scholarly journals Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence

2017 ◽  
Vol 375 (2088) ◽  
pp. 20160214
Author(s):  
Navin Khaneja
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Spin Dynamics ◽  
Resonance Spectroscopy ◽  
Control Problems ◽  
State Variables ◽  
Systems And Control ◽  
Time Optimal ◽  
Optimal Efficiency ◽  
And Control

In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system. This article is part of the themed issue ‘Horizons of cybernetical physics’.

scholarly journals A New Approach for Solving Optimal Nonlinear Control Problems Using Decriminalization and Rationalized Haar Functions

2011 ◽  
Vol 1 ◽  
pp. 387-394 ◽  
Author(s):  
Zhen Yu Han ◽  
Shu Rong Li
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Nonlinear Optimal Control ◽  
Control Problems ◽  
State Variables ◽  
Linear Quadratic ◽  
Control Variables ◽  
Linear Quadratic Optimal Control ◽  
Haar Functions ◽  
And Control

This paper presents a numerical method based on quasilinearization and rationalized Haar functions for solving nonlinear optimal control problems including terminal state constraints, state and control inequality constraints. The optimal control problem is converted into a sequence of quadratic programming problems. The rationalized Haar functions with unknown coefficients are used to approximate the control variables and the derivative of the state variables. By adding artificial controls, the number of state and control variables is equal. Then the quasilinearization method is used to change the nonlinear optimal control problems with a sequence of constrained linear-quadratic optimal control problems. To show the effectiveness of the proposed method, the simulation results of two constrained nonlinear optimal control problems are presented.

scholarly journals ON DIFFERENTIATION OF FUNCTIONALS OF APPROXIMATING PROBLEMS IN THE FRAME OF SOLUTION OF FREE TIME OPTIMAL CONTROL PROBLEMS BY THE SLIDING NODES METHOD

2018 ◽  
pp. 861-876
Author(s):  
Andrei Vladimirovich Chernov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Free Time ◽  
Time Optimal Control ◽  
Control Problems ◽  
Control Parametrization ◽  
Derivative Formulas ◽  
Control Parametrization Technique ◽  
Time Optimal ◽  
And Control

We give strict justification for derivative formulas of functionals in problems approximating free time optimal control problems in the frame of sliding nodes method and control parametrization technique. As example we present results of numerical solution for landing on the Moon problem.

scholarly journals On turnpike and dissipativity properties of continuous-time optimal control problems

Automatica ◽  
2017 ◽  
Vol 81 ◽  
pp. 297-304 ◽  
Author(s):  
Timm Faulwasser ◽  
Milan Korda ◽  
Colin N. Jones ◽  
Dominique Bonvin
Keyword(s):  
Optimal Control ◽  
Continuous Time ◽  
Optimal Control Problems ◽  
Time Optimal Control ◽  
Control Problems ◽  
Time Optimal
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