Guided optimal control

The remainder of this paper is organized as follows the global optimization procedure used in the formulation is discussed in Sect. 6.2. The semiclassical expression of the correlation function is derived in Sect. 6.3, and the properties of the semiclassical correlation function are discussed in Sect. 6.4. In Sect. 6.5 we introduce the idea of guided optimal control. The full control algorithm is provided. In Sect. 6.6 we provide three numerical examples i) the control of wavepacket motion where a two-dimensional model of H2O is used as an example, ii) the control of the H + OD —> HO + D reaction using a two-dimensional model of HOD, and iii) the control of the 4-D model of HCN-CNH isomerization (i.e., isomerization in a plane). Future perspectives from the authors point of view are summarized in Sect. 6.7. 

We consider, first, whether it is in principle possible to control the quantum dynamics of a many-body system. The goal of such a study is the establishment of an existence theorem, for which purpose it is necessary to distinguish between complete controllability and optimal control of a system. A system is completely controllable if an arbitrary initial state can be transformed, without loss to other states, into an arbitrary final state at some time T. A system is strongly completely controllable if an arbitrary initial state can be transformed, without loss to other states, into an arbitrary final state at a specified time T. Optimal control theory designs a field, subject to specified constraints, that guides the evolution of an initial state of the system to be as close as possible to the desired final state at time T. 

The formulation of the calculation of the optimal control field that guides the evolution of a quantum many-body system relies, basically, on the solution of the time-dependent Schrodinger equation. Messina et al. [25] have proposed an implementation of the calculation of the optimal control field for an n-degree-of-freedom system in which the Hartree approximation is used to solve the time-dependent Schrodinger equation. In this approximation, the n-degree-of-freedom wave function is written as a product of n single-degree-of-freedom wave functions, and the factorization is assumed to be valid for all time. 

We study optimal control problems of quantum chaos systems. Our goal of control is to obtain an optimal field s(t) that guides a quantum chaos system from an initial state target state (pj) at some specific time t = T. One such method is optimal control theory (OCT), which has been successfully applied to atomic and molecular systems [4]. 

Chapter 21. Chapter 7 in Shinskey [Ref. 3] is again an excellent reference for the practical considerations guiding the design of feedforward and ratio control systems. It also discusses the use of feedforward schemes for optimizing control of processing systems. Good tutorial references are the books by Smith [Ref. 2], Murrill [Ref. 8], and Luyben [Ref. 9]. The last one has a simple but instructive example on the nonlinear feedforward control of a CSTR. 

Physical synthesis is a multi-phase optimization process performed during IC design to achieve timing closure, though area, routability, power and yield must be optimized as well. Individual steps in physical synthesis, called transformations are invoked by dynamic controller functions in complex sequences called design flows (EDA flows). Transformations rely on abstract delay models to analyze timing requirements and guide optimization, as illustrated in Sect. 2.3. Finally, we describe recent evolution of requirements for physical synthesis and discuss current trends. 

The value objective function is oriented at the company s profit and loss definitions. Guiding principle is to only use value parameters that can be found in the cost controlling of the company signed by controlling. Penalty costs and without currency and weighting factors being applied to steer optimization results but having no actual financial impact - as it can be often found in supply chain optimization models - do not meet this requirement. 

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