Optimizing control design

It is clear that pulse sequences may not only be designed by analytical means, they may also be designed numerically (see, e.g., reviews on numerical aspects of solid-state NMR in [54, 65, 66]) using standard nonlinear optimization to well-defined analytical expressions [67, 68], by optimizing pulse sequences directly on the spectrometer [69], or by optimal control procedures [70-72] to name but a few of the possibilities. We will in this review restrict ourselves to optimal control design procedures that recently in analytical and numerical form have formed a new basis for efficient NMR experiment design. 

Annaswamy, A. M., M. Fleifil, J. W. Rumsey, R. Prasanth, J.P. Hathout, and A. F. Ghoniem. 2000. Thermoacoustic instability Model based optimal control designs and experimental vahdation. IEEE Transactions on Control Systems Technology 8(6). 

To fulfill these needs, we recently undertook the task of developing and implementing optimal control design procedures into the SIMPSON software and described the first applications of this method to solid-state NMR spectroscopy by designing new dipolar recoupling experiments. Optimal control theory is an ideal vehicle for optimizing... 

Some authors have been concerned with influence of flow or diffusion on measurements of and Anderson et al. discussed diffusion of spins between compartments, characterized by different states of longitudinal magnetization, leading to diffusion-driven longitudinal relaxation. The effects were explored experimentally and analyzed quantitatively. Herold and co-workers described an on-line NMR rheometer, able to measure NMR relaxation data. The corrections required for the analysis of relaxation data measured under flow conditions were discussed. The opposite problem how to avoid the detrimental effects of unequal relaxation rates on the diffusion measurements in complex mixtures - was discussed by Barrere et Relaxation can also cause problems in other kinds of NMR experiments. Skinner and co-workers described the optimal control design of band-selective excitation pulses that accommodates both relaxation and inhomogeneity of rf fields. 

Jaouadi A, Barrez E, Justum Y, Desouter-Lecomte M (2013) Quantum gates in hyperfine levels of ultracold alkali dimers by revisiting constrained-phase optimal control design. J Chem Phys 139 014310... 

N.I. Gershenzon, K. Kobzar, B. Luy, S.J. Glaser, T.E. Skinner, Optimal control design of excitation pukes that accomodate relaxation, J. Magn. Reson. 188 (2007) 330-336. 

Such a model can be developed to a new design to get a feedback (FB) and build up a quality control system for materials. This scheme also includes smart block (SB) for optimal control and generation of a feedback function (Figure 1). 

Some special requirements of continuous systems are (1) Metering the feed. A continuous system must be fed at a precise, uniform rate. (See Sec. 21.) (2) Dust collection. This is a necessary part of most diy-processing systems. Filters are available that can effectively remove dust down to 10 mg/m or less, and operate automatically. (Dust collection is covered in Sec. 17.) (3) Ondine analysis. For more precise operation, on-line analysis of product particle size and composition may be desirable. (4) Computer control. SiiTuilation can aid in optimizing system design and computer control. 

Using classical design techniques, the autopilot will be tuned to return the vessel on the desired course within the minimum transient period. With an optimal control strategy, a wider view is taken. The objective is to win the race, which means completing it in the shortest possible time. This in turn requires ... 

With //oo-optimal control the inputs F(jw) are assumed to belong to a set of norm-bounded functions with weight fF(jw) as given by equation (9.125). Each input V(iuj) in the set will result in a corresponding error E(iuj). The i/oo-optimal controller is designed to minimise the worst error that can arise from any input in the set, and can be expressed as... 

Optimal control theory, as discussed in Sections II-IV, involves the algorithmic design of laser pulses to achieve a specified control objective. However, through the application of certain approximations, analytic methods can be formulated and then utilized within the optimal control theory framework to predict and interpret the laser fields required. These analytic approaches will be discussed in Section VI. 

In early work in the optimal control theory design of laser helds to achieve desired transformations, the optimal control equations were solved directly, without constraints other than those imposed implicitly by the inclusion of a penalty term on the laser huence [see Eq. (1)]. This inevitably led to laser helds that suddenly increased from very small to large values near the start of the laser pulse. However, physically realistic laser helds should tum-on and -off smoothly. Therefore, during the optimization the held is not allowed to vary freely but is rather expressed in the form [60] ... 

One of the difficulties with optimal control theory is in identifying the underlying physical mechanism, or mechanisms, leading to control. Methods [2, 7, 9, 14, 26-29], that utilize a small number of interfering pathways reveal the mechanism by construction. On the other hand, while there have been many successful experimental and theoretical demonstrations of control based on OCT, there has been little analytical work to reveal the mechanism behind the complicated optimal pulses. In addition to reducing the complexity of the pulses, the many methods for imposing explicit restrictions on the pulses, see Section II.B, can also be used to dictate the mechanisms that will be operative. However, in this section we discuss some of the analytic approaches that have been used to understand the mechanisms of optimal control or to analytically design optimal pulses. Note that we will not discuss numerical methods that have been used to analyze control mechanisms [145-150]. 

The new pulse design equations for the optimal control of photodissociation may be summarized as... 

Off-line analysis, controller design, and optimization are now performed in the area of dynamics. The largest dynamic simulation has been about 100,000 differential algebraic equations (DAEs) for analysis of control systems. Simulations formulated with process models having over 10,000 DAEs are considered frequently. Also, detailed training simulators have models with over 10,000 DAEs. On-line model predictive control (MPC) and nonlinear MPC using first-principle models are seeing a number of industrial applications, particularly in polymeric reactions and processes. At this point, systems with over 100 DAEs have been implemented for on-line dynamic optimization and control. 

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