The second approach bases on quantum model of dissociation through B excited electronic state. This model doesn't assume the solving of any time-depended equations. The optimized scheme of iodine dissociation with different nuclear isotopes is obtained. The best isotope separation achieves up to 300 fs with 80% efficiency.

http://ieeexplore.ieee.org/iel5/10133/32429/01514061.pdf

Quantum control of dissociation of an iodine molecule by one and two femtosecond laser pulses excitation

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Quantum control of dissociation of an iodine molecule by one and two femtosecond laser pulses excitation